GRE Math
Set 1
° - ÁÂ
Catego Cate gorr y 1 Nu mbe mberr Ope Operr ati ations ons
1.
For which of the following expressions expressions is it true that the value of the expression expression is the same for
answer
x = 587 as for x = −587 ? 1 − 2 x 1 − 2x2 (1 − 2 x ) 2
I. II. III. (A) (A)
I only on ly
(B)
II only
(C)
I and III only
(D)
II and III only
(E)
I, II, and III
2. If the numbers
17 1 3 3 9 , , , , and were ordered from greatest to least, the middle 24 2 8 4 16
number of the resulting sequence would be (A) (B) (C) (D) (E)
17 24 1 2 3 8 3 4 9 16
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GRE Math
Set 1
° - ÁÂ
7 1 + is between 8 9 1 3 and 2 4 7 1 + and 1 8 9 1 1 and 1 4 1 1 1 and 1 4 2 1 1 and 2 2
3. The sum (A) (B) (C) (D) (E)
4. Of the following, which is closest to (A)
0.200
(B)
0.172
(C)
0.167
(D)
0.143
(E)
0.140
answer
1 ? 7
answer
a , b , c , and d , * (a , b, c, d ) is defined as a − b + c − d . What is the value of * (1,3,8,5) ? (A) − 1
5. For all integers
(B)
0
(C)
1
(D)
2
(E)
3
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GRE Math
Set 1
° - ÁÂ
6. The operation # is defined by the equation x # y =
x − y , where 2 x ≠ y . The value of 2 x − y
answer
which of the following is 0? (A) (B) (C) (D) (E)
− 2#2 2#−2 2# 2 2#1 3#2
7. The number 0.756 is how much greater than (A) (B) (C) (D) (E)
3 ? 4
answer
6 25 3 125 3 250 3 500 1 250
4 6 yields as the result? 7 7 3 24 7 (C) (D) (E) 2 7 2
8. What number when multiplied multiplied by (A)
2 7
(B)
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2 3
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Page 3
GRE Math
9. If the sum of 3 times
Set 1
° - ÁÂ
n , 11 times n , and 111 times n is equal to 1,000, what is the value of
n? (A)
8
(B)
12.5
(C)
16
(D)
25
(E)
125
10. Which of the following is equal to 0.042? (A) (B) (C) (D) (E)
answer
answer
4 2 + 10 10 4 + 2 10 100 4 + 2 100 100 4 2 + 100 1,000 4 2 + 1,000 1,000
11. In the addition problem above, if ¡ à and ∆ each represent a digit, then ¡ à represents (A)
9
(B)
8
(C)
5
(D)
2
(E)
0
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GRE Math
Set 1
° - ÁÂ
12. If ¡ à represents a digit in the subtraction problem above, ¡ à = (A)
1
(B) 5
(C) 6
(D) 7
answer
(E) (E ) 9
13. The figure above shows the arrangement arrangement and code numbers numbers of 9 fluorescent tubes. If a tube is
answer
illuminated whenever its code number is received, which of the following shows the arrangement of tubes illuminated when the digits in the result of 3,804 ÷ 3 are received?
50.2 × 0.49 ? 199.8 5 25 (D) (E) 4 2
14. Of the following, following, which is the closest approximation approximation of (A)
1 10
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(B)
1 8
(C)
1 4
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GRE Math
Set 1
° - ÁÂ
61.24 × (0.998) 2 403 15. The expression above is approximately equal to
16.
(A)
1
(B)
3
(C)
4
(D)
5
(E)
6
answer
( 2)(0.33)(15) is approximately equal to (0.24) (A)
2
(B)
5 2
(C)
15
(D)
36
(E)
40
17. Of the following, following, which is is the best approximation approximation for (A)
0.015
(B)
0.15
(C)
1.5
(D)
15
(E)
150
À±ÅÂÈ- ¿µ¾î ¿¬ ±¸ ½Ç,
answer
0.01 × 2.005 × 32.98 ? 11.12 × 0.04
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GRE Math
18. Of the following, the closest approximation to (A)
40
(B)
35
(C)
30
(D)
4
(E)
3
Set 1
° - ÁÂ
8.097(0.8745) is 0 .202
answer
19. If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is
answer
the sum of the terms of the sequence?
20.
(A)
22
(B)
32
(C)
36
(D)
40
(E)
44
If w, x, y, and z are positive and
w y = , which of the following is NOT always true? x z
(A) wz = xy
x z = w y x z = (C) y w (B)
w + x y + z = x z x + w z + y = (E) w y (D)
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GRE Math
21. If d =
(A) (B) (C) (D) (E)
Set 1
° - ÁÂ
a +b c 3c , a = , and b = , what is the value of d in terms of c ? ab 2 4 1+ 2 c
answer
10c 11 5c 2 10c 3 10 11c 5 2c
22. Tamara saves $35 each week. If she now has $100 saved, in how many weeks can she first
answer
have enough saved to buy a lawn mower that costs $250? (A)
2
(B)
3
(C)
4
(D)
5
(E)
6
23. If x > 3,000 , then the value of (A) (B) (C) (D) (E)
x is closest to 2 x + 1
answer
1 6 1 3 10 21 1 2 3 2
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GRE Math
Set 1
° - ÁÂ
24. A certain clock indicates 8 o’ clock. If the clock runs accurately for the next 11,995 hours,
answer
what hour will it indicate at the end of that time? (A)
1 o’ clock
(B)
2 o’ clock
(C)
3 o’ clock
(D)
5 o’ clock
(E)
10 o’ clock
25. If
1 the result obtained when 2 is subtracted from 5 x is equal to the sum of 10 and 3 x , 2
what is the value of (A) (B)
− 22
(C)
4
(D)
18
(E)
22
x ?
–4
26. A light-year is approximately 6 × 1012 miles. Approximately how many miles from Earth is a galaxy that is 2 × 10 6 light-years away? (A) (B) (C) (D) (E)
answer
3 .0 × 10 6 1.2 × 1018 1.2 × 1019 1.2 × 10 72 1.2 × 10 73
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GRE Math
Set 1
° - ÁÂ
27. If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,717
answer
minutes earlier? (Assume standard time in one location.) (A)
6:22
(B)
6:24
(C)
6:27
(D)
6:30
(E)
6:32
28. If the sum of two positive integers is 24 and the difference of their squares is 48, what is the answer
product of the two integers? (A)
108
(B)
119
(C)
128
(D)
135
(E)
143
29. On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 165 is how many times an intensity corresponding to a magnitude of 125? (A)
40
(B)
100
(C)
400
(D)
1,000
(E)
10,000
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GRE Math
Set 1
° - ÁÂ
1 , if r is halved, then V is multiplied by (2 r )3 1 1 (B) 8 (C) 1 (D) (E) 8 64
30. In the formula V = (A)
64
answer
31. In the subtraction problem above, ∆ , ¡ à, and Ο represent different positive digits. If ¡ àis 1
answer
greater than ∆ , what is the value of Ο ? (A)
9
(B)
7
(C)
5
(D)
3
(E)
2
32. Which of the following procedures is always equivalent to adding 5 given numbers and then answer
dividing the sum by 5? I.
Multiplying the 5 numbers and then finding the 5th root of the product.
II. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left. III. Ordering the 5 numbers numerically and then selecting the middle number. (A)
None
(B)
I only
(C)
II only
(D)
III only
(E)
I and III
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GRE Math
Çؼ³
¼öÇÐ
Set 1
° - ÁÂ
Category 1 N umber Oper ation s
1. For which of the following expressions is it true that the value of the expression is the same for
x = 587 as for x = −587 ? I. 1 − 2 x II. 1 − 2x2 (1 − 2 x ) 2 III. (A)
I only
(B)
II only
(C)
I and III only
(D)
II and III only
(E)
I, II, and III
ÁÖ¾î Áø ½Ä¿¡ x = 587 , x = −587 À» ´ ëÀÔ ÇÏ ¿´ À» ¶§ °ª ÀÌ °°°Ô µÇ´Â ½ÄÀ» ¹ °¾î º ¸°í ÀÖ½À´ Ï ´ Ù. x ÀÇ Àý´ ë°ª Àº °°°í À½¾çÀÇ ±âÈ£¸ ¸ ´ Ù¸ £±â ¶§¹ ®¿¡ À½¾çÀÇ ±âÈ£¿¡ ¿µÇâÀ» ¹ ÞÁö ¾Ê´  ½Ä À» °í ¸ £¸ é µË´ Ï ´ Ù. & ´ äÀº
(B)ÀÔ´ Ï ´ Ù.
2. If the numbers
17 1 3 3 9 , , , , and were ordered from greatest to least, the middle 24 2 8 4 16
number of the resulting sequence would be (A)
17 24
(B)
1 2
(C)
3 8
(D)
3 4
(E)
9 16
GRE¿¡ ¼ ¼ýÀÚ°£ ´ ë¼Ò¸ ¦ º ñ±³ ÇÏ ´  ¹ æ¹ ýÀº i) º и 𸠦 ¸ ðµÎ °°°Ô ÇØÁÖ°í º ÐÀÚ¸ ¦ º ñ±³ ÇÏ ´  ¹ æ ¹ ý° ú ii) º ÐÀÚ¸ ¦ °°°Ô ÇØÁÖ°í º и ðÀÇ Å©±â¸ ¦ º ñ±³ ÇÏ ´  ¹ æ¹ ýÀÌ ÀÖ½À´ Ï ´ Ù. ÈÄÀÚÀÇ ¹ æ¹ ýÀ» ÀÍ Çô µÎ ¸ é ¹ ®Á¦ ¸ ¦ »¡ ¸ ® Ǫ ´ µ¥ µµ¿òÀÌ µË´ Ï ´ Ù. 3 °ú 3 ´  º ÐÀÚ´  °° Áö¸ ¸ º и ðÀÇ Å©±â°¡ ´ Ù¸ £¹ Ç· Î º и ð°¡ Å« 3 ÀÌ 3 º ¸ ´ Ù ÀÛÀ» °Í ÀÌ ¶ó´  4 4 8 8
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GRE Math
Set 1
° - ÁÂ
°Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù.½ÇÁ¦ · Î ÀÌ ¹ ®Á¦ ¿¡ ¼ ´  17 , 1 , 3 , 3 °£¿¡´Â Åëº ÐÇÏ ´  °Í ÀÌ ¾î · ÆÁö ¾Ê 24
2
8
4
9 1 12 ½À´ Ï ´ Ù. ÀÌ ¼öµé° £¿¡ º и 𸦠Åëº ÐÇÏ ¿© Å©±â° ¡ 3 = , = , 17 , 3 = 18 ¼ø ÀÌ ¶ó´  °Í 8 24 2 24 24 4 24 À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù.ÀÌ Á¦
9 ¿Í ´ Ù¸ ¥ ¼öµé° £¿¡ Åëº ÐÇÏ ¿© Å©±â¸ ¦ º ñ±³ ÇÏ ´  °Í º ¸ ´ Ù´  º ÐÀÚ¸ ¦ 16
°°°Ô ÇØÁÖ°í º и ðÀÇ Å©±â¸ ¦ º ñ±³ ÇÏ ´  °Í ÀÌ ÈÎ ¾À ¼ö¿ùÇÕ´ Ï ´ Ù.
### µÎ ° ³ ÀÇ fractions( 22 , 11) ÀÇ ° ª À» º ñ±³ ÇÏ´ 如 ´ Ù¸ ¥ ¹ æ¹ ý 19 9
22 ¿Í 11 ÀÇ ° ª ÀÇ Å©±â¸ ¦ ¾Ë±â À§Çؼ- ´  cross-multiplying( 22 × 9, 11 × 19)À» Çؼ19 9
±× ° ª ÀÌ Å« ÂÊÀÌ ° ª ÀÌ Å©´ Ù.¿©±â¼- ´ Â22 × 9 < 11 × 19ÀÌ ¹ Ç· Î, so 22 < 11 19
&
9
´ äÀº (E)ÀÔ´ Ï ´ Ù.
7 1 + is between 8 9 1 3 7 1 (A) and (B) + and 1 2 4 8 9 1 1 1 (D) 1 and 1 (E) 1 and 2 4 2 2
3. The sum
(C) 1 and 1
1 4
ÀÌ ¹ ®Á¦ ¿¡ ¼ ´  º ÐÀÚ¸ ¦ °°° Ô ÇØÁÖ´  °Í º ¸ ´ Ù´  Åëº ÐÇÏ ¿© ¹ ®Á¦ ¸ ¦ Ç®¾î ÁÖ¸ é µË´ Ï ´ Ù.
7 1 71 + = ÀÌ ¹ Ç· Î ¿ì ¼± 1º¸ ´Ù ÀÛÀ¸ ¹ Ç· Î ´ ä¿¡ ¼ (C),(D),(E)¸ ¦ Á¦ °Å ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. ±× 8 9 72 3 54 71 ¸ ®°í = °ú ¸ ¦ º ñ±³ ÇÏ ¸ é ´ äÀÌ (B)¶ó´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. 4 72 72 7 1 À§¿¡ ¼ ó · ³ + ¸ ¦ °è»êÇÏ ¿© (C),(D),(E)¸ ¦ Á¦ °ÅÇÏ ´  ¹ æ¹ ýµµ ÀÖ°ÚÁö¸¸ ÀÌ · ¯ÇÑ ¹ æ¹ ýÀ» »ç 8 9 7 1 1 ¿ëÇÏ ¸ é ¾î ¶³ ±î ¿ä.. ÀÌ 1ÀÌ µÇ±â À§Çؼ ´  ÀÌ ´ õÇØÁ®¾ß ÇÕ´ Ï ´ Ù. ÇÏ Áö¸ ¸ ÀÌ ´ õÇØÁ³ °í 8 8 9 1 1 7 1 + Àº º ¸ ´ ÙÀÛ´ Ù´  °ÍÀ» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù.µû¶ó¼ ÀÌ 1º ¸ ´ Ù ÀÛÀ» ° Í ÀÌ ¶ó´  °Í À» ¾Ë 9 8 8 9 ¼ö ÀÖ½À´ Ï ´ Ù.
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GRE Math
Set 1
° - ÁÂ
GRE¿¡ ¼ °í µæÁ¡ À» ¹ Þ±â À§Çؼ ´  Á¤¼®´ ë· Î Çª ´  ¹ æ¹ ýµµ ¾Ë°í ÀÖ¾î ¾ß °ÚÁö¸ ¸ ÀÌ Ã³ · ³ ½Ã°£À» ÁÙÀÌ ´  ¹ æ¹ ýÀ» ¾Ë¾Æ°¡ ´  °Í µµ Áß¿ä ÇÕ´ Ï ´ Ù. & Á¤´ äÀº
(B)
4. Of the following, which is closest to
1 ? 7
(A) 0.200 (B) 0.172 (C) 0.167 (D) 0.143 (E) 0.140
ÀÌ ¹ ®Á¦ ¸ ¦ º ü¸£°Ô Ǫ ´  ¹ æ¹ ýÀº
1 ¿¡ ¾î ¶² ¼ö¸ ¦ °öÇÏ ¸ é º и 𸠦 100ÀÇ ±Ù»çÄ¡ · Î ¸ ¸ µå´ ÂÁö¸¦ 7
ãÀ¸ ¸ é µË´ Ï ´ Ù. & ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
a , b , c , and d , * (a , b, c, d ) is defined as a − b + c − d . What is the value of * (1,3,8,5) ? (A) − 1
5. For all integers
(B)
0
(C)
1
(D)
2
(E)
3
* (a , b, c, d ) ´  a − b + c − d · Î Á¤ÀÇµÉ ¶§ * (1,3,8,5) ÀÇ °ª À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¿¬»ê½ÄÀ» Á¤ÀÇÇÏ ¿© ÁÖ°í ¿¬»ê½Ä¿¡ µû¶ó ´ äÀ» ã´  ¹ ®Á¦ °¡ ÃâÁ¦ µÇ°ï ÇÕ´ Ï ´ Ù. ³ ÀÌ µµ°¡ ³ ôÁö ¾ÊÀº ¹ ®Á¦ µé· Î ½Ç¼ö¸ ¸ ÇÏ Áö ¾Ê°í Ç®¾î ÁÖ¸ é µË´ Ï ´ Ù. & ´ äÀº
(C)ÀÔ´ Ï ´ Ù.
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GRE Math
Set 1
° - ÁÂ
6. The operation # is defined by the equation x # y =
x − y , where 2 x ≠ y . The value of 2 x − y
which of the following is 0? (A) (B) (C) (D) (E)
x # y =
− 2#2 2#−2 2# 2 2#1 3#2 x − y ÀÏ ¶§ º ¸ ±â Áß ´ äÀÌ 0ÀÌ µÇ´  °Í À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. º мöÀÌ ±â ¶§¹ ®¿¡ º Ð 2 x − y
¸ ð°¡ 0ÀÌ µÉ ¼ö ¾ø±â ¶§¹ ®¿¡ º ÐÀÚ°¡ 0ÀÌ µÇ´  °ª À» ãÀ¸ ¸ é µÇ°Ú½À´ Ï ´ Ù. & ´ äÀº
(C)ÀÔ´ Ï ´ Ù.
7. The number 0.756 is how much greater than (A) (B) (C) (D) (E)
3 ? 4
6 25 3 125 3 250 3 500 1 250
3 º ¸ ´ Ù¾ó¸ ¶¸ ¸ Å ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÀÌ ¹ ®Á¦ ¸ ¦ Ç®±â À§Çؼ 4 ² Ù¾î ÁÖ´  ¹ æ¹ ýÀº µÎ °¡ Áö°¡ ÀÖ°ÚÁÒ. ¿ ì ¼± 3 ÷ 4 ÀÇ °è»êÀ» ÇÏ ´  ¹ æ¹ ý , 75 ¿¡ 25¸ ¦ °öÇÏ ¿© ¸ ¦ ¸ ¸ µé¾î ÁÖ´  ¹ æ¹ ýÀÌ ÀÖ½À´ Ï ´ Ù. GMATÀ» Ç® ¶§ 100 0.756°¡
3 À» ¼Ò¼öÇüÅ· Î ¹ Ù 4 ¾Æ´ Ï ¸ é º и ð¿Í º ÐÀÚ ÈÄÀÚÀÇ ¹ æ¹ ýÀ» »ç¿ë
ÇÏ ¸ é Æí ¸ ®ÇÑ °æ¿ì °¡ ÀÖ½À´ Ï ´ Ù. & ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
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GRE Math
Set 1
° - ÁÂ
4 6 yields as the result? 7 7 3 24 7 (C) (D) (E) 2 7 2
8. What number when multiplied by
2 7
(A)
¾î ¶² ¼ö¿¡
(B)
2 3
4 6 4 6 À» °öÇϸé ÀÌ ³ ª ¿À´ ÂÁö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.(°á±¹ Àº x × = ÀÌ ÁÒ.) 7 7 7 7
GREÀ» ° øº Î ÇÏ ¸ é¼ ÀÌ · ¯ÇÑ Ç¥Çö° ú Ä£¼÷ÇØ Á®¾ß ÇÕ´ Ï ´ Ù. & ´ äÀº
(C) ÀÔ´ Ï ´ Ù.
9. If the sum of 3 times
n , 11 times n , and 111 times n is equal to 1,000, what is the value of
n? (A)
8
(B)
12.5
(C)
16
(D)
25
(E) 125
n ÀÇ 3¹è, n ÀÇ 11¹ è, n ÀÇ 111¹ èÀÇ ÇÕÀÌ 1,000ÀÏ ¶§ n ÀÇ °ª À» ±¸ ÇÏ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. ( 3n + 11n + 111n = 1,000 ) & ´ äÀº
(A)ÀÔ´ Ï ´ Ù.
10. Which of the following is equal to 0.042? (A) (B) (C) (D) (E)
4 2 + 10 10 4 + 2 10 100 4 + 2 100 100 4 2 + 100 1,000 4 2 + 1,000 1,000
º и 𸦠1000À¸ · Î ¸ ¸ µé¾î ¼ Ç®¾î ÁÖ¼¼¿ä.’ & ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
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GRE Math
Set 1
° - ÁÂ
11. In the addition problem above, if ¡ à and ∆ each represent a digit, then ¡ à represents (A)
9
(B)
8
(C)
5
(D)
2
(E)
0
¡ à,∆ ° ¢°¢ ÀÚ¸ ´ ¼ö¸ ¦ Ç¥½ÃÇÒ ¶§ ¡ àÀÌ ¾ó¸ ¶¸ ¦ ³ ª Ÿ ³ »´ ÂÁö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ½Ê ÀÚ¸ ®ÀÇ ÇÕ°ú ¹ é ÀÚ¸ ®ÀÇ ÇÕÀÇ °á°ú° ¡ 2 + ¡ à = 2 ÀÌ ¶ó´Â °Í À» ÅëÇØ ¡ àÀº 0, 9. 10ÀÌ ¶ó´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. ÇÏ Áö¸ ¸ ¡ àÀº ÇÑ ÀÚ¸ ®ÀÇ ¼ö¸ ¦ ³ ª Ÿ ³ »´  °Í ÀÌ ±â ¶§¹ ®¿¡ 10ÀÏ ¼ö ¾ø½À´ Ï ´ Ù. ¶ÇÇÑ 0ÀÏ °æ¿ì ÀÏÀÇ ÀÚ¸ ® ¼öÀÇ ÇÕ¿¡ ¼ 2°¡ ³ ª ¿Í ¾ß ÇÏ ´ µ¥ ∆ℵ⊂³ ª ¿Ô±â ¶§¹ ®¿¡ 0ÀÌ ¾Æ´ Ï ¶ó´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. µû¶ó¼ 9° ¡ ´ õÇØÁø ´ Ù´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. (ÀÌ · ¯ÇÑ ¹ ®Á¦ ¸ ¦ »¡ ¸ ® Ǫ ´Â ¹ æ¹ ýÀº º ¸ ±â¸ ¦ ´ ë ÀÔÇÏ ¿© Ç®¾î ÁÖ´  °Í ÀÔ´ Ï ´ Ù.) & ´ äÀº
12.
(A)ÀÔ´ Ï ´ Ù.
If ¡ à represents a digit in the subtraction problem above, ¡ à= (A)
1
(B)
5
(C)
6
(D)
7
(E)
9
º¸±â¸¦ ´ ëÀÔÇÏ ¿© Ǫ ´  ¹ æ¹ ýÀÌ Á¦ ÀÏ º ü¸ £°ÚÁÒ. & ´ äÀº
(E)ÀÔ´ Ï ´ Ù.
À±ÅÂÈ- ¿µ¾î ¿¬ ±¸ ½Ç,
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GRE Math
Set 1
° - ÁÂ
13. The figure above shows the arrangement and code numbers of 9 fluorescent tubes. If a tube is illuminated whenever its code number is received, which of the following shows the arrangement of tubes illuminated when the digits in the result of 3,804 ÷ 3 are received?
»ó±âÀÇ ±×¸ ² ÀÌ 9° ³ ÀÇ fluorescent tube¿Í code¹ øÈ£ÀÇ ¹ èÄ¡ ¸ ¦ º ¸ ¿©ÁÖ°í ÀÖ´ Ù°í ÇÕ´ Ï ´ Ù. Code ¹ ø È£°¡ ÀÔ·  µÇ´  tube° ¡ ÄÑÁú ¶§ 3,804 ÷ 3 ÀÇ °ª ÀÇ ÀÚ¸ ´ ¼öµéÀÌ ÀÔ·  µÉ ¶§ º ÒÀÌ ÄÑÁö´  tube ÀÇ ¹ è¿ À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. & ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
50.2 × 0.49 ? 199.8 5 25 (D) (E) 4 2
14. Of the following, which is the closest approximation of (A)
1 10
(B)
1 8
(C)
1 4
GRE¿ ¡ ¼ °¡ ² û¾¿ º ¼ ¼ö ÀÖ´Â ¹ ®Á¦ ÀÔ´ Ï ´ Ù. Áö±Ý±î Áö ÃâÁ¦ µÇ¾ú´ ø ¹ ®Á¦ µéÀ» ¿¬½ÀÇÏ ½Ã¸ é °£´ ÜÈ÷ ÇØ°áÇÒ ¼ö ÀÖ´  À¯ÇüÀÇ ¹ ®Á¦ ÀÔ´ Ï ´ Ù.
50 × 0.5 1 = 200 8 & ´ äÀº
(B)ÀÔ´ Ï ´ Ù.
À±ÅÂÈ- ¿µ¾î ¿¬ ±¸ ½Ç,
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GRE Math
Set 1
° - ÁÂ
61.24 × (0.998) 2 403 15. The expression above is approximately equal to (A)
1
(B)
3
(C)
4
(D)
5
(E)
6
60 × (1)2 =3 20 & ´ äÀº
16.
(B)ÀÔ´ Ï ´ Ù.
( 2)(0.33)(15) is approximately equal to (0.24) (A)
(A) 2
(B)
5 2
(C)
15
(D)
36
(E)
40
& ´ äÀº
(E)ÀÔ´ Ï ´ Ù.
17. Of the following, which is the best approximation for (A)
0.015
(B)
0.15
(C)
1.5
(D)
15
(E)
150
& ´ äÀº
0.01 × 2.005 × 32.98 ? 11.12 × 0.04
(C)ÀÔ´ Ï ´ Ù.
À±ÅÂÈ- ¿µ¾î ¿¬ ±¸ ½Ç,
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GRE Math
Set 1
° - ÁÂ
18. Of the following, the closest approximation to
8.097(0.8745) is 0 .202
(A) 40 (B) 35 (C) 30 (D)
4
(E)
3
& ´ äÀº
(B)ÀÔ´ Ï ´ Ù.
19. If a sequence o f 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence? (A)
22
(B)
32
(C)
36
(D)
40
(E)
44
8° ³ ÀÇ Á¤¼ö°¡ ÀÖ´ µ¥ consecutive odd integersÀÌ °í increasing value¶ó Çß°í 7¹ ø ° Á¤¼ö°¡ 9¶ó°í Çß½À´ Ï ´ Ù. ÀÌ Á¶° ÇÀ» Ç¥ÇöÇÏ ¸ é: -3, -1, 1, 3, 5, 7, 9, 11. ÀÌ Á¤¼öµéÀÇ ÇÕÀº –3º Î ÅÍ 3±î Áö ÇÕÀº 0 ÀÌ µÇ¹ Ç· Î ³ ª ¸ ÓÁö Á¤¼öÀÇ ÇÕ5 + 7 + 9 + 11 = 32.
Tips -3, -1, 1, 3, 5, 7,, 9, 11ÀÇ Á¤¼ö´Â ù Ç×ÀÌ –3ÀÌ°í °øÂ÷(ÀÏ Á¤ÇÏ °Ô Áõ° ¡ ÇÏ´  ¼ö)°¡ 2ÀÌ ¸ç ³ ¡ Ç×ÀÌ 11ÀÌ ¹ Ç· Î °øÂ÷¼ö¿ ÀÇ ÇÕÀÇ °ø½ÄÀ» ÀÌ ¿ëÇؼ µµ Ç® ¼ö ÀÖ½À´ Ï ´ Ù. ù ° Ç×ÀÌ a , °øÂ÷°¡ d , ³ ¡ Ç×( n )ÀÌ l ÀÎ µî Â÷¼ö¿ ÀÇ Á¦ n Ç×±î ÁöÀÇ ÇÕÀ» S n ÀÌ ¶ó ÇÏ ¸ é
S n =
n( a + l ) , 2
. Á¤´ äÀº
S n =
n{2a + (n − 1)d } 2
(B)
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GRE Math
20. If w, x, y, and z are positive and (A) (B) (C) (D) (E)
Set 1
° - ÁÂ
w y = , which of the following is NOT always true? x z
wz = xy
x z = w y x z = y w w + x y + z = x z x + w z + y = w y
w y = ℵ≈´ ë° ¢¼±À¸ · Î °öÇÏ ¸ é wz = xy , ÀÌ °Í ÀÌ ¼º ¸ ³ ÇÏ Áö ¾Ê´  °Í Àº (C) x z . Á¤´ äÀº
(C)
21. If d =
(A)
a +b c 3c , a = , and b = , what is the value of d in terms of c ? ab 2 4 1+ 2 c
10c 11
(B)
5c 2
(C)
10c 3
(D)
¹ ®Á¦ ´  d °ª À» c °ª À¸ · ΠǥÇöÇÏ ¶ó´  °Í ÀÌ ¹ Ç· Î a = c ↵⊆ b = 2
10 11c
(E)
5 2c
3c ℵ≈ d = a+ b ↵ϒ ´ ëÀÔÇÏ ¸ é Á¤´ äÀ» 4 ab 1+
c2
±¸ ÇÒ ¼ö ÀÖ³ ׿ä. . Á¤´ äÀº
(A)
22. Tamara saves $35 each week. If she now has $100 saved, in how many weeks can she first have enough saved to buy a lawn mower that costs $250? (A)
2
À±ÅÂÈ- ¿µ¾î ¿¬ ±¸ ½Ç,
(B) 3
(C) 4
(D) 5
(E) 6
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GRE Math
Set 1
° - ÁÂ
ÇöÀç $100À» ÀúÃàÇß´ µ¥ $250ÀÇ lawn mowerÀ» »ì · Á¸ é ¸ î ÁÖ ÈÄ¿¡ °¡ ´ ÉÇÑÁö¸ ¦ ¹ ¯´Â ¹ ®Á¦ ÀÔ´ Ï ´ Ù. ÇöÀç $100ÀÌ ÀÖÀ¸ ¹ Ç· Î ¾ÕÀ¸ · Î $150À» ´ õ ÀúÃàÇÏ ¸ é µË´ Ï ´ Ù. ÇÑ ÁÖ¿¡ $35¾¿ ÀúÃàÇÏ ¹ Ç· Î 4 ÁÖ µÚ¿¡ ´  $140º ÒÀÌ ¸ ð¾ÆÁö°í ÃÑ $240À» ¸ ð¾Ò±â ¶§¹ ®¿¡ 5ÁÖ µÚ¿¡ ´  ÀÌ ¹ °°ÇÀ» »ì ¼ö°¡ ÀÖ½À ´ Ï ´ Ù. . Á¤´ äÀº
(D)
x is closest to + x 2 1 10 1 (C) (D) 21 2
23. If x > 3,000 , then the value of
1 6
(A)
x = 2 x + 1
(B)
1 3
(E)
3 2
1 ↵ϒ…↑1 ÀÇ °ª Àº x ÀÇ ÃÖ¼Ò°ª ÀÎ 3,001À» ´ ëÀÔÇغ ¸ ¸ é 1 = 0.00033322⋅⋅⋅ x x 1 2+ x
À§ÀÇ °ª Àº 1/2¿¡ °¡ ±î ¿öÁö³ ׿ä. . Á¤´ äÀº
(D)
24. A certain clock indicates 8 o’ clock. If the clock runs accurately for the next 11,995 hours, what hour will it indicate at the end of that time? (A)
1 o’ clock
(B)
2 o’ clock
(C)
3 o’ clock
(D)
5 o’ clock
(E)
10 o’ clock
ÇöÀç 8½ÃÀÌ °í ¾ÕÀ¸ · Î 11,995½Ã°£ÀÌ Áö³ ´ Ù¸ é ¸ î ½Ã°¡ µÇ´ ÂÁö¸ ¦ ±¸ ÇÏ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. 11,995½Ã °£¿¡ 8½Ã°£À» ´ õÇÏ ¸ é ÃÑ 12,003 hours°¡ µÇ°í ÀÌ °Í À» 24½Ã°£À¸ · Î ³ ª ´ ©¸ é ³ ª ¸ ÓÁö °ª ÀÌ 3ÀÌ µË ´ Ï ´ Ù. ÀÌ °ª ÀÌ Á¤´ äÀÌ µÇ°Ú³ ׿ä. . Á¤´ äÀº
(C)
À±ÅÂÈ- ¿µ¾î ¿¬ ±¸ ½Ç,
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Page 22
GRE Math
25. If
Set 1
° - ÁÂ
1 the result obtained when 2 is subtracted from 5 x is equal to the sum of 10 and 3 x , 2
what is the value of
x ?
(A) − 22 (B) 4 (C) 4 (D) 18 (E) 22 À§ÀÇ ¹ ®Á¦ ¸ ¦ ½ÄÀ¸ · ΠǥÇöÇÏ ¸ é À§ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é . Á¤´ äÀº
1 (5 x − 2) = 10 + 3 x 2
x = − 22
(A)
26. A light-year is approximately 6 × 1012 miles. Approximately how many miles from Earth is a galaxy that is 2 × 10 6 light-years away? (A) 3 .0 × 10 6 (B) 1.2 × 1018 (C) 1.2 × 1019 (D) 1.2 × 10 72 (E) 1.2 × 10 73
6 × 1012 miles ÀÏ ¶§, Áö±¸ ¿¡ ¼ 2 × 10 6 ±⁄≥� ¶³ ¾î Áø Àº ÇÏ ÀÇ °Å¸ ®¸ ¦ ±¸ ÇÏ ¶ó´Â ¹ ®Á¦ ³ ׿ä. 6 × 1012 × 2 × 10 6 = 1.2 × 1019 ÀÏ ±¤³ â( light-year )ÀÌ
. Á¤´ äÀº
(C)
27. If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,717 minutes earlier? (Assume standard time in one location.) (A) 6:22
(B) 6:24
(C) 6:27
(D) 6:30
(E) 6:32
ÇöÀç ½Ã°£ÀÌ 6:27º ÐÀÌ °í , ° Ų Ù· Î 2,880,717 minutes À» µ¹ · ÈÀ» ¶§ ±× ½Ã°£À» °è»êÇÏ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. 2,880,717 minutes = (48,011 × 60 minutes) + 57 minutes. Áï ÇöÀç ½Ã°£¿¡ ¼ 57º ÐÀ» °Å² Ù· Î °è»ê ÇÏ ¸ é 6: 30º ÐÀÌ µË´ Ï ´ Ù. . Á¤´ äÀº
(D)
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GRE Math
Set 1
° - ÁÂ
28. If the sum of two positive integers is 24 and the difference of their squares is 48, what is the product of the two integers? (A) 108
(B) 119
(C) 128
(D) 135
(E) 143
= 24 , x 2 − y 2 = 48 ÀÏ ¶§ xy ¸ ¦ ±¸ ÇÏ ¶ó´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. x 2 − y 2 = 48 Àº ( x + y )( x − y ) = 48 = (24)( x − y ) ⇒ ( x − y ) = 2 x + y = 24 ¿Í x − y = 2 À» ¿¬¸³ ¹ æÁ¤½ÄÀ¸ · Î Ç®¸ é x = 13, y = 11 ⇒ xy = 143 µÎ Á¤¼ö¸ ¦ x, y ¶ó °¡ Á¤ÇÏ ¸ é x + y
. Á¤´ äÀº
(E)
29. On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 165 is how many times an intensity corresponding to a magnitude of 125? (A)
40
(B)
100
(C)
400
(D)
1,000
(E)
10,000
ÀÏ ´ Ü 165¿ Í 125´  40ÀÇ magnitude Â÷ÀÌ °¡ ÀÖ½À´ Ï ´ Ù. ÀÌ magnitude¿¡ ¼ 10¾¿ Áõ°¡ ÇÏ ¸ é 10¹ 辿 ° Á¶(intensity)°¡ Áõ°¡ ÇÑ´ Ù°í ÇßÀ¸ ´ Ï 10 ×10 ×10 ×10 =10,000 . Á¤´ äÀº
(E)
30. In the formula V =
1 , if r is halved, then V is multiplied by 3 (2 r )
(A) 64 (B)
8
(C)
1
1 8 1 (E) 64 (D)
V =
1 1 1 ℵ∉ = ℵ⊂µË´ Ï ´ Ù. Áï V ¿¡ 8À» ° öÇÑ °ª ÀÔ´ Ï ´ Ù. ¶§, ÀÌ º ¯ÇÏ ¸ é r · Î V 8r 3 2 r r 3
. Á¤´ äÀº
(B)
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GRE Math
Set 1
° - ÁÂ
31. In the subtraction problem above, ∆ , ¡ à, and Ο represent different positive digits. If ¡ àis 1 greater than ∆ , what is the value of Ο ? (A)
9
(B) 7
¡à = ∆ + 1ÀÌ ¶ó¸ é
™
(D) 3
(E) 2
°ª À» ±¸ ÇÏ ¶ó´  ¹ ®Á¦ ³ ׿ä.
∆ = 1ÀÌ ¶ó ° ¡ Á¤ÇÏ ¸ é ¡ à= 2° ¡ µÇ°í . Á¤´ äÀº
(C) 5
™
= 9° ¡ µË´ Ï ´ Ù. ¾î ¶° ÇÑ Á¤¼ö¸ ¦ ´ ëÀÔÇصµ
™ = 9°¡
µÇÁÒ.
(A)
32. Which of the following procedures is always equivalent to adding 5 given numbers and then dividing the sum by 5? I.
Multiplying the 5 numbers and then finding the 5th root of the product.
II. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left. III. Ordering the 5 numbers numerically and then selecting the middle number. (A) None (B) I only (C) II only (D) III only (E) I and III 5°³ ÀÇ ÁÖ¾î Áø ¼ýÀÚµéÀ» ´õÇÑ ÈÄ¿¡ ±× ÇÕÀ» 5· Î ³ ª ´ « ° ª Àº °á±¹ ÀÌ ¼ýÀÚµéÀÇ Æò±ÕÀ» ±¸ÇÏ ´  °Í °ú °° ½À´ Ï ´ Ù. Ð 5°³ ÀÇ Á¤¼öµéÀ» ´ õÇÑ ÈÄ, ±× ÇÕÀ» µÎ ¹ è¸ ¦ ÇÕ´ Ï ´ Ù. ±× ´ ÙÀ½¿¡ ¼Ò¼öÁ¡ À» ¿ÞÂÊÀ¸ · Î 1ÀÚ¸® ¿Å ±â¸ é ° á±¹ 10À¸·Î ³ ª ´ « °Í °ú °°½À´ Ï ´ Ù. ´ ٽà Á¤¸ ®Çغ ¸ ¸ é 5° ³ ÀÇ Á¤¼öµéÀ» 2¹ è ÇÑ µÚ 10À¸ ·Î ³ ª ´ ©¸ é ±× °ª Àº Á¤¼öµéÀÇ ÇÕÀ» 5· Î ³ ª ´ « ° ª °ú ° °°í ÀÌ ½ÄÀº Æò±ÕÀ» ±¸ ÇÏ ´  °Í ÀÌ ³ ׿ä. . Á¤´ äÀº
(C)
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- ÁÂ GRE Math °
Set 2-1
Category 2 Number Proper ti es
1.
If
x is an even integer and y is an odd integer, which of the following CANNOT be true?
answer
y
(A) x is an even integer. (B)
y x is an odd integer.
x is a multiple of y . (D) y is a multiple of x . (E) xy is an even integer. (C)
2. If x is an even integer, which of the following is an odd integer? (A) 3 x + 2
answer
(B) 7 x (C) 8 x + 5 (D) x 2 (E) x 3
3. If
x is a positive odd integer and y is a negative even integer, which of the following could
be a negative odd integer? (A)
y x
(B) xy (C) x − y (D)
x 2 + y
(E)
x + y 2
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- ÁÂ GRE Math °
Set 2-1
4. An integer n that is greater than 1 is said to be “prime-saturated” if it has no prime factor greater than or equal to (A) 6 (B)
35
(C)
46
(D)
66
(E)
75
answer
n . Which of the following integers is prime-saturated?
5. If a, b , and c are three consecutive odd integers such that 10 < a < b < c < 20 and if b
answer
and c are prime numbers, what is the value of a + b ? (A)
24
(B)
28
(C)
30
(D)
32
(E)
36
6. If n is a positive integer, which of the following could be a prime number? (A) 6n (B) 6n + 1 (C) 6n + 2 (D) 6n + 3 (E) 6n + 4
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- ÁÂ GRE Math °
Set 2-1
7. What is the least common multiple of 3, 4, 5, and 8? answer
(A)
480
(B)
240
(C)
120
(D)
105
(E)
60
8. Which of the following is NOT a factor of 252? (A)
2
(B)
3
(C)
6
(D)
7
(E)
8
answer
9. There are 125 chips on a table. If as many of the chips as possible are to be arranged into an equal number of 3-chip and 4-chip stacks and the remaining chips are to be removed, how many of the chips are to be removed? (A)
One
(B)
Two
(C)
Five
(D)
Six
(E)
Seven
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answer
- ÁÂ GRE Math °
Set 2-1
x = 0.9 1 y = 0 .9 z = (0.9) 2 10. The values of x, y, and z are shown above. Which of the following gives these numbers
answer
in order from least to greatest? (A) x, y, z (B) x, z, y (C) y, z , x (D) z, y , x (E) z, x, y
11. If x and y are positive integers, which of the following is NOT necessarily an integer? (A) x + y
answer
(B) x − y
x y (D) xy (C)
(E) x y
12. For any number x, x denotes the least non-negative number y such that x + y is an integer. What is the value of 8.4 – 8.4? (A)
-0.4
(B)
0
(C)
0.6
(D)
7.8
(E)
8.0
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answer
- ÁÂ GRE Math °
Set 2-1
13. What is the least odd integer, greater than 1, that is both the square of an integer and the cube
answer
of an integer? (A) 9
(B) 27
(C) 81
(D) 243
(E) 729
14. What is the least possible product of 4 different integers, each of which has a value between –5
answer
and 10, inclusive? (A) (B) (C) (D) (E)
− 5040 − 3600 − 720 − 600 − 120
15. The number line above shows the position of a point that has coordinate x . Which of the following statements about x must be true? I. II. III.
2 < x < 4 − x < −3 0 < 2x − 3 < 1
(A)
I only
(B)
II only
(C)
III only
(D)
I and II
(E)
I and III
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- ÁÂ GRE Math °
Set 2-1
16. Which of the following must be true? answer
+ c then b < c . II. If a 2 b < a 2 c then b < c . III. If b 2 < c 2 then b < c . I.
If a + b < a
(A) None (B) I only (C) II only (D) I and II only (E) I, II, and III
17. If x and y are two consecutive odd integers and x + y = 2( x − y) 2 , what is the value of x + y ? (A)
2
(B)
4
(C)
8
(D)
12
(E)
16
18. Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer? (A)
75
(B)
42
(C)
32
(D)
25
(E)
12
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answer
answer
- ÁÂ GRE Math °
Set 2-1
19. When the integer n is divided by 6, the remainder is 3. Which of the following is NOT a
answer
multiple of 6? (A) n − 3 (B) n + 3 (C) 2 n (D) 3n (E) 4 n
20. If the remainder is 7 when positive integer
n is divided by 18, what is the remainder when
answer
n is divided by 6? (A)
0
(B)
1
(C)
2
(D)
3
(E)
4
N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N ?
21. If the two-digit integers M and (A)
181
(B)
165
(C)
121
(D)
99
(E)
44
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answer
- ÁÂ GRE Math °
Set 2-1
22. If the product of two positive integers is 630, which of the following must be true? I.
answer
Both integers are even numbers.
II. At least one of the integers is a multiple of 3. III. One of the integers is 10. (A) I only (B) II only (C) III only (D) I and II (E) II and III
a and b , a ⋅ b = a + b − ab . If a ⋅ b = 0 , which of the following CANNOT be a value of b ?
23. For any numbers (A)
2
(B)
1
(C)
0
(D)
−1
(E)
−3
answer
2
24. When the integer
k is divided by 12, the remainder is 3. Which of the following, when
divided by 12, will have a remainder of 6? I.
2k
II. 6k III. 4 k + 6 (A)
I only
(B)
II only
(C)
III only
(D)
I and II only
(E)
I, II, and III
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Set 2-1
25. What is the least number of digits (including repetitions) needed to express 10100 in decimal answer
notation? (A)
4
(B)
100
(C)
101
(D)
1,000
(E)
1,001
26. What is the smallest positive integer (A) 2 (B)
3
(C)
4
(D)
5
(E)
6
27. If
n is an integer, which of the following CANNOT be a factor of 3n + 4 ?
(A)
4
(B)
5
(C)
6
(D)
7
(E)
8
28. If
n for which 324 is a factor of 6 n ?
n and k are integers whose product is 400, which of the following statements must be
true? (A) (B) (C) (D) (E)
n + k > 0 n ≠ k Either n or k is a multiple of 10. If n is even, then k is odd. If n is odd, then k is even.
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answer
answer
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- ÁÂ GRE Math °
29. If
Set 2-1
a is a positive integer, and if the units’ digit of a 2 is 9 and the units’ digit of (a + 1)2 is
answer
2
4, what is the units’ digit of (a + 2) ? (A) 1
(B) 3
30. An “Armstrong number” is an
(C) 5
(D) 7
(E) 9
n -digit number that is equal to the sum of the n th powers of
answer
its individual digits. For example, 153 is an Armstrong number because it has 3 digits and
13 + 5 3 + 3 3 = 153 . What is the digit k in the Armstrong number 1, 6k 4 ? (A)
2
(B)
3
(C)
4
(D)
5
(E)
6
n positive integers is S , what is the sum of the first n positive even integers, in terms of S ? S (A) 2 (B) S (C) 2S (D) 2S + 2 (E) 4S
31. If the sum of the first
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32. The positive integers a, b, c, and
Set 2-1
d are such that a > b > c . If a + c = b + d , which
answer
of the following CANNOT be true? (A) (B) (C) (D) (E)
33.
d > a d = b d > b d > c b > d
If [ x ] is the greatest integer less than or equal to [ −1.6] + [3.4] + [2.7] ?
x , what is the value of
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
STOP
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¼öÇÐ
1. If
Çؼ³
Set 2-1
Category 2 N umber Pr oper ti es
x is an even integer and y is an odd integer, which of the following CANNOT be true?
(A) x y is an even integer. (B)
y x is an odd integer.
x is a multiple of y . (D) y is a multiple of x . (E) xy is an even integer. (C)
(A) x y , ¦ ¼ö°£¿¡ °ö¼À°ú ° °½À´ Ï ´ Ù. µû¶ó¼ ¦ ¼öÀÔ´ Ï ´ Ù. (B)
y x , Ȧ ¼ö°£¿¡ °ö¼ÀÀÌ ¹ Ç· ΠȦ ¼öÀÔ´ Ï ´ Ù.
(C) Ȧ ¼ö¿Í ¦ ¼öÀÇ °öÀº ¦ ¼öÀÔ´ Ï ´ Ù. (D) “ ¦ ¼ö × È¦ ¼ö”, “¦ ¼ö × Â¦ ¼ö” ¸ ðµÎ ¦ ¼öÀÔ´ Ï ´ Ù. “Ȧ ¼ö × È¦ ¼ö”¸ ¸ ÀÌ È¦ ¼öÀÔ´ Ï ´ Ù. ##Á» ´ õ ÀÚ¼¼ÇÑ »çÇ×Àº Çؼ³ ³ ¡ ÀåÀÇ summary of arithmeticÀ» Âü° í ÇÏ ¼¼¿ä. & ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
2. If x is an even integer, which of the following is an odd integer? (A) 3 x + 2 (B) 7 x (C) 8 x + 5 (D) x 2 (E) x 3 Ȧ ¼öÀÌ ±â À§ÇÑ Á¶°ÇÀº “¦ ¼ö + Ȧ ¼ö”, “Ȧ ¼ö
× È¦ ¼ö”
ÀÌ ¾î ¾ß ÇÕ´ Ï ´ Ù. x °¡ ¦ ¼öÀÌ ±â ¶ §¹ ®¿¡
º ¸ ±â¿ ¡ ¼ Ȧ ¼ö°¡ µÉ ¼ö ÀÖ´  ¿¬»êÀº 8 x + 5 (¦ ¼ö+Ȧ ¼ö)ÀÔ´ Ï ´ Ù. & ´ äÀº
(C)ÀÔ´ Ï ´ Ù.
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3. If
Set 2-1
x is a positive odd integer and y is a negative even integer, which of the following could
be a negative odd integer?
y x
(A)
(B) xy (C) x − y (D)
x 2 + y
(E)
x + y 2
x °¡ ¾çÀÇ È¦ ¼ö, y °¡ À½ÀÇ Â¦ ¼öÀÏ ¶§ º ¸ ±â Áß À½ÀÇ Â¦ ¼öÀÏ ¼ö ÀÖ´Â ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À ´ Ï ´ Ù. (A) À½ÀÇ Â¦ ¼öÀÇ È¦ ¼ö½ÂÀº À½ÀÇ Â¦ ¼öÀÔ´ Ï ´ Ù. (B) À½ÀÇ Â¦ ¼öÀÔ´ Ï ´ Ù. (C) ¾çÀÇ È¦ ¼ö ÀÔ´ Ï ´ Ù. (D) x 2
< y ÀÏ ° æ¿ì ,
& ´ äÀº
À½ÀÇ Â¦ ¼öÀÔ´ Ï ´ Ù. (E) ¾çÀÇ È¦ ¼öÀÔ´ Ï ´ Ù.
(D)ÀÔ´ Ï ´ Ù.
4. An integer n that is greater than 1 is said to be “prime-saturated” if it has no prime factor greater than or equal to (A) 6 (B)
35
(C)
46
(D)
66
(E)
75
Á¤¼ö n ÀÌ
n . Which of the following integers is prime-saturated?
n ° ú ° °° ų ª ¶Ç´Â
n º ¸ ´ ÙÅ« ¼ÒÀÎ ¼ö¸ ¦ °®Áö ¾Ê´  °æ¿ì prime-saturated¶ó°í ÇÒ
¶§, º ¸ ±â Áß prime-saturatedÀÎ Á¤¼ö¸ ¦ ¹ ¯°í ÀÖ½À´ Ï ´ Ù.
6 º ¸ ´ Ù ÀÛÁö¸¸ 3Àº 6 º ¸ ´ ÙÅ®´ Ï ´ Ù. µû¶ó¼ primesaturatedµÇÁö ¾Ê¾Ò½À´ Ï ´ Ù. ÇÏ Áö¸ ¸ 75ÀÇ ¼ÒÀÎ ¼ö 5´  75 º ¸ ´ ÙÀÛÀ¸ ¹ Ç· Î prime-saturatedµÇ¾ú½À 6Àº 2¿ Í3À» ¼ÒÀÎ ¼ö· Î °®½À´ Ï ´ Ù. 2´  ´ Ï ´ Ù. & ´ äÀº
(E)ÀÔ´ Ï ´ Ù.
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Set 2-1
5. If a, b , and c are three consecutive odd integers such that 10 < a < b < c < 20 and if b and c are prime numbers, what is the value of a + b ? (A)
24
(B)
28
(C)
30
(D)
32
(E)
36
a, b, c °¡ ¿¬¼ÓÇÏ ´  Ȧ ¼öÀÌ ¸ ç b ° ¡ c ¼Ú¼öÀÏ ¶§ a + b ÀÇ °ª À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 10 < a < b < c < 20 ÀÇ ±¸ °£¿¡ ¼ Á¶° ÇÀ» ¸ ¸ Á· ÇÏ ´  ¼öµéÀÇ Á¶ÇÕÀº ´ ÙÀ½°ú °°½À´ Ï ´ Ù. (11,13,15), (13,15,17), (15,17,19) ÀÌ Áß¿¡ b , c °¡ ¼Ú¼öÀÎ °æ¿ì ´  (15,17,19)ÀÔ´ Ï ´ Ù. µû¶ó¼ a + b =32ÀÔ´Ï´Ù. & ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
6. If n is a positive integer, which of the following could be a prime number? (A) 6n (B) 6n + 1 (C) 6n + 2 (D) 6n + 3 (E) 6n + 4 2¸ ¦ Á¦ ¿ÜÇÑ ¸ ðµç ¼Ú¼ö´Â Ȧ ¼öÀÔ´ Ï ´ Ù. µû¶ó¼ (B), (D)° ¡ °¡ ´ ɼº ÀÌ ÀÖ½À´ Ï ´ Ù. ÀÌ Áß (D)´ Â
6n + 3 = 3(2n +1) · Πǥ½ÃµÇ¾î 3ÀÇ ¹ è¼ö¶ó´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. & ´ äÀº
(B)ÀÔ´ Ï ´ Ù.
7. What is the least common multiple of 3, 4, 5, and 8? (A)
480
(B)
240
(C)
120
(D)
105
(E)
60
3,4,5,8 ÀÇ ÃÖ¼Ò°ø¹ è¼ö¸ ¦ (the least common multiple) ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. Çؼ³ ³ ¡ ¿¡ ÀÖ´  ¼³ ¸í À» ´ ٽà Çѹ ø Á¤¸ ®ÇÏ ¼¼¿ä. ±×³ É ³ Ñ¾î °¡ ½ÃÁö ¸ ¶¼¼¿ä!!! & ´ äÀº
(C)ÀÔ´ Ï ´ Ù.
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Set 2-1
8. Which of the following is NOT a factor of 252? (A)
2
(B)
3
(C)
6
(D)
7
(E)
8
252ÀÇ ¾à¼ö°¡ ¾Æ´ Ñ °Í À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. Çؼ³ µÞº Î º ÐÀ» Âü° í !!!
2 2 × 32 × 7 = 252 & ´ äÀº
(E)ÀÔ´ Ï ´ Ù.
9. There are 125 chips on a table. If as many of the chips as possible are to be arranged into an equal number of 3-chip and 4-chip stacks and the remaining chips are to be removed, how many of the chips are to be removed? (A)
One
(B)
Two
(C)
Five
(D)
Six
(E)
Seven
125°³ ÀÇ Ä¨ À» 3°³ ¾¿, 4°³ ¾¿ ½×¾Æ³ õ´ ´ Ù°í ÇÕ´ Ï ´ Ù. ±×¸ ®°í 3° ³ ¾¿ ½×¾Æ ¿Ã¸ ° ´ õ¹ Ì ÀÇ °³ ¼ö¿Í 4 °³ ¾¿ ½×¾Æ¿Ã¸ ° ´ õ¹ Ì ÀÇ °³ ¼ö¸ ¦ °°°Ô ÇÒ· Á¸ é 125°³ ÀÇ Ä¨ Áß ¸ î °³ ¸ ¦ ¾ø¾Ö¾ß ÇÏ ´ ÂÁö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 3° ³ ¾¿ ½×¾Æ ¿Ã¸ ° ´ õ¹ Ì ÀÇ °³ ¼ö¿Í 4° ³ ¾¿ ½×¾Æ ¿Ã¸ ° ´ õ¹ Ì ÀÇ °³ ¼ö°¡ °°´ Ù´  °Í Àº °á±¹ 7°³ ¾¿ ½× ¾Æ¿ ø ®´  °Í °ú ° °½À´ Ï ´ Ù. °á±¹ 125 ÷ 7 ÀÇ ³ ª ¸ ÓÁö ¸ ¸ ŠĨ À» Á¦ °ÅÇÏ ¸ é µË´ Ï ´ Ù. & ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
x = 0.9 1 y = 0 .9 z = (0.9) 2 10. The values of x, y, and z are shown above. Which of the following gives these numbers in order from least to greatest? (A) x, y, z (B) x, z, y (C) y, z , x (D) z, y , x (E) z, x, y 2 9 , 9 1 2 , x = 0.9 = = 9 z = (0.9) = y = 10 0.9 10
& ´ äÀº
(E)ÀÔ´ Ï ´ Ù.
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Set 2-1
11. If x and y are positive integers, which of the following is NOT necessarily an integer? (A) x + y (B) x − y
x y (D) xy (C)
(E) x y Á¤¼ö° £ÀÇ ³ ª ´ °¼ÀÀº Á¤¼ö° ¡ µÇÁö ¾ÊÀ» ¼öµµ ÀÖ½À´ Ï ´ Ù. & ´ äÀº
(C)ÀÔ´ Ï ´ Ù.
12. For any number x, x denotes the least non-negative number y such that x + y is an integer. What is the value of 8.4 – 8.4? (A)
-0.4
(B)
0
(C)
0.6
(D)
7.8
(E)
8.0
x ´  x ¿Í ´ õÇÏ ¿© Á¤¼ö°¡ µÇµµ· Ï ÇÏ ´  À½¼ö°¡ ¾Æ´ Ñ °¡ Àå ÀÛÀº ¼ö¸¦ Àǹ Ì ÇÑ´ Ù°í
ÇÕ´ Ï ´ Ù.
ÀÌ · ² ¶§ 8.4 – 8.4 ÀÇ °ª À» ¹ °¾î º ¸°í ÀÖ½À´ Ï ´ Ù. 8.4 °¡ Á¤¼ö°¡ µÇµµ· Ï ÇÏ ´  ¼ö´Â 0.6,1.6, …µî ÀÌ ÀÖ½À´ Ï ´ Ù. ÀÌ Áß ° ¡ Àå ÀÛÀº ¼ö´  0.6 ÀÔ´ Ï ´ Ù. & ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
13. What is the least odd integer, greater than 1, that is both the square of an integer and the cube of an integer? (A) 9
(B) 27
(C) 81
(D) 243
(E) 729
Á¤¼öÀÇ Á¦ °öÀÎ (the square of an integer) µ¿½Ã¿¡ »ï ½ÂÀÎ ¼ö¸¦ (the cube of an integer) ¹ °¾î º ¸°í ÀÖ ½À´ Ï ´ Ù.
36 = 32 × 32 × 32 = 33 × 33 = 729 & ´ äÀº
(E)ÀÔ´ Ï ´ Ù.
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Set 2-1
14. What is the least possible product of 4 different integers, each of which has a value between –5 and 10, inclusive? (A) (B) (C) (D) (E)
− 5040 − 3600 − 720 − 600 − 120
–5¿ ¡ ¼ 10»çÀÌ ¿¡ ¼ ¼ýÀÚ¸ ¦ 4° ³ »Ì ¾Æ°öÇÒ ¶§ °¡ Àå ÀÛÀº °ª Àº ¾ó¸ ¶ÀÎ Áö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.
− 5 × 8 × 9 ×10 = −3,600 & ´ äÀº
(B)ÀÔ´ Ï ´ Ù.
15. The number line above shows the position of a point that has coordinate x . Which of the following statements about x must be true? I. II. III.
2 < x < 4 − x < −3 0 < 2x − 3 < 1 (A) I only (B) II only (C) III only (D) I and II (E) I and III
Á÷¼±»ó¿¡ x °¡ Ç¥½ÃµÇ¾î ÀÖ°í x ¿¡ ´ ëÇÑ ¼³ ¸ í Áß ¿ÇÀº °Í À» ã´Â ¹ ®Á¦ ÀÔ´ Ï ´ Ù. Á÷¼±»ó¿¡ ¼ x ´  2¿Í 3»çÀÌ ¿¡ Ç¥½Ã µÇ¾î ÀÖ½À´ Ï ´ Ù. µû¶ó¼ ,¥±. − x < −3 ( x > 3 ) ¥². 0 < 2x − 3 < 1 (
3 < x < 2 ) 2
´  ¿ÇÄ¡ ¾Ê½À´ Ï ´ Ù. & ´ äÀº
(A)ÀÔ´ Ï ´ Ù.
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Set 2-1
16. Which of the following must be true?
+ c then b < c . II. If a 2 b < a 2 c then b < c . III. If b 2 < c 2 then b < c . I.
If a + b < a
(A)
None
(B)
I only
(C)
II only
(D)
I and II only
(E)
I, II, and III
º Î µî È£ÀÇ ¾çº ¯¿¡ °°Àº ¼ö°¡ ´ õÇØÁö°Å³ ª ¾çÀÇ ¼ö°¡ °öÇØÁö¸ é º Î µî È£ÀÇ ¹ æÇâÀº ¹ Ù² î Áö ¾Ê½À´ Ï ´ Ù. & ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
17. If x and y are two consecutive odd integers and x + y = 2( x − y) 2 , what is the value of x + y ? (A)
2
(B)
4
(C)
8
(D)
12
(E)
16
¿¬¼ÓÇÏ ´  µÎ °³ ÀÇ È¦ ¼ö¸ ¦ »« °á °ú´  2ÀÔ´ Ï ´ Ù. ½ÄÀ¸ · Î Ç®¸ é ´ ÙÀ½°ú °°½À´ Ï ´ Ù. ¿¬¼ÓÇÏ ´  µÎ °³ ÀÇ È¦ ¼ö¸¦ ½ÄÀ¸ · ΠǥÇöÇÏ ¸ é a − 1, a + 1 ÀÔ´ Ï ´ Ù . 2
x + y = 2( x − y) 2 ⇒ 2a = 2(− 2 ) & ´ äÀº
(C)ÀÔ´ Ï ´ Ù.
18. Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer? (A)
75
(B)
42
(C)
32
(D)
25
(E)
12
Á¤¼öÀÇ Á¦ °öÀ¸ · Î ³ ª ´ ©¾î ÁöÁö ¾Ê´Â ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 75´  25(= 5 2 ) · Î , 32´  4(= 2 2 ) · Î , 25´  25· Î, 12´Â 4(= 2 2 )· Î ³ ª ´ ©¾î Áý´ Ï ´ Ù. & ´ äÀº (B)ÀÔ´ Ï ´ Ù.
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Set 2-1
19. When the integer n is divided by 6, the remainder is 3. Which of the following is NOT a multiple of 6? (A) n − 3 (B) n + 3 (C) 2 n (D) 3n (E) 4 n . n À» 6À¸ · Î ³ ª ´ ©¸ é ³ ª ¸ ÓÁö°¡ 3ÀÌ ¶ó°í ÇÕ´ Ï ´ Ù. ÀÌ ¸ ¦ ½ÄÀ¸ · ΠǥÇöÇÏ ¸ é n = 6a + 3 ÀÔ´ Ï ´ Ù n = 6a + 3 À» 6À¸ · Î ³ ª ´ ©±â À§Çؼ ´  ³ ª ¸ ÓÁöÀÎ 3À» 6ÀÇ ¹ è¼ö· Î °í ÃÄ ÁÖ¸ é µË´ Ï ´ Ù. & ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
20. If the remainder is 7 when positive integer
n is divided by 18, what is the remainder when
n is divided by 6? (A)
0
(B)
1
(C)
2
(D)
3
(E)
4
n À» 18·Î ³ ª ´ ¶§ ³ ª ¸ ÓÁö°¡ 7ÀÌ µÈ´ Ù°í ÇÕ´ Ï ´ Ù.½ÄÀ¸ · ΠǥÇöÇÏ ¸ é n = 18 a + 7 ÀÔ´ Ï ´ Ù . n 18a 7 À» 6À¸ · Î ³ ª ´ ©¸ é n = + ÀÔ´ Ï ´ Ù . µû¶ó¼ ³ ª ¸ ÓÁö° ¡ 1ÀÌ µÈ´ Ù´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. 6 6 & ´ äÀº
(B)ÀÔ´ Ï ´ Ù.
N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N ?
21. If the two-digit integers M and (A)
181
(B) 165
(C) 121
(D) 99
(E) 44
M °ú N Àº µÎ ÀÚ¸ ® Á¤¼öÀÌ °í ¼ø¼ °¡ ¼ · Î ¹ Ý´ë ¹ æÇâÀÌ ¶ó Çß½À´ Ï ´ Ù ¿¹ ¸ ¦ µé¸ é 19¿Í 91°°Àº Á¤¼ö¸ ¦ ¸ »ÇÏ ´  °Í ÀÌ ³ ׿ä. ÀÌ µÎ Á¤¼öÀÇ °ü°è ¸ ¦ ½ÄÀ¸ · ΠǥÇöÇÏ ¸ é:
M = 10a + b, N = 10b + a ⇒ M + N = 11( a + b ) Áï M + N Àº Ç×»ó 11ÀÇ ¹ è¼ö¶ó´  °Í ÀÌ Áö¿ä . (A)º Î ÅÍ (E)Áß¿¡ 11ÀÇ ¹ è¼ö°¡ ¾Æ´ Ñ °Í À» ãÀ¸ ¸ é ±×°Í ÀÌ Á¤´ äÀÌ ³ ׿ä. ÿ Á¤´ äÀº
(A)
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Set 2-1
22. If the product of two positive integers is 630, which of the following must be true? I.
Both integers are even numbers.
II. At least one of the integers is a multiple of 3. III. One of the integers is 10. (A) I only (B) II only (C) III only (D) I and II (E) II and III µÎ Á¤¼öÀÇ °öÀÌ 630ÀÏ ¶§ Ç×»ó ÂüÀÎ °Í À» °í ¸ £´  ¹ ®Á¦ ³ ׿ä. ÀÏ ´ Ü630 = 2 × 32 × 5 × 7 ¦ ¼ö´  2¸ ¸ ÀÖÀ¸ ´ Ï ±î I Àº ¿À´ äÀÌ °í III Àº 3×210ÀÌ °¡ ´ ÉÇÏ ¹ Ç· Î Ç×»ó ÂüÀÌ ¾î ¾ß ÇÑ´ Ù´  Á¶°Ç ¿¡ ¹ þ¾î ³ µ³ ׿ä. II ¸ ¸ Ç×»ó ÂüÀÌ ³ ׿ä. ÿ Á¤´ äÀº
(B)
a and b , a ⋅ b = a + b − ab . If a ⋅ b = 0 , which of the following CANNOT be a value of b ? 3 (A) 2 (B) 1 (C) 0 (D) − 1 (E) − 2 a ⋅ b = a + b − ab = 0ÀÌ °í ÀÌ ½ÄÀ» b °ª À¸ · ΠǥÇöÇÏ ¸ é a − ab = −b ⇒ a = − a 1− b À§ÀÇ ½ÄÀÌ ¼º ¸ ³ ÇÏ · Á¸ é 1 − b ≠ 0 ÀÌ µÇ¾î ¾ß ÇÏ ¹ Ç· Î b = 1 ÀÎ °æ¿ì ´  ¼º ¸ ³ ÇÏ Áö ¾Ê½À´ Ï ´ Ù. 23. For any numbers
ÿ Á¤´ äÀº
(B)
24. When the integer
k is divided by 12, the remainder is 3. Which of the following, when
divided by 12, will have a remainder of 6? I.
2 k
II.
6 k
III. 4 k + 6 (A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
k = 12Q + 3 ÀÌ ¹ Ç· Î I. 2 k = 2( 12Q + 3 ) = 24Q + 6, ³ ª ¸ ÓÁö°¡ 6ÀÔ´ Ï ´ Ù. Á¤´ ä! II. 6 k = 6 × 12Q + 18 , ´ ٽà 18À» 12· Î ³ ª ´ ©¸ é ³ ª ¸ ÓÁö°¡ 6ÀÔ´ Ï ´ Ù. Á¤´ ä! III. 4 k + 6 = 4( 12Q + 3 ) + 6 = 4 × 12Q + 18 , ´ ٽà 18À» 12·Î ³ ª ´ ©¸ é ³ ª ¸ ÓÁö°¡ 6, ÀÌ °Í µµ Á¤´ ä! ÿ
Á¤´ äÀº (E)
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Set 2-1
25. What is the least number of digits (including repetitions) needed to express 10100 in decimal notation? (A) 10100
ÀÌ
4
(B) 100
(C) 101
(D) 1,000
(E) 1,001
¸ î ÀÚ¸ ®ÀÇ Á¤¼ö· Πǥ½ÃµÇ´ ÂÁö¸ ¦ °è»êÇÏ ´  ¹ ®Á¦ ³ ׿ä . ÀÏ´Ü 101 = 2ÀÚ¸ ®ÀÌ °í 10 2 =3
ÀÌ °í 10 3 = 4ÀÚ¸ ®ÀÔ´ Ï ´ Ù. µû¶ó¼ 10100 Àº 100¿¡ 1À» ´ õÇÑ 101ÀÚ¸ ®°¡ µÇ°Ú³ ׿ä. ÿ Á¤´ äÀº
(C)
26. What is the smallest positive integer (A) 2 (B)
3
(C)
4
(D)
5
(E)
6
n for which 324 is a factor of 6 n ?
324´Â 6 n ÀÇ factor° ¡ µÇ±â À§ÇÑ °¡ Àå ÀÛÀº Á¤¼ö¸ ¦ ±¸ÇÏ ¶ó´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. ÀÏ ´ Ü 324 = 62 × 32 ÀÌ ¹ Ç· Î 6 n = 324Q°¡ ¼º ¸ ³ ÇÏ ±â À§Çؼ ´  6 n ≥ 324. µû¶ó¼ n = 4 ÀÔ´ Ï ´ Ù . 6ÀÇ 4½ÂÀº 1296ÀÌ °í 324· Î ³ ª ´ ©¸ é ¸ òÀÌ 4°¡ µÇ¹ Ç· Î ¸ ðµç ° Í ÀÌ ¸ ¸ Á· µË´ Ï ´ Ù. ÿ Á¤´ äÀº
27. If
(C)
n is an integer, which of the following CANNOT be a factor of 3n + 4 ?
(A)
4
(B)
5
(C)
6
(D)
7
(E)
8
3n + 4 = 3(n + 1) + 1 , n °ª ¿¡ ¾î ¶° ÇÑ Á¤¼ö¸ ¦ ´ ëÀÔÇصµ 3ÀÇ ¹ è¼öÀÇ °ª Àº ³ ª ¿ÀÁö ¾Ê½À´ Ï ´ Ù. µû¶ó¼ 3ÀÇ ¹ è¼öÀÎ 6ÀÎ 3n + 4 ÀÇ factor°¡ µÉ ¼ö ¾ø³ ׿ä . ÿ Á¤´ äÀº
(C)
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28. If
Set 2-1
n and k are integers whose product is 400, which of the following statements must be
true?
n + k > 0 n ≠ k Either n or k is a multiple of 10. If n is even, then k is odd. If n is odd, then k is even.
(A) (B) (C) (D) (E)
nk = 400 = 2 45 2 ÀÏ ¶§ ÂüÀÎ °Í À» °í ¸ £¶ó´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. (A) n = -2, k = -5ÀÎ °æ¿ì ¿¡ µµ nk = 400 ÀÌ µÇ¹ Ç· Î n + k < 0 . False!
n = 25, k =16ÀÎ °æ¿ì ¿¡ ´  n °ú k °¡ 10ÀÇ ¹ è¼ö° ¡ ¾Æ´ Õ´ Ï ´ Ù. False! (D) n = 2, k = 200ÀÎ °æ¿ì ¿¡ ´  µÑ ´ ٠¦ ¼ö³ ׿ä. False! (C)
ÿ Á¤´ äÀº
29. If
(E)
a is a positive integer, and if the units’ digit of a 2 is 9 and the units’ digit of (a + 1)2 is 2
4, what is the units’ digit of (a + 2) ? (A) 1 ÀÏ ´ Ü
(B) 3
(C) 5
(D) 7
(E) 9
a ´  ¸ î ÀÚ¸ ® Á¤¼öÀÎ Áö¸ ¦ ¸ 𸠣°í ÀÏ ÀÚ¸ ®¿¡ ÀÖ´  ¼ö¸ ¦ ±¸ ÇÏ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù.
a 2 ÀÇ ÀÏ ÀÚ¸ ® ¼ö = 9. (a + 1)2 ÀÇ ÀÏ ÀÚ¸ ® ¼ö = 4, ¿©±â¼ (a + 1)2 = a 2 + 2a + 1 = 4 ÀÌ ¹ Ç· Î a 2 ÀÇ ÀÏ ÀÚ¸ ® ¼ö 9¿Í µÚÀÇ 1À» ÇÕÄ¡ ¸ é ³ ¡ ÀÚ¸ ®´  0ÀÌ µÇ°í ´Ù½Ã 2a ¿Í ´ õÇؼ ÀÏ ÀÚ¸ ® ¼ö°¡ 4 °¡ µÇ· Á¸ é 2a ÀÇ ³ ¡ ÀÚ¸ ®´  4° ¡ µÇ¾î ¾ß ÇÕ´ Ï ´ Ù. 2
±× ´ ÙÀ½ (a + 2) = (a + 1)2
+ 2 a + 3 , ¿ ©±â¼ (a + 1)2 ÀÇ ÀÏ ÀÚ¸ ® ¼ö´Â 4, 2a ÀÇ ÀÏ ÀÚ¸ ® ¼ö´ Â
4ÀÌ °í ³ ª ¸ ÓÁö ¼ö 3À» ¸ ðµÎ ÇÕÄ¡ ¸ é ÀÏ ÀÚ¸ ® ¼ö´  1ÀÌ µË´ Ï ´ Ù. ÿ
Á¤´ äÀº (A)
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30. An “Armstrong number” is an
Set 2-1
n -digit number that is equal to the sum of the n th powers of
its individual digits. For example, 153 is an Armstrong number because it has 3 digits and
13 + 5 3 + 3 3 = 153 . What is the digit k in the Armstrong number 1, 6k 4 ? (A)
2
(B) 3
(C) 4
(D) 5
(E) 6
n ÀÚ¸ ®¼öÀÏ ¶§ n ½ÂÀ» Çؼ ´ õÇÑ °ª À» “Armstrong number” ¶ó ÇÕ´ Ï ´ Ù. ÀÌ ¶§ 1, 6k 4 = 14 + 6 4 + k 4 + 4 4 = 1553 + k 4 , ¿©±â¼ ¾Ë ¼ö ÀÖ´  °Í Àº k 4 ÀÇ ÀÏ ÀÚ¸ ® ¼ö´  1553ÀÇ ÀÏ ÀÚ¸ ® 3° ú ´ õÇؼ 4° ú µÇ¾î ¾ß ÇÏ ÁÒ. µû¶ó¼ k 4 ÀÇ ÀÏ ÀÚ¸ ®´  1ÀÔ´ Ï ´ Ù. (A)¿Í (E) Áß¿¡ 4½ÂÀÌ 1ÀÌ µÇ´  °Í Àº 3»ÓÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(B)
n positive integers is S , what is the sum of the first n positive even integers, in terms of S ? S (A) (B) S (c) 2S (D) 2S + 2 (E) 4S 2 ÀÌ ¹ ®Á¦ ´  ÇлýµéÀÌ ÀÚÁÖ ½Ç¼ö¸ ¦ ÇÏ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. n °³ ÀÇ ¾çÀÇ Á¤¼öÀÇ ÇÕÀ» S ¶ó ÇÒ ¶§, n( n + 1) 1º Î ÅÍ n ±î ÁöÀÇ ÇÕÀº = S ÀÌ °í ¦ ¼öÀÇ ÇÕÀº n( n + 1) = 2 S ° ¡ µÇ³ ׿ä. 2 31. If the sum of the first
ÿ Á¤´ äÀº
(C)
32. The positive integers a, b, c, and
d are such that a > b > c . If a + c = b + d , which
of the following CANNOT be true? (A) (B) (C) (D) (E)
d > a d = b d > b d > c b > d
a > b > c ¿Í a + c = b + d , ¿ ©±â¼
a > b ÀÌ ¹ Ç· Î a + c = b + d °¡ ¼º ¸ ³ ÇÏ ±â À§Çؼ ´  d > a °¡
Àý´ ë· Î ¼º ¸ ³ ÇÏ Áö ¾Ê½À´ Ï ´ Ù. ¸¸ ¾à¿¡ d > a À̸é b > c ÀÌ ±â ¶§¹ ®¿¡ Àý´ ë·Î a + c = b + d °¡ ¼º ¸ ³ ÇÏ Áö ¾Ê½À´ Ï ´ Ù. ÿ Á¤´ äÀº
(A)
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33.
Set 2-1
If [ x ] is the greatest integer less than or equal to [ −1.6] + [3.4] + [2.7] ?
x , what is the value of
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
[ x ] ´  x º ¸ ´ Ù À۰ų ª °°Àº Á¤¼ö °ª À» Àǹ Ì ÇÒ ¶§, [− 1.6] = -2, [3.4 ] = 3, [2.7] = 2· Î ¹ Ù² ò ´ Ï ´ Ù. µû¶ó¼ ÇÕÀº 3ÀÌ ³ ׿ä . ÿ Á¤´ äÀº
(A)
< Summary of Arithmetic > Divisibility Tests for 2, 3, 5, and 10 A number is divisible by 2, if its last digit is even – 0, 2, 4, 6, or 8; 3, if the sum of its digits is a number divisible by 3 5, if its last digit is 0 or 5; and 10, if its last digit is 0
Rules for Odds and Evens odd
+
odd
=
even
odd
×
odd
=
odd
even
+
even
=
even
even
×
even
=
even
odd
+
even
=
odd
odd
×
even
=
even
Factors(ÀÎ ¼ö) The factors of a number are the positive integers that evenly divide that number. Ex: 36Àº 9° ³ ÀÇ factors °¡ ÀÖ´ Ù: 1, 2, 3, 4, 6, 9, 12, 18, 36 36 = 2 2 × 3 2 ↵ϒ…↑ 2ÀÇ Áö¼ö(exponent) 2¿¡ 1À» ´ õÇØ, 3ÀÇ Áö¼ö 2¿¡ ° ¢ ° ¢ 1À» ´ õÇØ° öÇØÁÖ¸ é ⇒ (2 + 1 )(2 + 1) = 9( Àüü factors ¼ö )
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Set 2-1
ÃÖ´ ë ° ø ¾à ¼ö(the greatest common divisor ) : µÎ °³ ÀÌ »óÀÇ´ ÙÇ×½ÄÀÌ ÀÖÀ» ¶§ , ÀÌ µé ¸ ðµÎ ¿¡ ° øÅëÀÎ ¾à¼ö¸ ¦ ° ø¾à¼ö¶ó ÇÏ°í , ° ø¾à¼ö ° ¡ ¿î µ¥ Â÷¼ö° ¡ ° ¡ Àå ³ ôÀº °ÍÀ» ÃÖ´ ë° ø¾à¼ö¶ó ÇÑ´ Ù.
ÃÖ¼Ò° ø ¹ è ¼ö (the lowest common divisor): µÎ °³ ÀÌ »óÀÇ´ ÙÇ×½ÄÀÌ ÀÖÀ» ¶§, ÀÌ µé ¸ ðµÎ ¿¡ °øÅë ÀÎ ¹ è¼ö¸ ¦ °ø¹ è¼ö¶óÇÏ°í , ° ø¹ è¼ö ° ¡ ¿î µ¥ Â÷¼ö° ¡ ° ¡ Àå ³ · Àº °ÍÀ» ÃÖ¼Ò° ø¹ è ¼ö¶ó ÇÑ´ Ù.
Ex. : 180, 420ÀÇ ÃÖ´ ë° ø¾à¼ö(GCD) ¿Í ÃÖ¼Ò° ø¹ è¼ö(LCD)´ Â? Çؼ³ )
180 = 2 × 2× 3× 3× 5, 420= 2 × 2× 3× 5× 7
GCD = 2 × 2× 3× 5= 60 , LCD = 2 × 2× 3× 3× 5× 7 = 1260
Decimals(¼Ò¼ö) À¯¸ ®¼ö ⇒
1) À¯ÇѼҼö : ¼Ò¼öÁ¡ ¾Æ·¡ ÀÇ 0ÀÌ ¾Æ´Ñ ¼ýÀÚ° ¡ À¯ÇÑ° ³ ÀÎ ¼Ò¼ö( 3 =0.6) 5
2) ¼øȯ¼Ò¼ö : ¼Ò¼öÁ¡ ¾Æ· ¡ ÀÇ ¾î ¶² ÀÚ¸ ®¿¡ ¼- º Î ÅÍ ÀÏ Á¤ÇÑ ¼ýÀÚÀÇ ¹ è ¿- ÀÌ ÇѾø •
•
ÀÌ ¹ ݺ ¹ µÇ´  ¹ «ÇѼҼö (0.123123123⋅⋅ ⋅ =0. 12 3 ) ¹ «¸ ®¼ö
⇒
3) ¹ «ÇѼҼö : ¼Ò¼öÁ¡ ¾Æ·¡ ÀÇ 0ÀÌ ¾Æ´Ñ ¼ýÀÚ° ¡ ¹ «ÇÑÈ÷ ¸ ¹ Àº ¼Ò¼ö ex) 1/6 = 0.1666 ⋅ ⋅ ⋅ ⋅ 4) À¯ÇѼҼöÀÇÆǺ ° ¹ æ¹ ý : º и ðÀÇ ¼ÒÀÎ ¼ö° ¡ 2 ¶Ç´  5»Ó ÀÏ ¶§ ex.) 12 = 3 = 80
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20
3 = 0 .15 22 × 5
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° - ÁÂ GRE Math
Category 2
Set 2-2
Number Properties
1. If k is a positive integer and if the numeral in the decimal system that represents the product
answer
60k contains only the digits 0 and 2, what is the least possible value of 60k ? (A)
220
(B)
2,020
(C)
2,220
(D)
20,020
(E)
20,220
2. There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a
answer
time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection? (A)
101
(B)
103
(C)
106
(D)
107
(E)
109
3. A necklace is made by stringing
N individual beads together in the repeating pattern red
bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then (A)
16
(B)
32
(C)
41
(D)
54
(E)
68
N could equal
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answer
° - ÁÂ GRE Math
Set 2-2
4. Mary Lou has 969 dimes in a piggy bank. What is the least number of dimes that she can
answer
remove from the bank so that she could divide the remaining dimes equally among 7 people? (A)
2
(B)
3
(C)
4
(D)
5
(E)
6
5. Which of the following integers equals the product of two prime numbers? answer
(A)
19
(B)
27
(C)
30
(D)
41
(E)
58
6. What is the smallest positive integer by which 126 can be multiplied so that the product is the square of an integer? (A)
4
(B)
7
(C)
9
(D)
14
(E)
126
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answer
° - ÁÂ GRE Math
Set 2-2
7. The sum of three consecutive odd integers, x, y , and z , in ascending order, is 39. What is
answer
the sum of the three consecutive odd integers that immediately follow z ? (A)
78
(B)
57
(C)
48
(D)
45
(E)
42
8. If the average (arithmetic mean) of x, y , and z is an even integer, then x + y + z could
answer
be (A)
15
(B)
16
(C)
18
(D)
20
(E)
21
9. The number
3 is what fraction of its reciprocal? 4
9 16 3 (B) 4 (A)
(C) 1
4 3 16 (E) 9 (D)
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answer
° - ÁÂ GRE Math
Set 2-2
10. If 0 < n < 1 , which of the following must be greater than 1? (A) (B) (C) (D) (E)
11. For how many of the integers from 10 to 99 is at least one of the two digits a 4? (A)
9
(B)
10
(C)
18
(D)
19
(E)
20
12. The series of numbers 3, 4, and 5 has the property that the square of the greatest number is equal to the sum of the squares of the other two numbers. Which of the following series of numbers does NOT have this property? (A) (B) (C) (D) (E)
answer
3n 2 n 1− n n n2 + 1 n 1+ n 3 n+ 2
0.6, 0.8, 1.0
3 1 5 , , 8 2 8 3 2, 4 2, 5 2 3, 4, 5 1.5, 2, 2.5
STOP
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answer
answer
° - ÁÂ GRE Math
¼öÇÐ
Set 2-2
Çؼ³ Category 2 Number Properties
1. If k is a positive integer and if the numeral in the decimal system that represents the product
60k contains only the digits 0 and 2, what is the least possible value of 60k ? (A)
220
(B)
2,020
(C)
2,220
(D)
20,020
(E)
20,220
k ° ¡ ¾çÀÇ Á¤¼öÀÌ ¸ ç 60k ÀÇ( 60 × k ) ¼ýÀÚµéÀÌ 0° ú 2¸ ¸ À» °¡ Áö°í ÀÖÀ» ¶§, ° ¡ Àå ÀÛÀº 60k ÀÇ °ª À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÀÌ · ± ¹ ®Á¦ ¸ ¦ °¡ Àå º ü¸£°Ô Ǫ ´  ¹ æ¹ ýÀº º ¸ ±â· Î º Î ÅÍ ´ äÀ» ã´Â °Í ÀÔ´ Ï ´ Ù. º ¸ ±â Áß 60À¸ · Î ³ ª ´ ©¾î Áö´  °¡ Àå ÀÛÀº ¼ö¸ ¦ ãÀ¸ ¸ é µË´ Ï ´ Ù. ´ äÀº (C)ÀÔ´ Ï ´ Ù. :
:
2. There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection? (A)
101
(B)
103
(C)
106
(D)
107
(E)
109
100 ~ 110Àå »çÀÌ ÀÇ Ä«µå°¡ ÀÖ´ Ù°í ÇÕ´ Ï ´ Ù ÀÌ Ä«µå¸ ¦ ÇÑ ¹ ø¿¡ 3À徿 ¼¼¾î ³ ª °¡ ¸ é 2ÀåÀÌ ³ ² °í , ÇÑ ¹ ø¿¡ 4À徿 ¼¼¾î ³ ª °¡ ¸ é 1ÀåÀÌ ³ ² ´  ´ Ù°í ÇÕ´ Ï ´ Ù ÀÌ ¶§ ¸ î ÀåÀÇ Ä«µå° ¡ ÀÖ´ ÂÁö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. Á¤¼ö100°ú 110»çÀÌ ¿¡ ¼- 3À¸ · Î ³ ª ´ ©¾î 2° ¡ ³ ² ´Â ¼ö´ Â101,104,107,110ÀÔ´ Ï ´ Ù. ÀÌ · ¯ÇÑ ¼öµé Áß 4 · Î ³ ª ´ ©¾î 1ÀÌ ³ ² ´  ¼ö´Â 101ÀÔ´ Ï ´ Ù. ´ äÀº (A)ÀÔ´ Ï ´ Ù. :
:
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° - ÁÂ GRE Math
3. A necklace is made by stringing
Set 2-2
N individual beads together in the repeating pattern red
bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then (A)
16
(B)
32
(C)
41
(D)
54
(E)
68
¸ ñ°Å¸ ®¸ ¦
N could equal
N °³ ÀÇ ±¸ ½½· Î ¸ ¸ µç´ Ù°í ÇÕ´ Ï ´ Ù. »¡ °£ ±¸ ½½, ³ ì »ö±¸½½, Èò ±¸ ½½, Ǫ ¸ ¥ ±¸½½,³ ë¶õ
±¸½½ÀÇ ¼ø¼- ¸ ¦ ¹ ݺ ¹ ÇÏ ¿© ¸ ñ°Å¸ ®¸ ¦ ¸ ¸ µé¸ ç »¡ °£ ±¸½½· Î ½ÃÀÛÇÏ ¿© Èò»ö±¸ ½½· Î ³ ¡ ³ ª µµ· Ï µðÀÚ ÀÎ À» Çß´ Ù¸ é º ¸ ±â Áß ¼ýÀÚ N ÀÌ µÉ ¼ö ÀÖ´  °Í À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¸ ñ°Å¸ ®´  »¡°£ ±¸½½· Î ½ÃÀÛÇÏ ¿© Èò ±¸½½· Î ³ ¡ ³ - ´ Ù°í ÇßÀ¸ ¹ Ç· Î 5°³ ÀÇ ±¸ ½½ÀÌ ¹ ݺ ¹ µÇ´ Ù°¡ ¼ø ¼- ÀÇ 3¹ ø°¿¡ ³ õ¿© ÀÖ´  Èò ±¸½½· Î ³ ¡ ³ ª °Ô µË´ Ï ´ Ù. µû¶ó¼- 5ÀÇ ¹ è¼ö¿¡ 3ÀÌ ´ õÇØÁ® ÀÖ´Â º ¸ ±â¸ ¦ ãÀ¸ ¸ é µË´ Ï ´ Ù. ´ äÀº (E)ÀÔ´ Ï ´ Ù. :
:
4. Mary Lou has 969 dimes in a piggy bank. What is the least number of dimes that she can remove from the bank so that she could divide the remaining dimes equally among 7 people? (A)
2
(B)
3
(C)
4
(D)
5
(E)
6
µÅÁö Àú±ÝÅë¿¡ 969°³ ÀÇ 10cent µ¿ÀüÀÌ ÀÖÀ» ¶§, ÃÖ¼Ò ¸ î °³ ÀÇ µ¿ÀüÀ» Àú±ÝÅë¿¡ ¼- »©³ »¸ é ³ ª ¸ ÓÁö µ¿ÀüÀ» 7»ç¶÷ÀÌ ¶È°°Àº °³ ¼ö· Î ³ ª ´ ©¾î °¡ Áú ¼ö ÀÖ´  Áö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÀÌ ¹ ®Á¦ ´  969º ¸ ´ Ù ÀÛÀº ÃÖ´ ëÀÇ 7ÀÇ ¹ è¼ö¸¦ ¹ °¾î º ¸ ´  °Í °ú °°½À´ Ï ´ Ù. 969º ¸ ´ Ù ÀÛÀº ÃÖ´ ëÀÇ 7ÀÇ ¹ è ¼ö´  966ÀÔ´ Ï ´ Ù. µû¶ó¼- 3°³ ÀÇ µ¿ÀüÀ» Á¦ °ÅÇÏ ¸ é Àú±ÝÅë¿¡ ³ ² ´  µ¿ÀüÀÇ °³ ¼ö´Â 966°³ °¡ µÇ¸ç ÀÌ µ¿ÀüÀ» 7»ç¶÷ÀÌ ¶È°°ÀÌ ³ ª ´ ©¾î °¡ Áú ¼ö ÀÖ½À´ Ï ´ Ù. ´ äÀº (B)ÀÔ´ Ï ´ Ù. :
:
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Set 2-2
5. Which of the following integers equals the product of two prime numbers? (A)
19
(B)
27
(C)
30
(D)
41
(E)
58
º¸±â Áß µÎ ¼Ú¼öÀÇ °ö¼À °ª ÀÌ ¹ «¾ùÀÎ Áö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÀÌ ¹ ®Á¦ ¸ ¦ ÇØ°áÇÏ ´  °¡ Àå ±âº » ÀûÀÎ ¹ æ¹ ýÀº ¼ÒÀÎ ¼öº ÐÇظ ¦ ÇÏ ´  °Í ÀÔ´ Ï ´ Ù. ÇÏ Áö¸ ¸ 2 ¸ ¦ Á¦ ¿ÜÇÑ ¸ ðµç ¼Ú¼ö°¡ Ȧ ¼ö¶ó´  »ç½ÇÀ» ÀÌ ¿ëÇÏ ¿© ¹ ®Á¦ ¸ ¦ ÇØ°áÇÏ ¸ é Á» ´ õ »¡ ¸ ® ÇØ´ ä¿¡ Á¢±ÙÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. º ¸ ±â Áß Â¦ ¼öÀÎ 30, 58 À» 2 · Î ³ ª ´ ©¾î ´ Ù¸ ¥ ¼ö ÇÏ ³ ª °¡ ¼Ú¼öÀÎ Áö È®ÀÎ ÇÏ ´  °Í ÀÔ´ Ï ´ Ù.. <<Âü°í >> ¼Ú¼ö Áß À¯ÀÏ ÇÑ Â¦ ¼ö°¡ 2 ¶ó´  ¼º ÁúÀ» ÀÌ ¿ë ÇÏ ¿© ÇØ°áÇÏ ´  ¹ ®Á¦ °¡ °¡ ² û¾¿ ÃâÁ¦ ! ´ äÀº (E)ÀÔ´ Ï ´ Ù. :
:
6. What is the smallest positive integer by which 126 can be multiplied so that the product is the square of an integer? (A)
4
(B)
7
(C)
9
(D)
14
(E)
126
126¿¡ °öÇÏ ¿© ±× °á°úµÈ ° ª ÀÌ Á¤¼öÀÇ Á¦ °öÀÌ µÇµµ· Ï ÇÏ ´  ¾çÀÇ Á¤¼öÀÇ ÃÖ¼Ò °ª À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.
126¸ ¦
¼ÒÀÎ ¼ö º ÐÇØÇÏ ¸ é 42 2 ( = 2 2 × 3 2 × 7 2 ) ℵ⊂µË´ Ï ´ Ù.
. µû¶ó¼2 × 32 × 7 ℵ™×∉×∧
14¸ ¦
°öÇØÁÖ¸ é
´ äÀº (D)ÀÔ´ Ï ´ Ù. :
:
7. The sum of three consecutive odd integers, x, y, and z , in ascending order, is 39. What is the sum of the three consecutive odd integers that immediately follow z ? (A)
78
(B)
57
(C)
48
(D)
45
(E)
42
¿¬¼ÓÇÏ ´  Ȧ ¼ö x, y , z ÀÇ ÇÕÀÌ 39ÀÏ ¶§, z ´ ÙÀ½¿¡ ¿À´  ¿¬¼ÓÇÏ ´  3° ³ ÀÇ È¦ ¼öÀÇ ÇÕÀ» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¿¬¼ÓÇÏ ´  ¼¼ °³ ÀÇ È¦ ¼ö¸¦
½ÄÀ¸ · ΠǥÇöÇÏ ¸ é a − 2, a, a + 2 ÀÔ´ Ï ´ Ù . µû¶ó¼-
3a = 39 À̸ç
z = 15 ¶ó´Â ° Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. z ´ ÙÀ½¿¡ ¿À´  ¿¬¼ÓÇÏ ´  3 °³ ÀÇ È¦ ¼ö´ Â17, 19, 21 ÀÔ´ Ï ´ Ù. ´ äÀº (B)ÀÔ´ Ï ´ Ù. :
:
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° - ÁÂ GRE Math
Set 2-2
8. If the average (arithmetic mean) of x, y , and z is an even integer, then x + y + z could be ? (A)
15
(B)
16
(C)
18
(D)
20
(E)
21
x, y, z ÀÇ Æò±ÕÀÌ Â¦ ¼öÀÌ ¸ é,
x + y + z = even ℵ⊂±� ¶§¹ ®¿¡ x, y, z ÀÇ ÇÕÀº ¦ ¼öÀÎ µ¿½Ã¿¡ 3 3
ÀÇ ¹ è¼ö°¡ µË´ Ï ´ Ù. º ¸ ±â Áß¿¡ ÀÌ · ¯ÇÑ Á¶° ÇÀ» ¸ ¸ Á· ÇÏ ´  Á¤¼ö´  18ÀÔ´ Ï ´ Ù. ´ äÀº (C)ÀÔ´ Ï ´ Ù. :
:
9. The number (A) (B) (C) (D) (E)
3 is what fraction of its reciprocal? 4
9 16 3 4 1
4 3 16 9
3 3 4 . ÀÌ ÀÚ½ÅÀÇ ¿ª ¼öÀÇ ¸ î º ÐÀÇ ¸ î ÀÎ Áö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÀÇ ¿ª ¼ö´  ÀÔ´ Ï ´ Ù 4 4 3 3 4 9 = 4 3 16 ´ äÀº (A)ÀÔ´ Ï ´ Ù. :
:
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° - ÁÂ GRE Math
Set 2-2
10. If 0 < n < 1 , which of the following must be greater than 1? (A)
3n 2
(B)
n 1− n
(C)
n n2 + 1
(D)
n 1+ n
(E)
3 n+2
n ÀÇ °ª ÀÌ 1º ¸´ Ù ÀÛ°í 0º ¸ ´ ٠Ŭ ¶§, 1º ¸ ´ Ù Å« °ª À» °¡ Áö´  º ¸ ±â¸ ¦ ã´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. n ÀÌ 1 º ¸ ´ Ù ÀÛÀº °ª À» °¡ Áö¹ Ç· Î n ÀÌ 1º ¸ ´ Ù Å« °ª À» °¡ Áö±â À§Çؼ- ´  n ÀÌ º и ð¿¡ ³ õÀÌ ¸ é µË´ Ï ´ Ù. 2 < n < 1 ÀÏ °æ¿ì ¿¡ ¸ ¸ 1º ¸ ´ Ù Å« °ª À» °¡ Áö°Ô µË´ Ï ´ Ù. º ¸ ±â(1)¿¡¼- ´  n ÀÇ °ª ÀÌ 3 1 º ¸ ±â(2) ºÐÀÚ¿Í º и 𸠦 °¢° ¢ n À¸ · Î ³ ª ´ ©¾î ÁÖ¸ é 1 − 1 ÀÔ´ Ï ´ Ù. n ÀÇ °ª ¿¡ µû¶ó¼ n 2 1 1 1 − 1 Àº 1º ¸ ´ Ù Ä¿Áö´Â °æ¿ì µµ( n = ) ÀÛ¾ÆÁö´  °æ¿ì µµ( n = ) ÀÖ½À´ Ï ´ Ù. 3 3 n 1 1 1 > 1 ℵ⊂≠∩•∈ º ¸ ±â(3) ºÐÀÚ¿Í º и 𸠦 °¢°¢ n À¸ · Î ³ ª ´ ©¾î ÁÖ¸ é 1 n + ℵ™×∉×∧ . 1 n + ℵ≡ n n n 1º ¸ ´ Ù ÀÛ°Ô µË´ Ï ´ Ù. º ¸ ±â(4) º ÐÀÚ¿Í º и 𸠦 °¢° ¢ n À¸ · Î ³ ª ´ ©¾î ÁÖ¸ é 1
1 1 1 + 1 ℵ™×∉×∧ > 1 ℵ⊂≠∩•∈1 + 1 ℵ≡ . n n n
1º ¸ ´ Ù ÀÛ°Ô µË´ Ï ´ Ù. º ¸ ±â(5) n Àº 1º ¸ ´ Ù À۱⠶§¹ ®¿¡ º и ð (n + 2) ÀÇ °ª ÀÌ º ÐÀÚ(3) º ¸ ´ ÙÄ¿Áú ¼ö ¾ø½À´ Ï ´ Ù. µû¶ó ¼- 1º ¸ ´ Ù Å« °ª ÀÌ µË´ Ï ´ Ù. ´ äÀº (E)ÀÔ´ Ï ´ Ù. :
:
11. For how many of the integers from 10 to 99 is at least one of the two digits a 4? (A)
9
(B)
10
(C)
18
(D)
19
(E)
20
10° ú 99»çÀÌ ÀÇ Á¤¼ö¿¡ ¼- µÎ ÀÚ¸ ® Áß Àû¾î µµ ÇÑ ÀÚ¸ ®¿¡ 4¸ ¦ °¡ Áö°í ÀÖ´  Á¤¼öÀÇ °³ ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 40~49¿¡ ¼- 10° ³ , ±×¸ ®°í 14,24,34,….94¿¡ ¼- 8°³ (44Á¦ ¿Ü) ÃÑ 18° ³ °¡ ÀÖ½À´ Ï ´ Ù. ´ äÀº (C)ÀÔ´ Ï ´ Ù. :
:
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° - ÁÂ GRE Math
Set 2-2
12. The series of numbers 3, 4, and 5 has the property that the square of the greatest number is equal to the sum of the squares of the other two numbers. Which of the following series of numbers does NOT have this property? (A) (B) (C) (D) (E)
0.6, 0.8, 1.0
3 1 5 , , 8 2 8 3 2, 4 2, 5 2 3, 4, 5 1.5, 2, 2.5
¼ýÀÚ 3, 4, 5 ÀÇ ³ ª ¿- ¿¡ ¼- °¡ Àå Å« ¼ö(5)ÀÇ Á¦ °öÀº ´ Ù¸¥ µÎ ¼ö(3, 4)ÀÇ Á¦ °öÀÇ ÇÕ°ú ° °Àº ¼º Áú À» °¡ Áö° í ÀÖ½À´ Ï ´ Ù. º ¸ ±â Áß ÀÌ · ¯ÇÑ ¼º ÁúÀ» °®Áö ¾Ê´  ¼öÀÇ ³ ª ¿- À» ã´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. ÀÌ ¹ ®Á¦ ¿¡ ¼- ÁÖ¾î Áø º ¸ ±â¸ ¦ »ì Æì º ¸ ¸ é ¼ýÀÚÀÇ ³ ª ¿- ÀÎ 3, 4, 5 ÀÇ º ¯ÇüÀÓÀ» ¾Ë°Ô µË´ Ï ´ Ù. (A) 0.2 · Î ³ ª ´ ©¾î ÁÖ¸ é ¼ýÀÚ3, 4, 5 ÀÇ ³ ª ¿- ÀÔ´ Ï ´ Ù. (B) 8 À» ° öÇÏ ¿© ÁÖ¸ é ¼ýÀÚ3, 4, 5 ÀÇ ³ ª ¿- ÀÔ´ Ï ´ Ù. º ¸ ±â (D)¸ ¦ Á¦ ¿ÜÇÏ °í ´ Ù¸ ¥ º ¸ ±âµéµµ ¸¶Âù°¡ Áö¶ó´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. ´ äÀº (D)ÀÔ´ Ï ´ Ù. :
:
GRE ¿¡ ¼- ÀÌ Â÷ ÇÔ¼ö½ÄÀ» ¼¼¿ö ¹ ®Á¦ ¸ ¦ ÇØ° áÇØ¾ß ÇÏ ´  ° æ¿ì ³ ª º ¹ ÀâÇÑ°è»êÀ» ÇØ¾ß ÇÏ ´  ¹ ®Á¦ ´  ° ÅÀÇ ¾ø½À´ Ï ´ Ù. ¿ÀÈ÷· Á ¾ÆÀÌ µð¾î ¸ ¦ ° ¡ Áö° í ÇØ° áÇØ¾ß ÇÏ ´  ¹ ®Á¦ ° ¡ ¸ ¹ ½À´ Ï ´ Ù. µû¶ó¼- ¿¬½À À» ÇÏ ´  µ¿¾È ÀÌ · ¯ÇÑ Á¢±Ù ¹ æ¹ ý µéÀ» ° è ¼ÓÀûÀ¸ · Î ¿¬½ÀÇÏ ´ ° Í ÀÌ ½ÇÀü¿¡ ¼- ÁÁÀº ° á°ú¸ ¦ ³ º À» ¼ö ÀÖ´  ¹ ÙÅÁÀÌ µË´ Ï ´ Ù.
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GRE Math °-ÁÂ Set 3
Category 3 Averages
1.
What is the average (arithmetic mean) of the numbers 15, 16, 17, 17, 18, and 19? (A) 14.2 (B) 16.5 (C) 17 (D) 17.5 (E) 18
2.
If n red pencils cost 10 cents each and m blue pencils cost 9 cents each, what is the average (arithmetic mean) cost, in cents, per pencil? 19(n + m) (A)
answer
answer
2
10 n + 9m 19 10 n + 9m (C) n+ m n+m (D) 2 19 (E) n+m (B)
3.
If the average (arithmetic mean) of a,b, and c is 40, what is the average (arithmetic mean) of (3a + 10), (3b + 10) , and (3c + 10) ? (A) 50 (B) 70 (C) 130 (D) 150 (E) It cannot be determined from the information given.
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GRE Math °-ÁÂ Set 3
4.
y t each and the cost of item B is each. What is the average 2 3 (arithmetic mean) cost per unit of a collection consisting of x units of A and k units of B ? 3 y + 2t (A) 12 ( x + k ) + (3 y + 2t ) (B) 12 3 xy + 2 kt (C) x + k 3 xy + 2 kt (D) 6 3 xy + 2 kt (E) 6( x + k )
The cost of item A is
If each of 4 subsidiaries of Corporation R has been granted a line of credit of $700,000 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R ? (A) $1,568,000 (B) $448,000 (C) $406,000 (D) $313,600 (E) $116,000
5.
6.
What is the average (arithmetic mean) of 8 numbers if the average of 5 of the numbers is 24 and the sum of the remaining 3 numbers is 40? (A) 8 (B) 20 (C) 29 (D) 30 (E) 37.5
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GRE Math °-ÁÂ Set 3
7. A manager’s annual salary is $8,400 greater than the annual salary of each of two assistant managers, who earn x dollars each per year. The average (arithmetic mean) of the 3 annual salaries, in dollars, is (A) x + 2,800
answer
(B) x + 4, 200 (C) 2 x + 2 ,800
2 x + 8,400 3 3 x + 8, 400 (E) 2 (D)
8.
If the average (arithmetic mean) of the four numbers K , 63, what is the value of K ? (A) 11 (B)
15
(C) (D)
22 23
(E)
25
2 K + 3 , 3 K − 5 , and 5 K + 1 is
answer
3 4 3 10
9. The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and (A) 15 (B) 25 (C) 35 (D) 45 (E) 55
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GRE Math °-ÁÂ Set 3
10.
A total of $2,000 was spent for a 30-day vacation. If transportation expenses were $230, lodging was $750, and exactly $20 was spent per day for meals and tips, what was the average (arithmetic mean) amount per day that was spent on other expenses? (A) $66 (B) $42 (C) $33 (D) $20 (E) $14
11.
In a certain company, the total monthly payroll for the 12 production workers is $18,000 and the total monthly payroll for the 36 office workers is $63,000. By how much does the average (arithmetic mean) monthly salary of an office worker exceed that of a production worker in this company? (A) $62.50 (B) $187.50 (C) $250.00 (D) $375.00 (E) $500.00
12.
On a certain test, 3 students each had a score of 90, 9 students each had a score of 80, 4 students each had a score of 70, and 4 students each had a score of 60. What was the average (arithmetic mean) score for the 20 students? (A) 70.5 (B) 75.0 (C) 75.5 (D) 80.0 (E) 80.5
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GRE Math °-ÁÂ Set 3
13. On 3 sales John has received commissions of $240, $80, and $110, and he has 1 additional sale pending. If John is to receive an average (arithmetic mean) commission of exactly $150 on the 4 sales, then the 4th commission must be. (A) $164 (B) $170 (C) $175 (D) $182 (E) $185
14. The 10 households on a certain street have household incomes that range from $34,000 to $150,000 and an average (arithmetic mean) household income of $60,000. If the household with the highest income and the one with the lowest income are excluded, what is the average household income for the remaining 8 households? (A) $41,600 (B) $47,000 (C) $52,000 (D) $61,000 (E) $75,000
15. The graph above shows the distribution of the 100 scores in a certain competition. What is the median score for the competition? (A) 7.5 (B) 7.75 (C) 8.0 (D) 8.25 (E) 8.5
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GRE Math °-ÁÂ Set 3
16. A certain elevator has a safe weight limit of 2,000 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 215 pounds? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11
17. For the month of April, the average (arithmetic mean) of the daily high temperatures recorded at a certain weather station was x degrees. If the average for the first 13 days of the month was ( x − 10) degrees, what was the average, in degrees, for the remaining 17 days of the month? (A) x + 10 (B) 17 x + 130 130 x + 17 (C)
answer
answer
x
17 x + 10 17 17 x + 130 (E) 17 (D)
18. A statistician calculated the average (arithmetic mean) for 20 measurements to be 50. On rechecking the calculations, the statistician found that a measurement of “78” had been treated as “18” and a measurement of “40” had been treated as “50”. If no other errors were made, what is the correct average for the 20 measurements? (A) 47.5 (B) 50.0 (C) 51.0 (D) 52.5 (E) 53.5
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GRE Math °-ÁÂ Set 3
19. If k is an integer and 15 < k < 25 , which of the following could be the average (arithmetic mean) of 12, 14, 17, 23, and k ? (A) 13.2 (B) 15.6 (C) 16.8 (D) 18.2 (E) 19.5
20. In performing a sequence of experiments, a scientist made 20 measurements. The average (arithmetic mean) of these measurements was 34. For security reasons the scientist coded the data by multiplying each of the measurements by 10 and then adding 40 to each product. What is the average of the coded measurements? (A) 1,140 (B) 380 (C) 342 (D) 57 (E) 19
21. The average (arithmetic mean) of n numbers is equal to If (A) (B) (C) (D) (E)
1 the sum of the n numbers. 3
1 the sum of the numbers is 15, what is the average of the n numbers? 2 3 5 10 30 45
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GRE Math °-ÁÂ Set 3
22. The average (arithmetic mean) of ten numbers on a list is m . If the numbers 10 and 24 are added to the list, the average (arithmetic mean) of these twelve numbers on the list is also m . What is the value of m ?
answer
1 3
(A)
11
(B) (C) (D) (E)
14 17 20 It cannot be determined from the information given.
23. The average (arithmetic mean) price of the 5 houses on a certain street is $60,000. If the price of the least expensive house is $55,000 which of the following could NOT be the price of the most expensive house? (A) $82,000 (B) $78,000 (C) $72,000 (D) $65,000 (E) $62,500
24. If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of z − x ? (A) 70 (B) 40 (C) 20 (D) 10 (E) It cannot be determined from the information given.
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GRE Math °-ÁÂ Set 3
Mon +2
1 2
Tue −1
Wed
1 4
−
Thu
1 8
0
Fri +1
3 8
25. The table above shows the net change, in dollars, in the price of a share of a certain stock each day last week. What was the average (arithmetic mean) daily net change, in dollars, for the 5day week? (A) −
1 2
(B)
+
1 4
(C) +
1 2
(D)
+
5 4
(E) +
5 2
26. If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degree Fahrenheit, could be (A) 6 x (B) (C) (D) (E)
answer
answer
4 x 5 x 3 3 x 2 3 x 5 Score
Number of Students
83
5
70
6
92
3 5
64
1
27. The incomplete table above shows a distribution of scores for a class of 20 students. If the average (arithmetic mean) score for the class is 78, what score is missing from the table? (A) 73 (B) 75 (C) 77 (D) 79 (E) 81
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GRE Math °-ÁÂ Set 3 28. If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true? I. x is an even integer. II. x is a nonzero integer. III. x is a multiple of 5. (A) I only (B) III only (C) I and II only (D) I and III only (E) I, II, and III
29. The average (arithmetic mean) of 4 positive integers is 50. If the average of 2 of these integers i s 45, what is the greatest possible value that one of the other 2 integers can have? (A) 55 (B) 65 (C) 100 (D) 109 (E) 115
30. The trade name for a product has 6 letters , and the length of the package for the product is l centimeters. The trade name of the product is printed lengthwise on one side of the package with a margin of m centimeters on each end of the side. If the space between each letter is considered negligible, what is the average (arithmetic mean) width, in centimeters, of each letter in the trade name? (A) l − 2m (B) l − m ÷8 (l − m) ÷ 6
(C) (D)
l
(E)
(l − 2m) ÷ 6
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GRE Math °-ÁÂ Set 3
¼öÇÐ
Çؼ³ Category 3 Average
1. What is the average (arithmetic mean) of the numbers 15, 16, 17, 17, 18, and 19? (A) 14.2 (B) 16.5 (C) 17 (D) 17.5 (E) 18 15 + 16 + 17 + 17 + 18 + 19 = 17 , 6 : Á¤´ äÀº (C) :
If n red pencils cost 10 cents each and m blue pencils cost 9 cents each, what is the average (arithmetic mean) cost, in cents, per pencil?
2.
(A)
19( n + m) 2
(B) 10n + 9m 19 (C) 10n + 9m n+m (D) n + m 2 19 (E) n + m N1(° ³ ¼ö)À» °¡ Áø ±×· ì ÀÇ Æò±ÕÀº A1, N2(°³ ¼ö)ÀÇ Æò±ÕÀº A2 ÀÏ ¶§
Combined Average(N1 °ú N2 ÀÇ È¥ÇÕµÈ Æò±Õ) =
n ÀÇ Æò±ÕÀº
10cents,
Á¤´ äÀº (C)
:
Point!
m ÀÇ Æò±ÕÀº
( N 1 × A1) + ( N 2 × A2) N 1 + N 2
9 cents ÀÌ ´ Ï ±î , À§ÀÇ °ø½Ä¿¡ ´ ëÀÔÇÏ ¸ é Á¤´ äÀ» ±¸ ÇÒ ¼ö ÀÖÁÒ.
:
È¥ÇÕÆò±Õ° ø½ÄÀ» ÀÌ ¿ë ÇÏ ´ ¹ ®Á¦ ° ¡ ÀÚÁÖ ÃâÁ¦ µË´ Ï ´ .Ù N1Àº ÇÑ Áý´ ÜÀÇ ¼ö¸ ¦ ³ ª Ÿ ³ »° í , N2µµ
. µÎ Áý´ ÜÀÇ Æò±ÕÀ» ÇÕÃļ- »õ· Î ¿î Æò±Õ(Combined Average)À» ±¸ ÇÏ ´  ´ Ù¸ ¥ Áý´ ÜÀÇ ¼ö¸ ¦ ³ ª Ÿ ³ ½´ Ù ¹ ®Á¦ ÀÌ ¹ Ç· Î À§ÀÇ ° ø½Ä¿¡ Á¤È®È÷ ´ ëÀÔÇÏ ¸ é ±×¸ ® ¾î · Á¿î ¹ ®Á¦ ´  ¾Æ´ Õ´ Ï ´ Ù.
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GRE Math °-ÁÂ Set 3
If the average (arithmetic mean) of a,b, and c is 40, what is the average (arithmetic
3.
mean) of (3a + 10), (3b + 10) , and (3c + 10) ? (A) 50 (B) 70 (C) 130 (D) 150 (E) It cannot be determined from the information given. a+b+c ( 3a + 10 ) + ( 3b + 10 ) + ( 3c + 10 ) =? = 40 , then 3 3
a + b + c = 120 À» À§ÀÇ ½Ä¿¡ ´ ëÀÔÇÏ ¸ é Á¤´ äÀ» ±¸ ÇÒ ¼ö ÀÖÁÒ. Á¤´ äÀº (C) :
:
4.
y t each and the cost of item B is each. What is the average 2 3 (arithmetic mean) cost per unit of a collection consisting of x units of A and k units of B ? The cost of item A is
(A) (B) (C) (D) (E)
3 y + 2t 12 ( x + k ) + (3 y + 2t ) 12 3 xy + 2 kt x + k 3 xy + 2kt 6 3 xy + 2kt 6( x + k )
N1( x )ÀÇ ±×· ì ÀÇ Æò±ÕÀº A1(
y ), 2
N2( k )ÀÇ Æò±ÕÀº A2(
t )ÀÏ 3
¶§
Combined Average(N1°ú N2 ÀÇ È¥ÇÕµÈ Æò±Õ)
( N 1× A1) + ( N 2 × A2) ( x × y ) + (k × t ) = = 2 3 ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é N 1+ N 2 x + k Á¤´ äÀº (E) :
:
5.
If each of 4 subsidiaries of Corporation R has been granted a line of credit of $700,000 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R ? (A) $1,568,000 (B) $448,000 (C) $406,000 (D) $313,600 (E) $116,000
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GRE Math °-ÁÂ Set 3
Combined Average¸ ¦ ¹ ¯´  ¹ ®Á¦ ³ ׿ä!! ( N 1× A1) + ( N 2 × A2) = ( 4 × $700,000) + ( 3 × $112,000) = $448,000 N 1+ N 2 7 :
6.
Á¤´ äÀº ( B ) :
What is the average (arithmetic mean) of 8 numbers if the average of 5 of the numbers is 24 and the sum of the remaining 3 numbers is 40? (A) 8 (B) 20 (C) 29 (D) 30 (E) 37.5
Combined Average °ø½ÄÀ» »ç¿ëÇÏ ¸ é µÇÁÒ! 8°³ ÀÇ ¼ýÀÚ Áß¿¡ ¼ 5°³ ÀÇ Æò±ÕÀº 24ÀÌ °í , ³ ª ¸ ÓÁö 3°³ ÀÇ ÇÕÀº 40ÀÌ ¶ó ÇßÀ¸ ´ Ï ±î ³ ª ¸ ÓÁö 3° ³ ÀÇ ¼ýÀÚÀÇ Æò±ÕÀº 40/3 ÀÌ ³ ׿ä. ÀÌ °Í À» ° ¡ Áö° í °ø½Ä¿¡ ´ ëÀÔÇÏ ¸ é : 40 ( 5 × 24 ) + ( 3 × ) 3 = 20 ( Average ) , 8
Á¤´ äÀº (B) :
:
7. A manager’ s annual salary is $8,400 greater than the annual salary of each of two assistant managers, who earn x dollars each per year. The average (arithmetic mean) of the 3 annual salaries, in dollars, is (A) x + 2,800 (B) x + 4, 200 (C) 2 x + 2 ,800
2 x + 8,400 3 3 x + 8,400 (E) 2 (D)
A manager’ s annual salary = $ x (salary of each of two assistant managers) + $8,400 Average= ( x + $8,400) + x + x = x + $2,800 , 3 Á¤´ äÀº (A) :
:
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8. If the average (arithmetic mean) of the four numbers K , 63, what is the value of K ? (A) 11 (B)
15
(C) (D)
22 23
(E)
25
2 K + 3 , 3 K − 5 , and 5 K + 1 is
3 4 3 10
K + ( 2 K + 3) + (3 K − 5) + ( 5K + 1) = 63 4
¿ÞÂÊÀÇ ½ÄÀ» Ç®¸ é K=23,
Á¤´ äÀº (D) :
:
9. The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and (A) 15 (B) 25 (C) 35 (D) 45 (E) 55
10 + 30 + 50 20 + 40 + x ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é X ° ª À» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. = 30 = 5 + 3 3 : Á¤´ äÀº (A) :
10. A total of $2,000 was spent for a 30-day vacation. If transportation expenses were $230, lodging was $750, and exactly $20 was spent per day for meals and tips , what was the average (arithmetic mean) amount per day that was spent on other expenses? (A) $66 (B) $42 (C) $33 (D) $20 (E) $14 Àüü°æº ñ($2,000) − ($230+$750+($20 ×30days) = $420(other expenses) $420 ÷30 = $14, Á¤´ äÀº (E) :
:
Tip :exactly $20 was spent per day for meals and tips Àǹ Ì ´  ¸ ÅÀÏ $20À» ½Ä»ç º ñ¿Í ÆÁÀ¸ · Î ¼¹ ´ Ù´  ° Í ÀÌ ¹ Ç· Î ¿©±â¿¡ 30 daysÀ» ° öÇؾßÁö Àüü ½Ä»ç º ñ¿Í ÆÁÀÌ ³ ª ¿É´ Ï ´ Ù.
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GRE Math °-ÁÂ Set 3
11.
In a certain company, the total monthly payroll for the 12 production workers is $18,000 and the total monthly payroll for the 36 office workers is $63,000. By how much does the average (arithmetic mean) monthly sal ary of an office worker exceed that of a production worker in this company? (A) $62.50 (B) $187.50 (C) $250.00 (D) $375.00 (E) $500.00
$18,000 = $1,500 12 $63,000 = $1,750 = 36
12 production workers ÀÇ Æò±Õ = 36 office workers ÀÇ Æò±Õ
µû¶ó¼ Æò±ÕÀÇ Â÷ÀÌ ´  $1,750 -- $1,500 = $250, : Á¤´ äÀº (C) :
12.
On a certain test, 3 students each had a score of 90, 9 students each had a score of 80, 4 students each had a score of 70, and 4 students each had a score of 60. What was the average (arithmetic mean) score for the 20 students? (A) 70.5 (B) 75.0 (C) 75.5 (D) 80.0 (E) 80.5
Combined average À» ¹ ¯´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù! Combined Average = (3 × 90) + (9 × 80) + (4 × 70) + (4 × 60) = 75.5 , 3+ 9+ 4+ 4 : Á¤´ äÀº (C) :
13. On 3 sales John has received commissions of $240, $80, and $110, and he has 1 additional sale pending. If John is to receive an average (arithmetic mean) commission of exactly $150 on the 4 sales, then the 4th commission must be. (A) $164 (B) $170 (C) $175 (D) $182 (E) $185
240 + 80 + 110 + x = $150 , ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é 4
Á¤´ äÀº (B)
:
x = $170
:
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GRE Math °-ÁÂ Set 3
14. The 10 households on a certain street have household incomes that range from $34,000 to $150,000 and an average (arithmetic mean) household income of $60,000. If the household with the highest income and the one with the lowest income are excluded, what is the average household income for the remaining 8 households? (A) $41,600 (B) $47,000 (C) $52,000 (D) $61,000 (E) $75,000
$34,000 + ( 8households) + $150,000 = $60,000 , 10 ÀÌ ½Ä¿¡ ¼ °¡ Àå ³ · Àº °ª °ú ³ ôÀº °ª À» Á¤¸ ®ÇÏ ¸ é 8 households income = $416,000, ÀÌ °ª À» ´Ù½Ã 8· Î ³ ª ´ ©¸ é $52,000. Á¤´ ä! : Á¤´ äÀº (C) :
15. The graph above shows the distribution of the 100 scores in a certain competition. What is the median score for the competition? (A) 7.5 (B) 7.75 (C) 8.0 (D) 8.25 (E) 8.5
x
median(Áß¾Ó°ª )À» ±¸ÇÒ ¶§´  º ¯· ®( n )À¸ · Î , ¿©±â¼ ´  scores, ±¸ ÇÏ ´  °Í ÀÌ ¾Æ´Ï ¶ó frequency(º óµµ) ° ª ÀÇ Áß¾Ó°ª À» ±¸ ÇÏ ´  °Í ÀÔ´ Ï ´ Ù. ¿©±â¼ frequency´  100ÀÌ°í medianÀº 50¹ ø ° °ª ÀÌ ¹ Ç· Î ÀÌ °ª À» ãÀ¸ ¸ é µË´ Ï ´ Ù. °¡ Àå Å« scoreÀÎ 10.0ÀÇ frequencyº Î ÅÍ ´ë·« °è»êÇÏ ¸ é 2(10.0) + 4(9.5) + 5(9.0) + 25(8.5) ≈ 36ÀÌ °í score 8.0ÀÇ frequency´  20ÀÌ ¹ Ç· Î 50¹ ø° frequency´  ¹ ݵå½Ã score 8.0¿¡ Á¸ ÀçÇÑ´ Ù´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. Á¤´ äÀº (C) :
:
16. A certain elevator has a safe weight limit of 2,000 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 215 pounds? (A) 7 (B) 8 (C ) 9 (D) 10 (E) 11 ¿¤¸ ®º £ÀÌ ÅÍ ¿¡ Å» ¼ö ÀÖ´  Àüü »ç¶÷¼ö¸ ¦ RÀÌ ¶ó ÇÏ ¸ é
R R 180 pounds + 215 pounds ≈ 2,000 pounds, 2 2 À§ÀÇ ½Ä¿¡ ¼ RÀÇ ÃÖ´ ë°ª Àº 10ÀÌ µÇ°ÚÁÒ.
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GRE Math °-ÁÂ Set 3
Á¤´ äÀº (D) : 17. For the month of April, the average (arithmetic mean) of the daily high temperatures recorded at a certain weather station was x degrees. If the average for the first 13 days of :
the month was ( x − 10) degrees, what was the average, in degrees, for the remaining 17 days of the month? 130 x + 17 17 x + 10 17 x + 130 (A) x + 10 (B) 17 x + 130 (C) (D) (E)
x
17
17
¿©±â¼ 17ÀÏ ÀÇ Æò±Õ ¿Âµµ¸ ¦ y ¶ó °¡ Á¤ÇÏ ¸ é ¾Æ· ¡ ÀÇ ½ÄÀ» ±¸ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù:
13( x − 10) + 17 y = x , ÀÌ ½ÄÀ» in terms of x ¿¡ ÀÇÇØ y ¸ ¦ ±¸ ÇÏ ¸ é ´ äÀ» ±¸ ÇÒ ¼ö ÀÖÁÒ. 30 Á¤´ äÀº (E)
:
:
18. A statistician calculated the average (arithmetic mean) for 20 measurements to be 50. On rechecking the calculations, the statistician found that a measurement of “78” had been treated as “18” and a measurement of “40” had been treated as “50”. If no other errors were made, what is the correct average for the 20 measurements? (A) 47.5 (B) 50.0 (C) 51.0 (D) 52.5 (E) 53.5 Åë°èÇÐÀÚ´  20° ³ ÀÇ ÃøÁ¤Ä¡ ¿¡ ´ ëÇÑ Æò±ÕÀº 50ÀÌ ¶ó°í °è»êÇß½À´ Ï ´ Ù. ° Ë»ê Áß¿¡ ÃøÁ¤Ä¡78À» 18· Î 40À» 50À¸ · Î À߸ ø °è»ê Çß´ Ù°í ÇÕ´ Ï ´ Ù.¿Ã¹ Ù¸ ¥ Æò±Õ°ª À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÃøÁ¤Ä¡ 78À» 18· Î °è»êÇßÀ¸ ¸ é +60¸ ¸ Å ÀÇ Â÷ÀÌ °¡ 40À» 50À¸ · Î °è»êÇßÀ¸ ¸ é –10¸ ¸ Å ÀÇ ¿À· ù°¡ ¹ ß»ýÇß½À´ Ï ´ Ù. µû¶ó¼ µÎ °ª ÀÇ ÇÕÀÎ 50À» 20À¸ · Î ³ ª ´ ©¾î ±× °ª 2.5À» ±âÁ¸ ¿¡ ±¸ Çß´ ø Æò±Õ °ª 50¿¡ ´ õÇÏ ¿© ÁÖ¸ é 52.5°¡ µË´ Ï ´ Ù. Á¤´ äÀº (D)ÀÔ´ Ï ´ Ù. :
:
19. If k is an integer and 15 < k < 25 , which of the following could be the average (arithmetic mean) of 12, 14, 17, 23, and k ? (A) 13.2 (B) 15.6 (C) 16.8 (D) 18.2 (E) 19.5 12, 14, 17, 23ÀÇ ÇÕÀº 66ÀÔ´ Ï ´ Ù. K°ª ÀÇ ¹ üÀ§¸ ¸ ÀÌ ÁÖ¾î Á® ÀÖÀ¸ ¹ Ç· Î Æò±Õ°ª À» ±¸ÇÏ ±â À§ÇÑ 5°³ Á¤¼ö ÇÕÀÇ ¹ üÀ§´  81(=66+15) < sum < 91(=66+25)ÀÎ °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. 81¿ Í 91À» 5· Î ³ ª ´ ©¾î Æò±ÕÀ» ±¸ Çغ ¸ ¸ é 16.2 < average < 18.2, º ¸ ±â Áß¿¡ ¼ ÀÌ ¹ üÀ§¿¡ ÇØ´ çÇÏ ´  Æò±ÕÀÇ °ª Àº 16.8»ÓÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(C)ÀÔ´ Ï ´ Ù.
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GRE Math °-ÁÂ Set 3
20. In performing a sequence of experiments, a scientist made 20 measurements. The average (arithmetic mean) of these measurements was 34. For security reasons the scientist coded the data by multiplying each of the measurements by 10 and then adding 40 to each product. What is the average of the coded measurements? (A) 1,140 (B) 380 (C) 342 (D) 57 (E) 19 20ȸ ÃøÁ¤ÀÇ Æò±Õ°ª ÀÌ 34, ±×· ¯¸ é ÃÑ ÇÕÀº
sum = 34( average) 20 ×34 = 680ÀÔ´ Ï ´ Ù. 20
¿©±â¼ °¢ measurement¿¡ 10À» °öÇß´ Ù¸ é ±× °ª Àº 680¿¡ 10À» °öÇÑ °ª 6800°ú °°½À´ Ï ´ Ù. ÀÌ ¹ ø¿¡ ´  °¢ measurement¿¡ 40¾¿ ´ õÇß´Ù¸ é ±× °ª Àº 40×20 = 800ÀÌ µÇ°í À§ÀÇ °ª 6800°ú 800À» ´ õÇÑ ÈÄ 20À¸ · Î ³ ª ´ ©¾î ÁÖ¸ é 7600 ÷ 20 = 380. ÀÌ °ª ÀÌ ¿ì ¸ ®°¡ ã´Â °ª ÀÌ ³ ׿ä. Á¤´ äÀº (B) :
:
21. The average (arithmetic mean) of n numbers is equal to
1 the sum of the n numbers. 3
1 the sum of the numbers is 15, what is the average of the n numbers? 2
If (A)
3
(B)
5
(C) 10
(D) 30
(E) 45
sum 1 1 = sum , ¿©±â¼ n Àº 3ÀÓÀ» ¾Ë ¼ö ÀÖÁÒ. ´ ٽà the sum of the numbers is n 3 2 30 = 10 15¿ ¡ ¼ the sum of number = 30, ¿©±â¼ n ÀÇ Æò±ÕÀº 3 Average =
Á¤´ äÀº (C) :
:
22. The average (arithmetic mean) of ten numbers on a list is m . If the numbers 10 and 24 are added to the list, the average (arithmetic mean) of these twelve numbers on the list is also m . What is the value of m ?
1 3
(A)
11
(E)
It cannot be determined from the information given.
(B) 14
(C) 17
(D) 20
sum sum + 34 =m= , ¿ÞÂÊ ½Ä¿¡ ¼ sumÀ» m° ª À¸ · ΠǥÇöÇÏ ¸ é 10 12 jsum
= 10m,
ksum
= 12m – 34 ⇒ 10m = 12m − 34 ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é m = 17
Á¤´ äÀº (C) :
:
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GRE Math °-ÁÂ Set 3
23. The average (arithmetic mean) price of the 5 houses on a certain street is $60,000. If the price of the least expensive house is $55,000 which of the following could NOT be the price of the most expensive house? (A) $82,000 (B) $78,000 (C) $72,000 (D) $65,000 (E) $62,500
5houses = $60,000 , ´ Ù¼¸ Áý °¡ °ÝÀÇ sumÀº $300,00ÀÔ´ Ï ´ Ù. ¿©±â¼ °¡Àå ½Ñ ÁýÀÇ °¡ °ÝÀÌ 5 $55,000À̶ó ÇßÁÒ. ³ ª ¸ ÓÁö ³ × Áý Áß °¡ Àå º ñ½Ñ ÁýÀ» Á¦ ¿ÜÇÑ ¼¼ ÁýÀÇ °¡ °ÝÀ» ÃÖÀú °¡ °ÝÀÎ $55,000ÀÌ¶ó °¡ Á¤ÇÏ ¸ é ³ × ÁýÀÇ °¡ °ÝÀº 4×$55,000 = $220,000. ´ ٽà $300,00¿ ¡ ¼ $220,000À» »©¸ é °¡ Àå º ñ½Ñ ÁýÀÇ ÃÖ´ ë°ª $80,000À» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. µû¶ó¼ ¸ ¶Áö¸ · ÁýÀº $80,000À» Àý´ ë· Î ³ Ñ¾î ¼ ´  ¾ÈµË´ Ï ´ Ù. Á¤´ äÀº (A) :
:
24. If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of z − x ? (A) 70 (B) 40 (C) 20 (E) It cannot be determined from the information given.
(D) 10
½±Áö¸ ¸ ÇÑ ¹ ø Ç®¾î º ¸ ´  °Í ÀÌ ÁÁÀº ¹ ®Á¦ ³ ׿ä . x + y y + z = 60, = 80 ⇒ x + y = 120, y + z = 160
2
2
µû¶ó¼ z − x = 40 Á¤´ äÀº (B) :
:
Mon +2
Tue
1 2
−1
1 4
Wed −
Thu
1 8
Fri +1
0
3 8
25. The table above shows the net change, in dollars, in the price of a share of a certain stock each day last week. What was the average (arithmetic mean) daily net change, in dollars, for the 5day week? (A) −
1 2
(B)
+
1 4
(C) +
1 2
(D)
+
5 4
(E) +
5 2
¾ÆÁÖ ½¬¿î ¹ ®Á¦ ÀÎ µ¥ ° ¡ ² û ÇлýµéÀÌ ½Ç¼ö¸ ¦ Çß´ø ¹ ®Á¦ ÀÔ´ Ï ´ Ù. Æò±ÕÀ» ±¸ÇÏ ´  ¹ ®Á¦ ÀÌ ¹ Ç· Î 5° ³ ÀÇ net changeÀ» ¸ ðµÎ ´ õÇÑ ÈÄ ¹ ݵå½Ã 5· Î ³ ª ´ ©¾î ÁÖ¸ é µË´ Ï ´ Ù. Á¤´ äÀº (C) :
:
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GRE Math °-ÁÂ Set 3 26. If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degree Fahrenheit, could be (A)
6 x
(B)
4 x
(C)
5 x 3
(D)
3 x 2
(E)
3 x 5
(a + b + c ) + d + e = x ⇒ ( a + b + c) + d + e = 5 x ↵ϒ…↑a + b + c ÀÇ ÃÖ´ ë° ª À» ±¸ ÇÏ ¶ó´  ¹ ®Á¦ ³ ׿ä. 5 ÀÏ ´ Ü d ¿Í e °¡ µÑ ´ Ù 0µµ(ÃÖ¼Ò°ª , ½ÇÁ¦ ÃÖ¼Ò°ª Àº 0ÀÌ µÉ ¼ö ¾øÁö¸ ¸ ´Ù¸¸ ½ÄÀ» À§ÇØ 0ÀÌ ¶ó°í °¡ Á¤ÇÔ)ÀÏ ¶§¸¦ ¿À¸ ¥ÂÊ ½Ä¿¡ (a + b + c) + d + e = 5 x ¿¡ ´ ëÀÔÇÏ ¸ é
a+b+c <
5 x À» À¯µµÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. Áï a + b + c ÀÇ ¹ üÀ§´  5 x º ¸ ´ ÙÀÛ´ Ù´  °Í À» ±¸ ÇÒ ¼ö ÀÖ´Â ¼ÀÀÌ ³ ׿ä. 5 x º ¸ ´ ÙÀÛÀ¸ ¸ é¼ °¡ Àå Å« ° ª Àº (B)ÀÔ´ Ï ´ Ù. Á¤´ äÀº (B) :
:
Score 83 70 92 64
Number of Students 5 6 3 5 1
27. The incomplete table above shows a distribution of scores for a class of 20 students. If the average (arithmetic mean) score for the class is 78, what score is missing from the table? (A) 73 (B) 75 (C) 77 (D) 79 (E) 81 20 students × 78( average) = 15×60 = 83×5 + 70×6 + 92×3 + x ×5 + 64×1 5 x = 385 → x = 77 Á¤´ äÀº (C) :
:
28. If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true? I. x is an even integer. II. x is a nonzero integer. III. x is a multiple of 5. (A) I only (B) III only (C) I and II only (D) I and III only (E) I, II, and III °¡ Àå ÀÛÀº even integerÀ» n ÀÌ ¶ó ÇÏ ¸ é x = n + (n + 2) + (n + 4) + (n + 6) + (n + 8) = n + 4 5 Áï x = n + 4 , ¿©±â¼ n Àº Ç×»ó ¦ ¼öÀÌ ¹ Ç· Î “¦ ¼ö + ¦ ¼ö = ¦ ¼ö”ÀÌ ¹ Ç· Î I Àº Ç×»ó trueÀÔ´ Ï ´ Ù. II¿¡ ¼ ´  n = -4ÀÌ ¸ é falseÀÔ´ Ï ´ Ù. Á¤´ äÀº (A) :
:
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GRE Math °-ÁÂ Set 3
29. The average (arithmetic mean) of 4 positive integers is 50. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have? (A) 55 (B) 65 (C) 100 (D) 109 (E) 115 4°³ ÀÇ ¾çÀÇ Á¤¼öÀÇ Æò±ÕÀÌ 50À̸é ÇÕÀº 200ÀÔ´ Ï ´ Ù. ±× Áß¿ ¡ µÎ Á¤¼öÀÇ Æò±ÕÀÌ 45ÀÌ ¹ Ç· Î ÀÌ µÎ Á¤¼öÀÇ ÇÕÀº 90ÀÌ µÇ³ ׿ä . Àüü ÇÕ 200¿¡ ¼ 90À» »©¸ é 110ÀÌ µÇ°í ³ ª ¸ ÓÁö µÎ Á¤¼ö Áß¿¡ ¼ ÃÖ´ ë°ª Àº ¸ ðµç Á¤¼ö°¡ 0ÀÌ ¾Æ´Ñ Á¤¼ö¶ó ÇßÀ¸ ¹ Ç· Î ³ ª ¸ ÓÁö Á¤¼ö°¡ 1ÀÎ °æ¿ì ÃÖ´ ë° ª ÀÌ µÇÁÒ. µû¶ó¼ 110 − 1 = 109 ÿ Á¤´ äÀº
(D)
30. The trade name for a product has 6 letters , and the length of the package for the product is l centimeters. The trade name of the product is printed lengthwise on one side of the package with a margin of m centimeters on each end of the side. If the space between each letter is considered negligible, what is the average (arithmetic mean) width, in centimeters, of each letter in the trade name? (A) l − 2m (B) l − m (C) l ÷ 8 (D) (l − m) ÷ 6 (E) (l − 2m) ÷ 6 m
m
l °¢ ±ÛÀÚÀÇ Æò±Õ width = ( l − 2m ) ÷ 6 ÿ Á¤´ äÀº (E)
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- ÁÂ Set 4 GRE Math °
Chapter 4 Rati o, Pr oporti on, and F r action
1.
A certain club has 35 male members and 45 female members. Which of the following equals the ratio of the number of male members to the number of female members? (A) 7 :16 (B) 5 : 9 (C) 5 : 7 (D) 3 : 4 (E) 7 : 9
2. What is the ratio of
3 to the product 4
3 4 ? 4
answer
answer
1 4 1 (B) 3 4 (C) 9 9 (D) 4 (A)
(E) 4
3.
If
2 of the 210 students in a class attended graduate school, what was the total number of 7
students in the class who did not attend graduate school? (A) 42 (B) 60 (C) 105 (D) 142 (E) 150
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- ÁÂ Set 4 GRE Math °
4.
A certain test consists of 8 sections with 25 questions numbered from 1 to 25, in each section.
3 If a student answered all of the even-numbered questions correctly and of the odd4
answer
numbered questions correctly, what was the total number of questions he answered correctly? (A) 150 (B) 172 (C) 174 (D) 175 (E) 176
5.
Two cities that are geographically 380 miles apart are 2 inches apart on a certain map. If the map is drawn to scale, how many miles apart are two cities that are 7
1 inches apart on 2
answer
the map? (A) 665 (B) 1,330 (C) 1,425 (D) 2,090 (E) 2,850
6.
Lou and Selma were hired to paint a room for a total of $72. They completed the job with Lou working 3 hours and 20 minutes and Selma working 2 hours and 40 minutes. If they decided to split the $72 in proportion to the amount of time each spent on the job, how much did Lou receive? (A) $32.00 (B) $36.00 (C) $40.00 (D) $41.14 (E) $43.20
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7.
Kathy bought 4 times as many shares in Company X as Carl, and Carl bought 3 times as many shares in the same company as Tom. Which of the following is the ratio of the numbers of shares bought by Kathy to the number of shares bought by Tom? (A) (B) (C) (D) (E)
answer
3 4 4 3 3 1 4 1 12 1
7 agreed to participate. If 60 8 4 questionnaires were sent to each of the participating schools and of these questionnaires 5
8. Of the 40 schools invited to participate in a research study,
answer
were completed and returned, what was the total number of questionnaires completed and returned? (A) 28 (B) 1,344 (C) 1,680 (D) 1,920 (E) 2,100
9. If a printer can 2 pages of text per second, then, at this rate, approximately how many minutes will it take to print 5,000 pages of text? (A) 4 (B) 25 (C) 42 (D) 250 (E) 417
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10. If $160 is divided among 3 people in the ratio 3 : 5 : 8 , what is the least amount received by any one person? (A) $80 (B) $50 (C) $30 (D) $20 (E) $10
11. Which three of the following fractions are equivalent?
v=
answer
answer
5 0. 05 0 .5 0.05 0.05 , w= , x = , y = , z = 80 0. 08 8.0 0.8 0.008
v , w , and x v , x , and y w , x , and y (D) w , y , and z (E) x , y , and z (A) (B) (C)
12. A study based on a random sample revealed that, on average, 2 out of 5 adults have high blood pressure. If these results hold true for the 580,000 adults in City A , approximately how many adults in City A have high blood pressure? (A) 116,000 (B) 145,000 (C) 232,000 (D) 250,000 (E) 290,000
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13. Two boxes of pudding mix cost a total of $0.73 and 1 box of cake mix costs twice as much as two boxes of pudding mix. At these rates, what is the cost of 3 boxes of pudding mix and 3 boxes of cake mix? (A) $1.10 (B) $3.29 (C) $4.38 (D) $5.48 (E) $6.57
14. Out of their annual net income, a couple spent 25 percent for food, 13.5 percent for entertainment, 20 percent for housing, 8 percent for car expenses, 15 percent for clothing, and saved the rest. What was the ratio of the amount saved to the amount spent for entertainment? (A) (B) (C) (D) (E)
answer
19 27 6 5 37 27 19 9 7 3
15. Approximately how many minutes will it take a secretary who types at an average rate of 60 words per minute to type a 5-page report with 250 words per page? (A) 4 (B) 12 (C) 21 (D) 30 (E) 75
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answer
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16. If the speed of an airplane is 360 kilometers per hour, how many meters will it travel in one second? (1 kilometer = 1,000 meters) (A) 100 (B) 360 (C) 1,000 (D) 3,600 (E) 6,000
answer
17. The total time required to transport rail freight from City X to City Y is 4 days, 15 hours. If, by eliminating certain intermediate stops, the total time were reduced by
answer
1 , the total 3
transport time required would be
1 3
(A)
1 day, 5 hours
(B)
1 day, 13 hours
(C)
2 days, 10
2 hours 3 2 2 days, 15 hours 3
(D) (E)
3 days, 2 hours
18. A small firm spent spent
1 of its annual budget during the first 2 months of its fiscal year and 4
1 of its remaining budget during the next 5 months. What fraction of the annual 2
budget remained unspent at the end of the first 7 months? (A) (B) (C) (D) (E)
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3 16 1 4 5 16 3 8 5 12
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19. Members of a social club met to address 280 newsletters. If they addressed newsletters during the first hour and
1 of the 4
answer
2 of the remaining newsletters during the second hour, 5
how many newsletters did they address during the second hour? (A) 28 (B) 42 (C) 63 (D) 84 (E) 112
20. In a certain used-car lot, there are 4 times as many blue cars as green cars and
1 as many 3
answer
green cars as red cars. If there are 4q red cars in the lot, how many blue cars are in the lot? (A) 12q (B)
16q
3 (C) 3q 4q (D) 3 3q (E) 4
21. When Inez and Fernando purchased a property for $20,000. Fernando contributed
1 the 3
amount contributed by Inez for the purchase. If they sold the property for $40,000 and shared this amount in proportion to their respective contributions, how much was Fernando’ s share? (A) $5,000 (B) $10,000 (C) $13,333 (D) $20,000 (E) $26,666
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22. Of Amy’s monthly salary,
1 1 goes to rent and to food. If the remainder of her monthly 4 5
answer
salary amounts to $990, what is Amy’ s monthly salary? (A) $1,042 (B) $1,273 (C) $1,800 (D) $1,980 (E) $2,200
23. When
2 3 of the votes on a certain resolution have been counted, of those counted are in 9 4
answer
favor of the resolution. What fraction of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution? (A) (B) (C) (D) (E)
11 14 13 18 4 7 3 7 3 14
24. In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is (A) 1 to 2 (B) 1 to 3 (C) 1 to 4 (D) 2 to 3 (E) 3 to 4
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25. Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year? (A) (B) (C) (D) (E)
answer
1 4 4 15 1 3 4 11 4 5
1 2
26. Millie and Rick addressed 150 invitations. If Millie addressed 1 times as many as Rick
answer
addressed, how many of the invitations did Rick address? (A) 30 (B) 60 (C) 75 (D) 90 (E) 100
27. In 1990 a total of x earthquakes occurred worldwide, some but not all of which occurred in Asia. If m of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did not occur in Asia? (A) (B) (C) (D) (E)
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x m m x m x − m x x − m m 1− x
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28. The ratio of two quantities is 3 to 4. If each of the quantities is increased by 5, what is the ratio of these two new quantities?
answer
3 4 8 (B) 9 18 (C) 19 23 (D) 24 (A)
(E) It cannot be determined from the information given.
29. Of the people who responded to a market survey, 120 preferred Brand X and the rest preferred Brand Y . If the respondents indicated a preference for Brand X over Brand Y by a ratio of 3 to 1, how many people responded to the survey? (A) 80 (B) 160 (C) 240 (D) 360 (E) 480
30. Orange juice of normal strength is prepared by adding three 6-ounce cans of water to the contents of a 6-ounce can of orange juice concentrate. If 1 ounce of the can of concentrate was already used for some other purpose, how many 6-ounce cans of water should be added to the remainder of the concentrate to prepare juice of normal strength? (A) 1
2 3
(B) 2
1 3 1 (D) 2 2 5 (E) 2 6 (C) 2
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31. A coffee merchant makes a house blend of coffee using 4 pounds of Arabian beans costing $3 per pound, 2 pounds of Java beans costing $4 per pound, and 4 pounds of Brazilian beans costing $1 per pound. If the merchant sold all of the blend for 50 percent more than the total cost of the beans used, at what price per pound was the blend sold? (A) $1.20 (B) $2.40 (C) $3.00 (D) $3.60 (E) $4.50
32. The current ratio of men to women on a certain board of trustees is 2 to 5. If 4 men were added to the board, the ratio of men to women would be 2 to 3. How many men are currently on the board? (A) 2 (B) 4 (C) 5 (D) 6 (E) 8
33. A custom blend of paint is made by mixing red, yellow, and black paints in the ratio of 12 to 11 to 1. If all of the paints are sold only in pint-sized containers, how many containers of yellow are used in preparing 6 gallons of the blend? (8 pints = 1 gallon) (A) 2 (B) 3 (C) 11 (D) 22 (E) 24
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34. A rectangular office floor is 28 meters by 20 meters. A custodian, working at a constant rate, waxes a section of the floor that is 5 meters by 20 meters in
answer
3 hour. How many hours does 4
it take the custodian, working at this same constant rate, to wax the entire floor? (A) 2.52 (B) 3 (C) 3.45 (D) 4.2 (E) 7
35. A glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution. If 45 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container? (A) 3.00 (B) 5.00 (C) 5.50 (D) 6.50 (E) 6.75
36. Dan bought x pencils, some at 10 cents each and the rest at 6 cents each. For the same amount of money that he spent on these pencils, he could have bought x pencils at 9 cents each. What is the ratio of the number of 10-cent pencils purchased to the number of 6-cent pencils purchased? (A) 1 : 1 (B) 2 : 1 (C) 3 : 1 (D) 4 : 1 (E) 5 : 1
37. A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half-gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture? (A) 2
1 2
(B)
2
(C)
3
(D)
3
(E)
4
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1 2
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answer
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38. Working alone, printers X , Y , and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates? (A) (B) (C) (D) (E)
4 11 1 2 15 22 22 15 11 4
39. The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? (A) 50 (B) 200 (C) 400 (D) 625 (E) 800
40. Tom and Carlos begin to play a series of four games with 400 chips each. At the end of each game, there is a loser who must surrender half of his chips to the winner. If Tom wins only the first and third games, how many chips does he have after the pay-off at the end of the fourth game? (A) 200 (B) 275 (C) 400 (D) 525 (E) 550
STOP
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¼öÇÐÇؼ³
1.
Category 4 Ratio and Proportion
A certain club has 35 male members and 45 female members. Which of the following equals the ratio of the number of male members to the number of female members? (A) 7 :16 (B) 5 : 9 (C) 5 : 7 (D) 3 : 4 (E) 7 : 9
35 : 45 = 5 ×7: 5 ×9 = 5 × 7 = 7 = 7 : 9 5× 9 9 Á¤´ äÀº (E)
:
:
2. What is the ratio of (A)
3 3 to the product 4 ? 4 4
1 4
1 3 4 (C) 9 9 (D) 4 (B)
(E) 4
3 1 3 : 4 = 1: 4 = 4 4 4 Á¤´ äÀº (A)
:
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3. If
2 of the 210 students in a class attended graduate school, what was the total number of 7
students in the class who did not attend graduate school? (A) 42 (B) 60 (C) 105 (D)
142
(E)
150
210 ¸ í Áß¿¡ 2/7 °¡ ´ ëÇпø¿¡ ´ Ù³ æ´ Ù¸ é, 5/7 Àº ´ ëÇпø¿¡ ´ Ù´ Ï Áö ¾ÊÀº »ç¶÷ÀÌ ³ ׿ä. µû¶ó¼ 210 ×
5 = 150, 7
Á¤´ äÀº (E)
:
:
4. A certain test consists of 8 sections with 25 questions numbered from 1 to 25, in each section. If a
student answered all of the even-numbered questions correctly and
3 of the odd4
numbered questions correctly, what was the total number of questions he answered correctly? (A) 150 (B) 172 (C) 174 (D) 175 (E) 176 25 ¹ ®Á¦ · Î 8 °³ ÀÇ sections À¸·Î ±¸ ¼º µÈ ½ÃÇè¿¡ ¼ ÇÑ ÇлýÀÌ Â¦ ¼ö ¹ ®Á¦ ´  ¸ ðµÎ ¸ ÂÃß¾ú°í , Ȧ ¼ö ¹ ®Á¦ ´  3/4 ¸ ÂÃß¾ú´Ù¸ é ÃÑ ¸ ÂÀº ¹ ®Á¦ ¼ö°¡ ¸ î °³ ÀÎ °¡ ¸ ¦ ¹ ¯´  ¹ ®Á¦ ³ ׿ä . ÀÏ ´ Ü 25 ¹ ®Á¦ ¿¡ ¼ ¦ ¼ö ¹ ®Á¦ ¼ö´  12 ¹ ®Á¦ ÀÌ °í ÀÌ °Í ÀÌ 8sections ÀÌ ´ Ï ±î 8 À» °öÇÏ ¸ é 96 À» ±¸ ÇÒ ¼ö ÀÖ³ ׿ä . ¸ ¶ Âù°¡ Áö ¹ æ¹ ýÀ¸ · ΠȦ ¼ö ¹ ®Á¦ ´  13 × 8 = 104 ¹ ®Á¦ ³ ׿ä . ¦ ¼ö ¹ ®Á¦ ´  ´ Ù ¸ ÂÇûÀ¸ ´ Ï ±î 96, Ȧ ¼ö¹® Á¦ ´  104 ×
3 = 78 ¹ ®Á¦ , ÀÌ µÑÀ» ÇÕÄ¡ ¸ é 96 + 78 = 174 ÀÔ´ Ï ´ Ù. 4
Á¤´ äÀº (C)
:
:
5. Two cities that are geographically 380 miles apart are 2 inches apart on a certain map. If the map is drawn to scale, how many miles apart are two cities that are 7
1 inches apart on the 2
map? (A) 665 (B) 1,330 (C) 1,425 (D) 2,090 (E) 2,850 Proportion À» ¹ ¯´  ¹ ®Á¦ ³ ׿ä. A : B = C : D ⇒ AD = BC, ¶Ç´  A = C B D 380 miles : 2 inches = X : 7 Á¤´ äÀº (C)
:
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1 inches , ¿ÞÂÊÀÇ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é X = 1,425 ÀÔ´ Ï ´ Ù. 2
:
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6. Lou and Selma were hired to paint a room for a total of $72. They completed the job with Lou working 3 hours and 20 minutes and Selma working 2 hours and 40 minutes. If they decided to split the $72 in proportion to the amount of time each spent on the job, how much did Lou receive? (A) $32.00 (B) $36.00 (C) $40.00 (D) $41.14 (E) $43.20 LouÀº 3½Ã°£ 20º Ð = 200º Ð , SelmaÀº 2½Ã°£ 40º Ð = 160º Ð µÑÀÇ ½Ã°£¿¡ ¼ Lou ° ¡ Â÷ÁöÇÏ ´  º ñÀ² Àº
200 5 , ¿©±â¿¡ µÑÀÌ ³ ª ´ ©±â· Î ÇÑ µ· $72À» °öÇÏ = 360 9
¸ é LouÀÇ ¸ òÀÌ ³ ª ¿À³ ׿ä 5 × $72 = $40 , 9 : Á¤´ äÀº (C) :
7. Kathy bought 4 times as many shares in Company X as Carl, and Carl bought 3 times as many shares in the same company as Tom. Which of the following is the ratio of the numbers of shares bought by Kathy to the number of shares bought by Tom? (A)
3 4
(B)
4 3
(C)
3 1
(D)
4 1
(E)
12 1
jKathy
ÀÇ Áֽļö = 4 Carl, kCarl = 3 Tom k ½ÄÀ» j ¿¡ ´ ëÀÔÇÏ ¸ é Kathy = 12 Tom ½ÄÀ» ¸ ¸ µé ¼ö ÀÖ³ ׿ä. µû¶ó¼ ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é Kathy : Tom = 12 : 1 ÀÔ´ Ï ´ Ù. : Á¤´ äÀº (E) :
7 agreed to participate. If 60 8 4 questionnaires were sent to each of the participating schools and of these questionnaires 5
8. Of the 40 schools invited to participate in a research study,
were completed and returned, what was the total number of questionnaires completed and returned? (A) 28 (B) 1,344 (C) 1,680 (D) 1,920 (E) 2,100
7 7 ÀÌ research study ¿¡ Âü°¡ ÇÏ ±â· Î Çß´ Ù :40× = 35 Çб³ 8 8 4 4 Âü°¡ Çб³ ¿¡ 60 ¹ ®Á¦ °¡ º ¸ ³ »Á³ ´ µ¥ ÀÇ ¹ ®Á¦ ¸ ¸ ÀÛ¼º µÇ¾î ¼ µ¹ ¾Æ¿È : 60 × =48 5 5 40° ³ Çб³ Áß¿¡ ¼
¹ ®Á¦ ´  40° ³ Çб³ ¿¡ ¼ completed µ¹ ¾Æ¿Â ÃÑ ¹ ®Á¦ ÀÇ ¼ö¸ ¦ ¹ ¯´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. Áï (35 Çб³ × 48) = 1,680, : Á¤´ äÀº (C) :
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9. If a printer can 2 pages of text per second, then, at this rate, approximately how many minutes will it take to print 5,000 pages of text? (A) 4 (B) 25 (C) 42 (D) 250 (E) 417 2 pages : 1 second = 5,000 pages : X À§ÀÇ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é X= 2,500 seconds ÀÌ ³ ׿ä. ´ ٽà secondÀ» minute ´ ÜÀ§· Î ¹ Ù² Ù¸ é 2,500÷60 ≅ 42 minutes ÀÔ´ Ï ´ Ù. : Á¤´ äÀº (C) :
10. If $160 is divided among 3 people in the ratio 3 : 5 : 8 , what is the least amount received by any one person? (A) $80 (B) $50 (C) $30 (D) $20 (E) $10 $160ÀÌ ¼¼ »ç¶÷¿¡ °Ô
3 5 8 , , °¢° ¢ ³ ª ´ ©¾î Áú ¶§, ´ ©°¡ ¾ó¸ ¶ÀÇ °¡ Àå ÀûÀº µ·À» ¹ Þ 16(= 3 + 5 + 8) 16 16
´ ÂÁö¸ ¦ °è »êÇÏ ´  ¹ ®Á¦ ³ ׿ä . ¼¼ º мö Áß¿¡ ¼ 3/16ÀÌ Á¦ ÀÏ ÀÛÀ¸ ´ Ï ±î (3/16) ×$160 = $30 : Á¤´ äÀº ( C ) :
11. Which three of the following fractions are equivalent?
v=
5 0. 05 0 .5 0.05 0.05 , w= , x = , y = , z = 80 0. 08 8.0 0.8 0.008
v , w , and x v , x , and y (C) w , x , and y (D) w , y , and z (E) x , y , and z (A) (B)
Çؼ³ ÀÌ ÇÊ¿ä ¾ø´  ¹ ®Á¦ ÀÌ ³ ׿ä . °¡ ² ûÀº ÀÌ · ± ¹ ®Á¦ µµ ½ÇÁ¦ ½ÃÇè¿¡ ¼ ³ ª ¿É´ Ï ´ Ù. ÇÏ Áö¸¸ 37¹ ®Á¦ Áß¿¡ 2 ~ 3 ° ³ Á¤µµ ³ ª ¿À´ Ï ±î ÀÌ · ± ¹ ®Á¦ ¸ ¦ º ¸ °í ¼öÇÐÀÌ ½±´Ù°í ¸ »ÇÏ ¸ é ¾ÈµÇÁÒ! v , x , and y ÀÇ fractionsÀ» Á¤¸ ®ÇÏ ¸ é ¸ ðµÎ 0.0625 ÀÇ °ª ÀÌ ³ ª ¿À³ ׿ä. Á¤´ äÀº (B)
:
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12. A study based on a random sample revealed that, on average, 2 out of 5 adults have high blood pressure. If these results hold true for the 580,000 adults in City A , approximately how many adults in City A have high blood pressure? (A) 116,000 (B) 145,000 (C) 232,000 (D) 250,000 (E) 290,000 5
¸í
Áß¿¡
2¸ í ÀÌ
°í Ç÷¾ÐÀ»
°Þ°í
ÀÖ´ µ¥,
ÀÌ °Í À»
580,000¸ í ¿¡ °Ô
Àû¿ë½ÃÅ°¸ é
2 × 580,000 = 232,000 , 5
Á¤´ äÀº (C)
:
:
13. Two boxes of pudding mix cost a total of $0.73 and 1 box of cake mix costs twice as much as two boxes of pudding mix. At these rates, what is the cost of 3 boxes of pudding mix and 3 boxes of cake mix? (A) $1.10 (B) $3.29 (C) $4.38 (D) $5.48 (E) $6.57 Two boxes of pudding mix = $0.73 ⇒ one box of pudding mix = $0.3650 1 box of cake mix = 2($0.73) = $1.46 µû¶ó¼ 3 boxes of pudding mix = 3 ×$0.3650 = $1.0950, 3 boxes of cake mix = 3×$1.46 = $4.38 µÎ °ª À» ÇÕÇÏ ¸ é $5.48, : Á¤´ äÀº (D) :
14. Out of their annual net income, a couple spent 25 percent for food, 13.5 percent for entertainment, 20 percent for housing, 8 percent for car expenses, 15 percent for clothing, and saved the rest. What was the ratio of the amount saved to the amount spent for entertainment? (A)
19 27
(B)
6 5
(C)
37 27
(D)
19 9
(E)
7 3
Income Áß¿¡ ¼ 25% + 13.% + 20% + 8% + 15% = 81.5% À» ¾² °í ³ ª ¸ ÓÁö 18.5%´  ÀúÃàÇÏ ´ µ¥ , ÀúÃà ÆÛ¼¾Æ®¿Í entertainment¿¡ ¾´ µ· ÀÇ ratio À» ±¸ÇÏ ´  ¹ ®Á¦ ³ ׿ä . 18.5%: 13.5% = 0. 185 = 37 0. 135 27 : Á¤´ äÀº (C) :
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- ÁÂ Set 4 GRE Math °
15. Approximately how many minutes will it take a secretary who types at an average rate of 60 words per minute to type a 5-page report with 250 words per page? (A) 4 (B) 12 (C) 21 (D) 30 (E) 75 1º п¡ 60 words À» Ä¡ ´  º ñ¼ °¡ 1,250 words ( 250 × 5 pages) Ä¡ ´ µ¥ ¾ó¸ ¶³ ª °É¸ ®´ °¡ ¸ ¦ ¹ ¯´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù.´ Ù.60 = X : 1,250 ¿¡ ¼ X = 20. 8333 ÀÇ ±Ù»çÄ¡ ´  21, : Á¤´ äÀº (C) :
16 If the speed of an airplane is 360 kilometers per hour, how many meters will it travel in one second? (1 kilometer = 1,000 meters) (A) 100 (B) 360 (C) 1,000 (D) 3,600 (E) 6,000 ÀÏ´ Ü 360 kilometersÀ» meters· Î ¹ Ù² Ù¸ é 360×1,000 = 360,000 meters 1 hours À» one secondÀ¸ · Î ¹ Ù² Ù¸ é 1 ×60 × 60 = 3600 seconds 360,000 metersÀ» 3600 seconds· Î ³ ª ´ ©¸ é 1ÃÊ¿¡ °¡ ´  °Å¸ ®°¡ 100 meters°¡ ³ ª ¿É´ Ï ´ Ù. : Á¤´ äÀº ( A ) :
17. The total time required to transport rail freight from City X to City Y is 4 days, 15 hours. If, by eliminating certain intermediate stops, the total time were reduced by
1 , the total 3
transport time required would be
1 3
(A)
1 day, 5 hours
(B)
1 day, 13 hours
(C)
2 days, 10
(D) (E)
2 hours 3 2 2 days, 15 hours 3 3 days, 2 hours
2 1 1 ¸ ¸ Å °¨ ¼Ò Ç߱⠶§¹ ®¿¡ (be reduced by ) ÀÌ Á¦ ¸ ¸ Å Àǽð£ÀÌ ¼Ò¿äµË´ Ï ´ Ù. 3 3 3 2 111(hours ) × = 74(hours) 3
½Ã°£ÀÌ
( 4 days, 15 hoursÀº 111½Ã°£ ÀÔ´ Ï ´ Ù. ) ÿ
´ äÀº (E)ÀÔ´ Ï ´ Ù.
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1 of its annual budget during the first 2 months of its fiscal year and 4
18. A small firm spent spent
1 of its remaining budget during the next 5 months. What fraction of the annual 2
budget remained unspent at the end of the first 7 months? (A)
3 16
(B)
1 4
5 16
(C)
(D)
3 8
(E)
5 12
3 ÀÌ ³ ² °Ü Á³ À¸ ¸ ç , ±× ÈÄ 5°³ ¿ù µ¿¾È 4 1 3 ³ ² °ÜÁø ¿¹ »êÀÇ ¸ ¸ Å ÀÌ ÁýÇà µÇ¾úÀ¸ ¹ Ç· Î ¹ Ì ÁýÇàµÈ ¿¹ »êÀº . ÀÔ´ Ï ´ Ù 2 8 »õ·Î¿î ȸ °è¿¬µµ°¡ ½ÃÀÛÇÏ ¿© 2°³ ¿ùÀÌ Áö³ ÈÄ ¿¹ »êÀÇ
´ äÀº (D)ÀÔ´ Ï ´ Ù.
:
:
19. Members of a social club met to address 280 newsletters. If they addressed newsletters during the first hour and
1 of the 4
2 of the remaining newsletters during the second hour, 5
how many newsletters did they address during the second hour? (A) 28 (B) 42 (C) 63 (D) 84
(E) 112
2 3 × . ÀÌ Áß °¡ µÎ 280 ÀÔ´ Ï ´ Ù 5 4
ÇÑ ½Ã°£µ¿¾ÈÀÇ ÀÛ¾÷ ÈÄ¿¡ ³ ² Àº ȸ º ¸ ´  210Àå =
¹ ø° ÇÑ ½Ã
°£µ¿¾È¿¡ ÀÛ¾÷ÀÌ ÀÌ · ç¾î Áø ° Í ÀÔ´ Ï ´ Ù. : ´ äÀº (D)ÀÔ´ Ï ´ Ù. :
20. In a certain used-car lot, there are 4 times as many blue cars as green cars and
1 as many 3
green cars as red cars. If there are 4q red cars in the lot, how many blue cars are in the lot? (A) 12q
(B)
16q 3
(C) 3q
ÆĶõ»ö Â÷°¡ ³ ì »ö Â÷º ¸ ´ Ù 4¹ è° ¡ ¸ ¹ °í ³ ì »öÂ÷ÀÇ
(D)
4q 3
(E)
3q 4
1 ¸ ¸ Å ÀÌ º ÓÀº »ö Â÷¶ó°í ÇÕ´ Ï ´ Ù.(º ÓÀº »ö Â÷ 3
°¡ ³ ì »öÂ÷º ¸ ´ Ù 3¹ è°¡ ¸ ¹ ´ Ù´  Àǹ Ì ÀÔ´ Ï ´ Ù.) »ö»ó¿¡ µû¸¥ ÀÚµ¿Â÷µé° £¿¡ º ñÀ² À» ±¸ ÇÏ ¸ é “ÆĶõ»ö : ³ ì »ö : º ÓÀº »ö = 4 : 1 : 3” ÀÔ´ Ï ´ Ù. µû¶ó ¼ ÆĶõ»ö ÀÚµ¿Â÷ ´ ë º ÓÀº »ö ÀÚµ¿Â÷°£¿¡ º ñÀ² Àº 4:3ÀÔ´ Ï ´ Ù. ´ äÀº (B)ÀÔ´ Ï ´ Ù. :
:
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21. When Inez and Fernando purchased a property for $20,000. Fernando contributed
1 the 3
amount contributed by Inez for the purchase. If they sold the property for $40,000 and shared this amount in proportion to their respective contributions, how much was Fernando’ s share? (A) $5,000 (B) $10,000 (C) $13,333 (D) $20,000 (E) $26,666 Inez¿Í Fernando´  $20,000¿¡ º Î µ¿»êÀ» ±¸ ÀÔÇß´Ù°í ÇÕ´ Ï ´ Ù. º Î µ¿»ê ±¸ ÀÔÀ» À§ÇÏ ¿©Fernando´  Inez° ¡ Áö±ÞÇÑ µ· ÀÇ
1 ¸ ¸ Å À»Áöº Ò Çß´ Ù°í ÇÕ´ Ï ´ Ù. ÀÌ º Î µ¿»êÀ» $40,000¿¡ ÆȾÒÀ» ¶§, ±¸ ÀÔ 3
½Ã ±â¿©ÇÑ º ñÀ² ¸ ¸ Å ÀÇ µ· À» °¢ »ç¶÷¿¡ °Ô º й èÇÏ ¸ é Fernando° ¡ ¹ Þ°Ô µÉ ±Ý¾×À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. Fernando´  Inez°¡ Áö±ÞÇÑ µ· ÀÇ
1 ¸ ¸ Å À» ÁöºÒ Çß´Ù°í ÇßÀ¸ ¹ Ç· Î , Inez´  Fernando°¡ Áö±ÞÇÑ 3
µ·ÀÇ 3¹ è¸ ¦ Áö±ÞÇÑ °Í ÀÔ´ Ï ´ Ù. µû¶ó¼ Fernando¿Í Inez°¡ Áöº ÒÇÑ ±Ý¾×ÀÇ º ñÀ² Àº Fernando : Inez = 1 : 3ÀÇ º ñÀ² ÀÌ µË´ Ï ´ Ù. $40,000À» ¹ Þ°í º Î µ¿»êÀ» ÆȾҴ Ù°í ÇßÀ¸ ¹ Ç· Î ÀÌ µ·À» 4µî º ÐÇÏ ¿© Fernando´  1º Î º Ð ¸ ¸ Å ÀÇ µ· À» °®°Ô µË´ Ï ´ Ù. ½ÄÀ» ¼¼¿ö¼ ¹ ®Á¦ ¸ ¦ Ç® ¼ö µµ ÀÖ°ÚÁö¸ ¸ percent, ratio ¿Í °ü· ÃµÈ ¹ ®Á¦ µéÀº ¹ ®Á¦ ¸ ¦ ÀÐ¾î °¡ ¸ é¼ Æ÷ÀÎ Æ®¸ ¦ ÆľÇÇØ °¡ ´  ÈÆ· ÃÀ» ½×¾Æ°¡ ´  °Í ÀÌ ÁÁ½À´ Ï ´ Ù. : ´ äÀº (B)ÀÔ´ Ï ´ Ù. :
22. Of Amy’s monthly salary,
1 1 goes to rent and to food. If the remainder of her monthly 4 5
salary amounts to $990, what is Amy’ s monthly salary? (A) $1,042 (B) $1,273 (C) $1,800 (D) $1,980 (E) $2,200 ¿ù±ÞÀÇ
1 1 Àº rent º ñ¿ëÀ¸ · Î , Àº ½Ä· áÇ° ±¸ÀÔÀ» À§ÇØ »ç¿ëÇÑ ÈÄ ³ ² ´  ±Þ¿©´  $990ÀÌ ¶ó°í ÇÕ 4 5
´ Ï ´ Ù. ÀÌ ¶§ ¿ ù±ÞÀÇ ¾×¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. Àüü ¿ù±Þ¿¡ ¼
9 1 1 11 ¿¡ ÇØ´ çÇÏ ´  ±Ý¾×ÀÌ $990ÀÔ = + ¸ ¸ Å À»»ç¿ëÇÏ °í ³ ² ´  ¿ù±ÞÀÇ 20 4 5 20
20 × $990 ÀÔ´ Ï ´ Ù . 11
´ Ï ´ Ù. µû¶ó¼ ¿ù±ÞÀº $1,800 = ´ äÀº (C)ÀÔ´ Ï ´ Ù :
:
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23. When
2 3 of the votes on a certain resolution have been counted, of those counted are in 9 4
favor of the resolution. What fraction of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution? (A) (B) (C) (D) (E)
°³ Ç¥°¡
11 14 13 18 4 7 3 7 3 14 2 3 . ¹ Ý´ ë ´ ë Âù¼º ÀÇ º ñÀ² ÀÌ 2 : 1ÀÌ µÇ ¸ ¸ Å ÀÌ · ç¾î Á³ À» ¶§, Âù¼º Ç¥°¡ ÀÌ ¾ú½À´ Ï ´ Ù 9 4
±â À§Çؼ ´  ¹ Ì °³ Ç¥µÈ Ç¥ Áß ¾ó¸ ¶° ¡ ¹ Ý´ ëÇ¥¿©¾ß ÇÏ ´ ÂÁö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.
3 ÀÌ ¾úÀ¸ ¹ Ç· Î ¹ Ý´ ëÇ¥´  Àüü ÅõÇ¥ÀÇ 4 1 2 1 12 . ¹ Ý´ ë ´ ë Âù¼º ÀÇ º ñÀ² ÀÌ 2:1À̱â À§Çؼ ´  ÀüüǥÀÇ °¡ ¹ Ý´ ëÇ¥ÀÌ ¸ é = × ÀÔ´ Ï ´ Ù 18 9 4 18 7 11 µË´ Ï ´ Ù. µû¶ó¼ ´ ÙÀ½ÀÇ ½Ä¿¡ ¼ x ¸ ¦ ±¸ ÇØ ÁÖ¸ é µË´ Ï ´ Ù. × x = 9 18 Àüü ÅõÇ¥ÀÇ
:
2 °¡ °³ Ç¥ µÇ¾úÀ» ¶§ Âù¼º Ç¥°¡ 9
´ äÀº (A)ÀÔ´ Ï ´ Ù
:
24. In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is (A) 1 to 2 (B) 1 to 3 (C) 1 to 4 (D) 2 to 3 (E) 3 to 4 Àǹ Ì ¸ ¸ Á¤È®È÷ ÆľÇÇÏ ¸ é ½¬¿î ¹ ®Á¦ ÀÔ´ Ï ´ Ù. 21¼¼ ÀÌ ÇÏ ÀÇ »ç¶÷ÀÌ (people aged twenty-one or underÀÌ · ± Ç¥ÇöµéÀ» Àß ±â¾ï ÇØ µÎ¸é ÁÁ½À´ Ï ´ Ù.) 22¼¼ ÀÌ »óÀÇ »ç¶÷ÀÇ(people over twenty-one – 21¼¼ ´  Æ÷ÇÔµÇÁö ¾Ê½À´ Ï ´ Ù.) 3¹ è¶ó°í ÇÕ´ Ï ´ Ù. 21¼¼ ÀÌ ÇÏ »ç¶÷ ´ ëº ñ Àüü ÀÎ ¿øº ñÀ² Àº 3 : 4°¡ µË´Ï ´ Ù. : ´ äÀº (E)ÀÔ´ Ï ´ Ù. :
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25. Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year? (A) (B) (C) (D) (E)
1 4 4 15 1 3 4 11 4 5
12¿ ù ÇÑ ´ Þ°£ÀÇ ÆǸ Å· ®ÀÌ 1¿ùº Î ÅÍ 11¿ù »çÀÌ ÀÇ ¿ùÆò±Õ ÆǸ Å· ®ÀÇ 4¹ èÀÏ ¶§, 12¿ù ÆǸ Å· ® ´ ë 1³ â µ¿¾ÈÀÇ ÆǸ Å· ®ÀÇ º ñÀ² À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 1¿ùº Î ÅÍ 11¿ù »ç ÀÌ ÀÇ ¿ùÆò±ÕÆǸ Å· ®À» q ¶ó ÇÏ ¸ é 12¿ùÀÇ ÆǸ Å· ®Àº 4 q ÀÔ´ Ï ´ Ù . µû¶ó¼ 1³ â° £ ÀÇ ÃÑÆǸ Å· ®Àº 15q °¡ µË´ Ï ´ Ù. ::
´ äÀº (B)ÀÔ´ Ï ´ Ù.
::
1 2
26. Millie and Rick addressed 150 invitations. If Millie addressed 1 times as many as Rick addressed, how many of the invitations did Rick address? (A) 30 (B) 60 (C) 75 (D) 90 (E) 100 Millie¿Í RickÀº ÃÊûÀå 150ÀåÀ» º ¸ ³ ´ Ù°í ÇÕ´ Ï ´ Ù. MilleÀÌ ¹ ß¼ÛÇÑ ÃÊûÀåÀÌ RickÀÌ ¹ ß¼ÛÇÑ
1 2
ÃÊûÀå ¼öÀÇ 1 ¹ èÀÏ ¶§, RickÀÌ º ¸ ³ ½ ÃÊûÀå ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. RickÀÌ º ¸ ³ ½ ÃÊûÀå ¼ö¸ ¦ R ÀÌ ¶ó ÇÏ ¸ é ´ ÙÀ½°ú ° °ÀÌ ½ÄÀ» ¼¼¿ö ¹ ®Á¦ ¸ ¦ Ç® ¼ö ÀÖ½À´ Ï ´ Ù.
1 1 R + R = 150 2 ÇÏ Áö¸ ¸ ¹ ®Á¦ ¸ ¦ º ¸ ´ Ù »¡ ¸ ® Ç®±â À§Çؼ ´  MillieÀÌ ¹ ß¼ÛÇÑ ÃÊûÀåÀÌ RickÀÌ ¹ ß¼ÛÇÑ ÃÊûÀåº ¸ ´ Ù
1 1 ¹è¶ó´Â°Í À» ÀÐÀ¸ ¸ é¼ MillieÀÌ º ¸³ ½ ÃÊûÀå ¼ö°¡ RickÀÌ º ¸ ³ ½ ÃÊûÀå ¼öº ¸ ´ Ù 50%°¡ ¸ ¹ 2 ´ Ù´  »ç½ÇÀ» ÆľÇÇÏ ¿© º ¸ ±â· Î º Î ÅÍ ´ äÀ» ã´  °Í ÀÔ´ Ï ´ Ù. ::
´ äÀº (B)ÀÔ´ Ï ´ Ù
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27. In 1990 a total of x earthquakes occurred worldwide, some but not all of which occurred in Asia. If m of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did not occur in Asia? (A)
x m
(B)
m x
(C)
m x − m
(D)
x x − m
(E) 1 −
m x
¾Æ½Ã¾Æ¿¡ ¼ ÀÏ ¾î ³ ÁöÁø Ƚ¼ö ´ ë ¾Æ½Ã¾ÆÀÌ ¿Ü Áö¿ª ¿¡ ¼ ÀÏ ¾î ³ ÁöÁøÀÇ º ñÀ² À» ¹ °¾î º ¸ °í ÀÖ ½À´ Ï ´ Ù. :: ´ äÀº (C)ÀÔ´ Ï ´ Ù. :: 28. The ratio of two quantities is 3 to 4. If each of the quantities is increased by 5, what is the ratio of these two new quantities? (A) (B) (C) (D) (E)
3 4 8 9 18 19 23 24 It cannot be determined from the information given.
µÎ º з ®ÀÇ º ñÀ² ÀÌ 3 : 5ÀÌ¸ç °¢°¢ÀÇ º з ®ÀÌ 5 ¸ ¸ Å ¾¿ Áõ°¡ ÇÒ ¶§ »õ· Î ¿î º з ®ÀÇ º ñÀ² À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¿ø· ¡ ÀÖ´ ø º з ®ÀÌ ¾ó¸ ¶ÀÎ Áö ¾Ë ¼ö ¾ø±â ¶§¹ ®¿¡ »õ· Î Ãß°¡ µÇ´  5° ¡ µÎ º з® °£ÀÇ º ñÀ² À» ¾î ¶»° Ô º ¯È ½Ãų Áö ¾Ë ¼ö ¾ø½À´ Ï ´ Ù. . ¿¹ ) 300 : 500 ⇒ 305 : 505, 30 : 50 ⇒ 35 : 55 :: ´ äÀº (E)ÀÔ´ Ï ´ Ù. ::
29. Of the people who responded to a market survey, 120 preferred Brand X and the rest preferred Brand Y . If the respondents indicated a preference for Brand X over Brand Y by a ratio of 3 to 1, how many people responded to the survey? (A) 80 (B) 160 (C) 240 (D) 360 (E) 480
X ºê·£µå¸¦ ¼±È£ÇÑ´ Ù°í ´ äº ¯ÇÑ »ç¶÷ÀÌ 120¸ í ÀÌ ¾úÀ¸ ¸ ç X ºê·£µå ´ë Y º ê· £µå¸ ¦ ¼±È£ÇÏ ´  »ç¶÷ÀÇ º ñÀ² ÀÌ 3 : 1ÀÌ ¶ó° í ÇÕ´ Ï ´ Ù. ÀÌ ¶§ ¼³ ¹ ®Á¶»ç ¿¡ ÀÀÇÑ Àüü ÀÀ´ äÀÚ ¼ö¸¦ ¹ °¾î º ¸ °í ÀÖ ½À´ Ï ´ Ù.
X º ê· £µå¸ ¦ ¼±È£ÇÑ´ Ù´  ÀÀ´ äÀÚÀÇ ¼ö° ¡ 120¸ í ÀÌ ¾úÀ¸ ¹ Ç· Î Y º ê· £µå¸ ¦ ¼±È£ÇÑ´ Ù°í ÀÀ´ äÇÑ »ç ¶÷Àº 40¸ í ÀÔ´ Ï ´ Ù. ::
´ äÀº (B)ÀÔ´ Ï ´ Ù.
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30. Orange juice of normal strength is prepared by adding three 6-ounce cans of water to the contents of a 6-ounce can of orange juice concentrate. If 1 ounce of the can of concentrate was already used for some other purpose, how many 6-ounce cans of water should be added to the remainder of the concentrate to prepare juice of normal strength? (A) 1
2 3
(B) 2
1 3 1 (D) 2 2 5 (E) 2 6 (C) 2
ÀϹ ݳ óµµÀÇ ¿À· »Áö Á꽺 ´  6-ounce ¿À· »Áö ³ óÃà¾× ÇÑ °³ ÀÇ can° ú 6-ounce ¹ ° ¼¼ °³ ÀÇcanÀ» ¼¯¾î ¼ ¸ ¸ µç´ Ù°í ÇÕ´ Ï ´ Ù. 1-ounce ¿À· »Áö ³ óÃà¾×ÀÌ ´ Ù¸ ¥ ¿ëµµ· Î »ç¿ë µÇ¾úÀ» ¶§, ÀÏ ¹ ݳ óµµÀÇ ¿À· »ÁöÁ꽺 ¸ ¦ ¸ ¸ µé±â À§ÇØ ¸ î canÀÇ ¹ °ÀÌ »ç¿ ëµÇ´ ÂÁö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¿À· »Áö ³ óÃà¾× 6 ounce¿Í ¹ ° 18ounce¸ ¦ È¥ÇÕÇÏ ¿© ÀÏ ¹ ݳ 󵵸 ¦ ¸ ¸ µé¹ Ç· Î “¿À· »Áö ³ óÃà¾× : ¹ °= 1 : 3 ”ÀÔ´ Ï ´ Ù. 5 ounce¸ ¸ Å ÀÇ ¿À· »Áö ³ óÃà¾×ÀÌ ³ ² ¾ÆÀÖÀ¸ ¹ Ç· Î 15ounce¸ ¸ Å ÀÇ ¹ °ÀÌ ÇÊ¿äÇÕ´ Ï ´ Ù. ::
´ äÀº (D)ÀÔ´ Ï ´ Ù.
::
31. A coffee merchant makes a house blend of coffee using 4 pounds of Arabian beans costing $3 per pound, 2 pounds of Java beans costing $4 per pound, and 4 pounds of Brazilian beans costing $1 per pound. If the merchant sold all of the blend for 50 percent more than the total cost of the beans used, at what price per pound was the blend sold? (A) $1.20 (B) $2.40 (C) $3.00 (D) $3.60 (E) $4.50 ÆÄ¿î µå ´ ç $3ÇÏ ´  Arabian»ê Ä¿ÇÇ 4ÆÄ¿î µå(ÃÑ $12) , ÆÄ¿î µå ´ ç $4ÇÏ´Â Java»ê Ä¿ÇÇ 2ÆÄ¿î µå (ÃÑ $8), ÆÄ¿î µå ´ ç $1ÇÏ ´  Brazil Ä¿ÇÇ 4ÆÄ¿î µå(ÃÑ $4)¸ ¦ ÀÌ ¿ëÇÏ ¿© º ê· £µåÄ¿ÇǸ ¦ ¸ ¸ µì ´ Ï ´ Ù. ÆǸ Å°¡ °ÝÀº º ê· £µåÄ¿ÇǸ ¦ ¸ ¸ µé±â À§ÇØ ±¸ ÀÔÇÑ Ä¿ÇÇÀÇ º ñ¿ëº ¸ ´ Ù 50%°¡ ³ ôÀ» ¶§ 1ÆÄ¿î µå ´ ç °¡ °ÝÀ» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 10ÆÄ¿î µåÀÇ Ä¿ÇǸ ¦ ±¸ÀÔÇÏ ´ µ¥ ÃÑ $24ÀÌ ¼Ò¿ä µÇ¾ú½À´ Ï ´ Ù. 1ÆÄ¿î µå ´ ç $2 4°¡ ¼Ò¿äµÈ °Í ÀÌ ¸ ç ÆǸ Å°¡ °ÝÀº $ 2.4º ¸ ´ Ù 50% ¸ ¹ À¸ ¹ Ç· Î $3.6ÀÔ´ Ï ´ Ù. ::
´ äÀº (D)ÀÔ´ Ï ´ Ù.
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32. The current ratio of men to women on a certain board of trustees is 2 to 5. If 4 men were added to the board, the ratio of men to women would be 2 to 3. How many men are currently on the board? (A) 2 (B) 4 (C) 5 (D) 6 (E) 8 ³ ² ¼º ´ ë ¿©¼º ÀÇ º ñÀ² ÀÌ 2 : 5¶ó°í ÇÕ´ Ï ´ Ù. À§¿øȸ ¿¡ ³ ² ¼º ÀÌ 4¸ í ´ õ Âü°¡ ÇÏ ¸ é ³ ² ¼º ´ ë ¿©¼º ÀÇ º ñÀ² ÀÌ 2 : 3À¸ · Î ¹ Ù² ï ´ Ù°í ÇÕ´ Ï ´ Ù. ÇöÀç ¸ î ¸ í ÀÇ ³ ² ¼º ÀÌ À§¿øȸ ¿¡ ÀÖ´ ÂÁö ¹ °¾î º ¸ °í ÀÖÁÒ. . ³ ² ¼º ÀÌ 4¸ í Âü°¡ ÇÏ ¸ é m , ¿©¼º ÀÇ ¼ö¸ ¦ f ¶ó Çϸ é m : f = 2 : 5 ÀÔ´ Ï ´ Ù m + 4 : f = 2 : 3 ÀÌ µË´ Ï ´ Ù. µû¶ó¼ µÎ ½ÄÀ» ¿¬¸ ³ ÇÏ ¿© °è»êÇÏ ¸ é ³ ² ¼º ÀÇ ¼ö¸ ¦ ±¸ ÇÒ ¼ö ÀÖÁÒ.
³ ² ¼º ÀÇ ¼ö¸ ¦
::
´ äÀº (D)ÀÔ´ Ï ´ Ù.
::
33. A custom blend of paint is made by mixing red, yellow, and black paints in the ratio of 12 to 11 to 1. If all of the paints are sold only in pint-sized containers, how many containers of yellow are used in preparing 6 gallons of the blend? (8 pints = 1 gallon) (A) 2 (B) 3 (C) 11 (D) 22 (E) 24 º ÓÀº »ö , ³ ë¶õ»ö, °ËÀº »öÀ» 12:11:1ÀÇ ºñÀ² · ΠȥÇÕÇÏ ¿©a custom blend of paint¸ ¦ ¸ ¸ µç´ Ù°í ÇÕ´ Ï ´ Ù. ¸ ðµç ÆäÀÎ Æ®°¡ ÆÄÀÎ Æ®(pint : 1/8gallon) ´ ÜÀ§ÀÇ ¿ë±â¿¡ ´ ã°ÜÁ® Æȸ± ¶§, 6 gallonÀÇ blendÀ» Áغ ñ ÇÏ ±â À§Çؼ ³ ë¶õ»ö ÆäÀÎ Æ® ¸ î ÅëÀ» »ç¿ëÇØ¾ß ÇÏ ´ ÂÁö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. < Ç®ÀÌ1 > A custom blend of paint¿¡ ¼ ³ ë¶õ»öÀÌ Â÷ÁöÇÏ ´  º ñÀ² Àº
2.75gallon = 6 gallon ×
11 . ³ ë¶õ»öÀÇ ÆäÀÎ Æ®´  ÀÔ´ Ï ´ Ù 24
11 ÀÌ ÇÊ¿äÇÕ´ Ï ´ Ù. µû¶ó¼ ³ ë¶õ»ö 22 (= 2. 75gallon × 8) ÆÄÀÎ Æ®° ¡ÇÊ 24
¿ä ÇÕ´ Ï ´ Ù. < Ç®ÀÌ 2 > 6gallonÀº 48ÆÄÀÎ Æ® ÀÔ´ Ï ´ Ù. 48ÆÄÀÎ Æ®ÀÇ
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- ÁÂ Set 4 GRE Math °
34. A rectangular office floor is 28 meters by 20 meters. A custodian, working at a constant rate, waxes a section of the floor that is 5 meters by 20 meters in
3 hour. How many hours does 4
it take the custodian, working at this same constant rate, to wax the entire floor? (A) 2.52 (B) 3 (C) 3.45 (D) 4.2 (E) 7
3 ½Ã°£ µ¿¾È 5 meters by 20 meters¸ ¸ Å ¾¿ ¸ ¶· ç¹ Ù´ ÚÀ» ´ ÛÀ» ¶§, 28 meters by 20 meters Å©±âÀÇ Á÷ 4 »ç°¢Çü ¹ Ù´ ÚÀ» ´ Û´ µ¥ ¾ó¸ ¶¸ ¸ Å ÀÇ ½Ã°£ÀÌ ¼Ò¿äµÉÁö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 28 meters by 20 metersÅ©±âÀÇ Á÷»ç°¢Çü ¹ Ù´ ÚÀº metersÅ©±âÀÇ 5.6¹ è ÀÔ´ Ï ´ Ù.
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3 ½Ã°£ µ¿¾È¿¡ ´ ÛÀ» ¼ö ÀÖ´Â 5 meters by 20 4
28 × 20 = 5.6 µû¶ó¼ 5 × 20
½Ã°£µµ 5.6¹ è ¸ ¸ Å ¼Ò¿ä µË´ Ï ´ Ù.
::
35. A glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution. If 45 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container? (A) 3.00 (B) 5.00 (C) 5.50 (D) 6.50 (E) 6.75 Æ÷µµ´ ç ¿ë¾×Àº ¹ ° 100 cubic centimeter´ ç 15±×· ¥ÀÇ Æ÷µµ´çÀ» Æ÷ÇÔÇÏ °í ÀÖ´ Ù°í ÇÕ´ Ï ´ Ù. ÀÌ ¶§ Æ÷µµ´ ç ¿ë ¾× 45 cubic centimeter³ »¿¡ Æ÷ÇԵǾî ÀÖ´  Æ÷µµ´ çÀÇ Áú· ®À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.
45 × 15 = 6.75 100 ::
´ äÀº (E) ÀÔ´ Ï ´ Ù
::
36. Dan bought x pencils, some at 10 cents each and the rest at 6 cents each. For the same amount of money that he spent on these pencils, he could have bought x pencils at 9 cents each. What is the ratio of the number of 10-cent pencils purchased to the number of 6-cent pencils purchased? (A) 1 : 1 (B) 2 : 1 (C) 3 : 1 (D) 4 : 1 (E) 5 : 1 DanÀº x °³ ÀÇ ¿¬ÇÊÀ» ±¸ÀÔÇß°í ±¸ÀÔÇÑ ¿¬ÇÊ Áß ÀÏ º Î ´  ÇÑ ÀÚ· ç ´ ç ° ¡ °ÝÀÌ 10cent ¿´ À¸ ¸ ç ³ ª ¸ ÓÁö´  6cent¿´ ´ Ù°í ÇÕ´ Ï ´ Ù. ¿¬ÇÊÀ» ±¸ ÀÔÇÏ ´ µ¥ Áöº ÒÇÑ µ¿ÀÏ ÇÑ ±Ý¾× ¸ ¸ Å À» ° ¡ Áö°í ÇÑ ÀÚ·ç ´ ç 9cent ÇÏ´Â ¿¬ÇÊÀ» x ÀÚ· ç »ì ¼ö ÀÖ´ Ù°í ÇÕ´ Ï ´ Ù. 10 cent¿¬ÇÊ°ú 6cent ¿¬ÇÊÀÇ º ñÀ² À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¿¬ÇÊÀ» ±¸ÀÔÇÏ ´ µ¥ Áöº ÒÇÑ µ¿ÀÏ ÇÑ ±Ý¾× ¸ ¸ Å À» °¡ Áö°í ÇÑ ÀÚ· ç ´ ç 9centÇÏ ´  ¿¬ÇÊÀ» x ÀÚ· ç »ì ¼ö ÀÖ´ Ù°í ÇßÀ¸ ¹ Ç· Î , ±¸ ÀÔÇÑ ¿¬ÇÊÀÇ ÇÑ ÀÚ· ç ´ ç Æò±Õ±Ý¾×ÀÌ 9cent¶ó´  °Í À» Àǹ Ì ÇÕ´ Ï ´ Ù.
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Æò±Õ±Ý¾×ÀÌ 9cent° ¡ µÇ±â À§Çؼ ´  6cent ¿¬ÇÊ ÇÑ ÀÚ· ç ´ ç10 cent¿¬ÇÊÀÌ 3ÀÚ· 羿 ÀÖ¾î ¾ß ÇÕ´Ï ´ Ù. µû¶ó¼ 10 cent ¿¬ÇÊ ´ ë 6 cent ¿¬ÇÊÀÇ º ñÀ² Àº 3:1ÀÔ´ Ï ´ Ù. ::
´ äÀº (C)ÀÔ´ Ï ´ Ù.
::
37. A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half-gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture? (A) 2
1 2
(B)
2
(C)
3
(D)
3
(E)
4
1 2
ƯÁ¤³ óµµÀÇ È¸ »ö ÆäÀÎ Æ®´  Èò»ö ÆäÀÎ Æ®¸ ¦ 3, °ËÀº »ö ÆäÀÎ Æ®´  5¸ ¸ ŠȥÇÕÇÏ ¿© ¸ ¸ µç´ Ù°í ÇÕ ´ Ï ´ Ù. 2 gallonÀÇ È¸ »öÆäÀÎ Æ®°¡ ÇÊ¿äÇÏ ¸ ç °³ º ° »öÀº 1 gallon ¶Ç´Â
1 gallon¾¿ ±¸ ÀÔ ÇÒ ¼ö ÀÖÀ» 2
¶§, ȸ »öÆäÀÎ Æ®¸ ¦ ¸ ¸ µé±â À§ÇØ ±¸ ÀÔÇØ¾ß ÇÏ ´  ÆäÀÎ Æ®ÀÇ ÃÖ¼Ò· ®À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.
ȸ »öÆäÀÎ Æ®¸ ¦ ¸ ¸ µé±â À§ÇØ ÇÊ¿äÇÑ °ËÀº »ö ÆäÀÎ Æ®´  Àüü ÆäÀÎ Æ® ¾çÀÇ
5 5 1 . ´Â ÀÔ´ Ï ´ Ù 8 8 2
º ¸ ´ Ù´ ÂÅ©Áö¸ ¸ 1º ¸ ´ Ù´  ÀÛ½À´ Ï ´ Ù. µû¶ó¼ °ËÀº »ö ÆäÀÎ Æ®°¡ 1.5gallonÀÌ ÇÊ¿äÇÏ ´ Ù´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. ¹ °· Ð 1.5gallonÀÌ ¸ ðµÎ ÇÊ¿äÇÑ °Í Àº ¾Æ´Ï ÁÒ. ´ Ù¸ ¸ ÆäÀÎ Æ®¸ ¦ ±¸ ÀÔÇÒ ¼ö ÀÖ´  ´ ÜÀ§°¡ 1 gallon
1 gallonÀÌ ±â ¶§¹ ®¿¡ 1.5gallonÀ» ±¸ÀÔÇÏ ¿© 1.25gallon¸¸ Å À» »ç¿ëÇÏ °Ô µË´ Ï ´ Ù. Èò»öÆäÀÎ 2 3 3 1 1 ) ≡÷×∧ º ¸ ´ Ù´ ÂÀÛ½À´ Ï ´ Ù. µû¶ó¼ Æ®´  Àüü ÆäÀÎ Æ® ¾çÀÇ ÀÌ ÇÊ¿äÇÕ´ Ï ´ Ù. Àº (= 0.25 8 8 4 2 3 1gallon¸ ¸ Å ±¸ÀÔÇÏ ¸ é µË´ Ï ´ Ù.(½ÇÀç »ç¿ ë· ®Àº 0.75 gallon = 2 × ÀÔ´ Ï ´ Ù .) 8 ¶Ç´ Â
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- ÁÂ Set 4 GRE Math °
38. Working alone, printers X , Y , and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates? (A)
4 11
1 2
(B)
(C)
15 22
(D)
22 15
(E)
11 4
ÇÁ¸ °ÅÍ X , Y , Z °¡ ƯÁ¤ ÀÎ ¼âÀÛ¾÷À» ÇÏ ´  µ¥ °¢°¢ 12½Ã°£, 15½Ã°£, 18½Ã°£ÀÌ ¼Ò¿äµÈ´ Ù°í ÇÕ´ Ï ´ Ù. ÇÁ¸ °ÅÍ X °¡ ƯÁ¤ ÀÛ¾÷À» ¿Ï ¼öÇÏ ´ µ¥ ¼Ò¿äµÇ´  ½Ã°£ ´ ë ÇÁ¸ °ÅÍ Y , Z °¡ µ¿½Ã¿¡ ÀÛ¾÷À» ÇÏ ¿© ÀÏ À» ³ ¡ ³ »´ µ¥ ¼Ò¿äµÇ´  ½Ã°£ÀÇ º ñÀ² À» ±¸ ÇÏ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. ÇÁ¸ °ÅÍ Y , Z °¡
µ¿½Ã¿¡ ÇÑ ½Ã°£ ³ »¿¡ ÇÒ ¼ö ÀÖ´  ÀÛ¾÷ÀÇ ¾çÀº
µû¶ó¼ ÀÛ¾÷À» ¿Ï ¼öÇÏ ´ µ¥
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´ äÀº (D)ÀÔ´ Ï ´ Ù.
11 90
= 1 + 1 ÀÔ´ Ï ´ Ù . 15 18
90 90 . ½Ã°£ÀÌ ¼Ò¿äµË´ Ï ´ Ù. ½Ã°£Àº º ñÀ² Àº 12 ÀÔ´ Ï ´ Ù 11 11
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39. The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? (A) 50 (B) 200 (C) 400 (D) 625 (E) 800 ºñ´© : ¾ËÄÚ¿Ã : ¹ ° = 2 : 50 : 100 ÀÏ ¶§, ¾ËÄڿÿ¡ ´ ëÇÑ º ñ´ ©ÀÇ º ñÀ² Àº 2¹ è°¡ µÇµµ· Ï ¹ °¿¡ ´ ë ÇÑ º ñ´©ÀÇ º ñÀ² Àº 1/2¹ è° ¡ µÇµµ· Ï ¿ë¾×ÀÌ º ¯Çß´ Ù°í ÇÕ´ Ï ´ Ù. º ¯È µÈ ¿ë¾×¿¡ ¼ ¾ËÄÚ¿ÃÀÌ 100 cubic centimeters (Cm 3 ) ÀÏ ¶§, ¹ °Àº ¸ î cubic centimetersÀÎ Áö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.
2 ÀÔ´ Ï ´ Ù . º ñÀ² ÀÌ µÎ 50 2 Áõ° ¡ 2 ⋅ ÇÏ ¸ é µË´ Ï ´ Ù. º ñ´ ©ÀÇ º ñÀ² 50
¿ø· ¡ ¿ë¾×¿¡ ¼ ÀÇ º ñ´ ©ÀÇ º ñÀ² ´ ë ¾ËÄÚ¿ÃÀÇ ºñÀ² Àº 2 : 50 =
¹ è°¡ µÇ
±â À§Çؼ ´  ÇöÀç º ¸´Ù ºñ´©ÀÇ ¾çÀÌ 2¹ è· Î
´ ë ¹ °ÀÇ
º ñÀ² ÀÌ 1/2¹ è°¡ µÇ±â À§Çؼ ´  ¹ °ÀÇ ¾çÀº 2¹ è°¡ Áõ°¡ ÇØ¾ß µË´ Ï ´ Ù. º ñ´ ©ÀÇ º ñÀ² ´ ë ¾ËÄÚ¿ÃÀÇ º ñÀ² ÀÌ 2 ¹ è° ¡ µÇ±â À§Çؼ ÀÌ ¹ Ì º ñ´ ©ÀÇ ¾çÀÌ µÎ ¹ è° ¡ Áõ°¡ Ç߱⠶§¹ ®¿¡ ¹ °ÀÇ ¾çÀº 4¹ è°¡ Áõ° ¡ ÇØ¾ß ÇÕ´ Ï ´ Ù.
2 → 2 × 2 = 1 »õ· Î ¿î × 100 100 4 100
¿ë¾×¿¡ ¼ ÀÇ º ñÀ² Àº “º ñ´ © : ¾ËÄÚ¿Ã : ¹ °
= 4 : 50 : 400” ÀÔ´ Ï ´ Ù. ¾ËÄÚ¿ÃÀÌ 100 cubic centimetersÀÌ ¹ Ç· Î ¹ °Àº 800cubic centimetersÀÔ´ Ï ´ Ù. ::
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- ÁÂ Set 4 GRE Math °
40. Tom and Carlos begin to play a series of four games with 400 chips each. At the end of each game, there is a loser who must surrender half of his chips to the winner. If Tom wins only the first and third games, how many chips does he have after the pay-off at the end of the fourth game? (A) 200 (B) 275 (C) 400 (D) 525 (E) 550 Tom°ú Carlos´  °¢ÀÚ 400° ³ ÀÇ Ä¨ À» °¡ Áö°í 4°æ±â¸ ¦ ½ÃÀÛÇÕ´ Ï ´ Ù. ¸ Å °æ±â ÆÐÀÚ°¡ ½ÂÀÚ¿¡ °Ô ÀÚ½ÅÀÌ °¡ Áø Ĩ ÀÇ Àý¹ ÝÀ» ÁÙ ¶§, TomÀÌ Ã¹ ¹ ø°, ¼¼ ¹ ø° °ÔÀÓ¸ ¸ À» ÀÌ °åÀ» ° æ¿ì TomÀÌ 4 °æ±â° ¡ ³ ¡ ³ ÈÄ °®°Ô µÇ´  Ĩ ÀÇ °³ ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. TomÀÌ ¸ Å °æ±â ÈÄ °®°Ô µÇ´  Ĩ ÀÇ °³ ¼ö´  ´ ÙÀ½°ú °°½À´ Ï ´ Ù.(µÎ »ç¶÷ÀÌ °¡ Áö° í Àִ Ĩ ÀÇ °³ ¼ö´  ÃÑ 800°³ ÀÔ´ Ï ´ Ù. µû¶ó¼ “800 – TomÀÌ °®°í ÀÖ´  Ĩ ÀÇ °³ ¼ö”°¡ Carlos°¡ °¡ Áö°í Àִ Ĩ ÀÇ °³ ¼ö ÀÔ´ Ï ´ Ù.) ù ¹ ø° °æ±â 600°³ + 200(½Â¸ ®) ::
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µÎ ¹ ø° °æ±â 300°³ -300(Æй è)
¼¼ ¹ ø° °æ±â 550°³ +250(½Â¸ ®)
³ × ¹ ø° °æ±â 275°³ -275(Æй è)
::
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° - ÁÂ Set 5 GRE Math
Category 5 Percents 1.
What is 37.5 percent of (A) (B) (C) (D) (E)
2.
2 ? 3
answer
1 8 1 4 3 8 1 2 3 4
If 18 is 15 percent of 30 percent of a certain number, what is the number? (A) 9 (B)
36
(C)
40
(D) (E)
81 400
3. In a recent survey 65 percent of those responding were in favor of recycling. If 780 people were in favor of recycling, how many responded to the survey? (A) (B)
1,287 1,200
(C)
900
(D)
845
(E)
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507
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answer
answer
° - ÁÂ Set 5 GRE Math
4. If x is 11 percent greater than 80, then x = (A)
70.9
(B) (C)
71.2 88.0
(D)
88.8
(E)
91.0
answer
5. What is 25 percent of 20 percent of 75? answer
(A) 3.75 (B) 15 (C) 18.75 (D) 25 (E) 33.75
6. If 70 percent of 600 is 40 percent of x , then x = (A) (B)
105 168
(C)
342
(D)
660
answer
6 7
(E) 1,050
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° - ÁÂ Set 5 GRE Math
7. Last year if 97 percent of the revenues of a company came from domestic sources and the remaining revenues, totaling $450,000, came from foreign sources, what was the total of the
answer
company’s revenues? (A)
$1,350,000
(B) (C)
$1,500,000 $4,500,000
(D)
$15,000,000
(E)
$150,000,000
8. A certain telescope increases the visual range at a particular location from 90 kilometers to 150
answer
kilometers. By what percent is the visual range increased by using the telescope? (A)
30%
(B)
1 33 % 2
(C)
40%
(D)
60%
(E)
2 66 % 3
9. If x > 0 , x + x is what percent of x ? 50 25 (A) 6%
answer
(B) 25% (C) 37
1 % 2
(D) 60% (E) 75%
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10. If Juan sold 100 of the 15,522 shares of stock that he held, approximately what percent of his shares did he sell? (A)
0.3%
(B)
0.6%
(C) (D)
0.9% 1.2%
(E)
1.5%
11. A store reported total sales of $385 million for February of this year. If the total of sales for
answer
answer
the same month last year was $320 million, approximately what was the percent increase in sales? (A) (B)
2% 17%
(C)
20%
(D)
65%
(E)
83%
12. In a certain certain fund, 40 percent percent of the money money is invested invested in stocks, and of that portion, 20 20 percent is invested in preferred preferred stocks. If the fund has $576 invested in preferred stocks, what is the total amount of the fund? (A)
$960
(B) $1,440 (C) $2,880 (D) $4,608 (E) $7,200
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answer
° - ÁÂ Set 5 GRE Math
13. A certain tax rate is $0.82 per $100.00. What is this rate, expressed as a percent? (A) 82% (B) 8.2% (C) 0.82% (D) 0.082%
answer
(E) 0.0082%
1 2
14. A mouse treated with a certain growth hormone weighs 1 ounces, and an untreated mouse weighs
answer
3 ounce. The weight of the treated mouse is what percent of the weight of the 4
untreated mouse? (A) (B)
50% 112.5%
(C)
150%
(D)
200%
(E)
225%
15. The graph above shows the percent of the people in a certain survey who belonged to each of four occupational categories. Of those surveyed, if 160 were in blue-collar occupations, how many were in occupations classified as “Other”? (A) 15 (B) 24 (C) 60 (D) 70 (E) 240
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° - ÁÂ Set 5 GRE Math
16. An employee of Company X is entitled to a disability d isability benefit equal to the sum of 60 percent
answer
of the first $2,000 of monthly salary and 40 percent of the amount of monthly salary in excess of $2,000. What is the monthly salary salary of an employee employee who receives receives $1,400 in disability disability benefits under this plan (A) $1,700 (B) $2,200 (C) $2,240 (D) $2,500 (E) $3,000
17. In January 1981 the cost of dictating and transcribing a business letter was $6.60, a 10 percent
answer
increase over the cost in January 1980. If the percent increase from January 1979 to January 1980 was
6 of a percentage point less than the percent increase from January 1980 to 10
January 1981, approximately what was the cost of dictating and transcribing a business letter in January 1979? (A) (B)
$3.96 $5.48
(C)
$5.60
(D)
$5.94
(E)
$6.00
18. In 1986 the book value of a certain car was book value was
2 of the original purchase price, and in 1988 its 3
1 of the original purchase price. By what percent did the book value of this 2
car decrease from 1986 to 1988? (A)
2 16 % 3
(B)
25%
(C)
1 33 % 3
(D)
50%
(E)
75%
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° - ÁÂ Set 5 GRE Math
19. The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by 20 percent. What percent of the
answer
projected attendance was the actual attendance? (A)
45%
(B) (C)
56% 64%
(D)
75%
(E)
80%
1 8
20. On the first business day of a certain week, the opening price of a stock was 27 and the
3 4
answer
3 4
closing price was 32 ; on the second day, the opening price was 32 and the closing price was 30
7 . The decrease in price on the the second day was what percent percent of the increase in price price 8
on the first day? (A) 25% (B)
1 33 % 3
(C)
40%
(D)
50%
(E)
2 66 % 3
21. A circle graph shows how the budget of a certain company was spent: 63 percent for salaries, 12 percent for research and development, 6 percent for utilities, 5 percent for equipment, 4 percent for supplies, and the remainder remainder for transportation. transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation? (A)
10°
(B)
18 °
(C)
36°
(D)
90°
(E)
324 °
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° - ÁÂ Set 5 GRE Math
22. Mr. Kranter, Kranter, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 40 percent percent of all the votes cast. cast. Approximately Approximately what percent of the remaining remaining
answer
votes would he need to have received in order to have won at least 50 percent of all the votes cast? (A) (B)
10% 12%
(C)
15%
(D)
17%
(E)
20%
23. In year Y imported machine tools accounted for 25 percent of total machine-tool sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine
answer
tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars? (A) (B) (C) (D) (E)
9 x 80 13 x 20 80 9 x 20 x 13 80 x 9
24. Ann can have her bicycle repaired for $50, or she can trade it in, as is, and receive $22 credit toward the purchase of a new bi cycle that sells for $107. If Ann trades in her current bicycle, the cost to her of purchasing the new bicycle is what percent greater than the cost of having her current bicycle repaired? (A)
44%
(B)
60%
(C) (D)
70% 114%
(E)
170%
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answer
° - ÁÂ Set 5 GRE Math
25. The original retail price of an appliance was 60 percent more than its wholesale cost. If the appliance was actually sold for 20 percent less than the original retail price, then it was sold for
answer
what percent more than its wholesale cost?
26.
(A)
20%
(B) (C)
28% 36%
(D)
40%
(E)
42%
The cost C of manufacturing a certain product can be estimated by the formula
= C =
2
0.03rst , where
answer
r and s are the amounts, in pounds, of the two major ingredients
and t is the production time, in hours. If r is increased by 50 percent, s is increased by 20 percent, and t is decreased by 30 percent, by approximately what percent will the estimated cost of manufacturing the product change? (A) (A) (B)
40% increase 12% increase
(C)
4% increase
(D)
12% decrease
(E)
24% decrease
27. In a certain community, 39,285 more apartments were converted to condominiums and sold in 1981 than in 1980. If this was a 30 percent increase, how many apartments were were converted and sold in 1981? (A) 11,786 (B)
51,070
(C)
91,665
(D) (E)
130,950 170,235
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° - ÁÂ Set 5 GRE Math
28. If the length and width of a rectangular rectangular diagram diagram 12 inches inches by 8 inches inches are to be reduced by the same percent so that the diagram will exactly fit into a rectangular space 4.5 inches by 3
answer
inches, by what percent should the dimensions be reduced? (A)
25%
(B) (C)
37.5% 62.5%
(D)
75%
(E)
87.5%
29. In a certain certain orchestra, orchestra, 30 percent of the musicians musicians can play the violin and 24 percent percent can play the piano. If
answer
1 of those who can play the violin can also play the piano, what percent of the 3
orchestra musicians can play neither the violin nor the piano? (A) 36% (B)
44%
(C)
46%
(D) (E)
54% 56%
30. In an office, 40 40 percent of the workers have have at least 5 years of service, service, and a total total of 16 workers workers have at least 10 years of service. If 90 percent of the workers have fewer fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service? (A)
48
(B) (C)
64 80
(D)
144
(E)
160
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answer
° - ÁÂ Set 5 GRE Math
31. A factory has 500 workers, 12 percent of whom are women. If 80 additional workers are to be hired and all of the present workers remain, what percent of the new workers must be
answer
women in order to raise the total percent of female workers to 20 percent? (A)
70%
(B) (C)
50% 32%
(D)
20%
(E)
8%
Q
R
10%
40% P
30 %
S 20%
32. A rectangular rectangular parcel of land is divided divided into four lots, lots, P , Q, R , and S , as as shown shown above. above. If
answer
25 percent of the entire parcel of land is plowed and this includes 20 percent of lot P , what percent of the plowed land is not in lot P ? (A) (B)
5% 6%
(C)
10%
(D)
76%
(E)
80%
33. In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? (A)
400
(B) (C)
625 1,250
(D)
2,500
(E)
10,000
STOP
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° - ÁÂ Set 5 GRE Math
¼öÇÐÇØ ¼ö ÇÐÇؼ³
2 ? 3 1 (B) 4
Category 5 Percents
1. What is 37.5 percent of (A)
1 8
(C)
3 8
1 2
(D)
(E)
3 4
Percent Perce nt ¹ ®Á¦ ÀÇ ° ¡ Àå ½¬¿î ÇüÅÂÀÔ´ Ï ´ Ù. 37.5%´ 37 .5%´Â  0.375· Î ¹ Ù² Ü ¼ö ÀÖ ÀÖ½À´ Ï ´ Ù. Áï Áï percentÀ percentÀ»» decimal· Î ¹ Ù² Ù´  ¹ æ¹ ýÀº ¿ÞÂÊÀ¸ · Î µÎ ÀÚ¸ ®¸ ¦
¿Å±â¸ ¿Å ±â¸ é µÇ µÇÁÒ. °Å² °Å² Ù· Î decim decimalÀ alÀ» percent· percent· Î
2 3
¹ Ù² Ù´  ¹ æ¹ ýÀº ¿À ¿À¸¸ ¥ÂÊÀ¸ · Î µÎ ÀÚ¸ ® ¿Å ¿Å± ±â¸ é µË´ Ï ´ Ù. 0.375× = 0.25, Áï & Á¤´ ä Àº
2.
1 4
(B)
If 18 is 15 percent of 30 percent of a certain number, what is the number? (A) (A)
9
(B)
36
(C)
40
(D)
81
(E)
400
18 = 0.15 ×0.3 ×X, ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é X = 400 40 0 & Á¤´ Á¤´ äÀ äÀºº
(E)
3. In a recent survey 65 percent of those responding were in favor of recycling. If 780 people were in favor of recycling, how many responded to the survey? (A) (B)
1,287 1,200
(C)
900
(D)
845
(E)
507
ÀÀ´ äÀÚÀÇ 65%°¡ recyclin recycling¿¡ g¿¡ Âù¼º ÇÏ ¸ ç , ±× 65%Àº 780¸ í ÀÏ ¶§ ¼³ ¼³ ¹ ®¿¡ ÀÀ´ äÇ äÇÑ Ñ »ç¶÷ÀÇ ¼ö¸¦ ¹ ¯´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. Àüà üü ¼ ÀÎ ¿øÀ ¿øÀ»» T¶ó ° ¡ Á¤Ç ¤ÇÏÏ ¸ é, T×0.65 = 78 7 80 ÀÇ ½ÄÀ» ¸ ¸ µé ¼ö ÀÖÁÒ. ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é T = 1,200 & Á¤´ ä Àº
À±ÅÂÈ ÂÈ- -
(B)
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4. If x is 11 percent greater than 80, then x = (A)
70.9
(B) (C)
71.2 88.0
(D)
88.8
(E)
91.0
x ° ¡ 80º ¸ ´ Ù 11% Å©´ Ù´  ° Í Àº 10 100%À 0%À» ±âÁØ ±âÁØÀ¸ · Î 11% Å©´ Ù´  Àǹ Ì ÀÌ ¹ Ç· Î °á °á± ±¹ 111%À» 80¿¡ 80¿ ¡ ° öÇ öÇØ Ø¾ß ÇÕ´ Ï ´ Ù. µû¶ µû¶ó¼ ó¼- X = 1.1 1.111× 80, then X = 88.8 & Á¤´ Á¤´ äÀ äÀºº
(D)
5. What is 25 percent of 20 percent of 75? 75? (A) 3.75 (B) 15 (C) 18.75 (D) 25 (E) 33.75 X = 0.25 ×0.2 ×75 75,, ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é x = 3.75 3.7 5 & Á¤´ ä Àº
(A)) (A
6. If 70 percent of 600 is 40 percent of x , then x = (A)
105
(B)
168
(C)
342
(D)
660
(E)
1,050
6 7
0.7 × 600 = 0.4 × x , x = 1,050 Á¤´ äÀ äÀºº & Á¤´
À±ÅÂÈ ÂÈ- -
(E)
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7. Last year if 97 percent of the revenues of a company came from domestic sources and the remaining revenues, totaling $450,000, came from foreign sources, what was the total of the company’ s revenues? (A)
$1,350,000
(B) (C)
$1,500,000 $4,500,000
(D)
$15,000,000
(E)
$150,000,000
97% = domestic sources, 3% = for foreig eignn sou source rcess = $450 $450,00 ,000, 0, Áï Àüà üü ¼ÀÇ 3%° ¡ $45 $450, 0,000 000À ÀÌ ¶ó´  ¶æ ¶æÀ ÀÌ ÁÒ. µû¶ó¼-µû¶ó¼
(Àüà (À üü ¼ rev revenue enues) s) ×0.3 = $45,000 ⇒ Àüürevenues = $15,000,000
&Á
äÀº (D)
8. A certain telescope increases the visual range at a particular location from 90 kilometers to 150 kilometers. By what percent is the visual range range increased by using the telescope? telescope? (A) (A)
30% 30 %
% Áõ°¡ =
(B)
1 33 % 2
(C) 40% 40 %
(D) 60%
(E)
2 66 % 3
Áõ° ¡ µÈ µÈ °ª ( ³ ª Áß °ª -- ó À½ À½ ° ª ) ó À½ À½ ° ª
À§ÀÇ ½Ä¿ ¡ ´ ë ÀÔÇغ ¸ ¸ é 150 − 90 = 60 = 66 2 % 90
& Á¤´ Á¤´ äÀ äÀºº
3
(E)
9. If x > 0 , (A) (A)
90
6%
x
+
x
50 25
is what percent of x ?
(B)
25%
(C) 37
1 % 2
(D) 60% 60 %
(E) 75% 75 %
3 x ° ¡ x ÀÇ ¸ î %ÀÎ Áö¸ ¦ ¹ ¯´  ¹ ®Á¦ ³ ׿ä . ´ ܼøÇ øÇÏÏ ° Ô Ç®¸ é 3 = 0.06 = 6% ∂⌠° ´ äÀ äÀ»» 50 25 50 50 x
+
x
=
±¸Ç ±¸ ÇÒ ¼ö µµ µµ ÀÖ° í , °³ ° ³ ³ äÀ äÀûÀ ûÀ¸ · Î Ç®¸ é &Á
À±ÅÂÈ ÂÈ- -
Percen t =
part whole
3 x = 50 = 0 .06 = 6 % x
(A) äÀº
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10. If Juan sold 100 of the 15,522 shares of stock that he held, approximately what percent of his shares did he sell? (A)
0.3%
(B) 0.6%
(C) 0.9%
(D) 1.2%
(E) 1.5%
Percent = part = 100 = 0.0065 ≈ 0. 6% whole 15, 222 &Á
(B) äÀº
Tip!! decimal À» percent· Î ¹ Ù² Ù´ Â ¹ æ¹ ý
] ¿À¸
µÎ ÀÚ¸ ®¸ ¦ ¿Å±è, ex) 0.93 = 93%
ÂÊÀ¸
11. A store reported total sales of $385 million for February of this year. If the total of sales for the same month last year was $320 million, approximately what was the percent increase in sales? (A) 2% (B)
17%
(C)
20%
(D) (E)
65% 83%
Çؼ³ : % Áõ°¡ À² À» ¹ ¯´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. °ø½Ä¿¡ ´ ëÀÔÇÏ ¸ é $385million − $320million ≅ 0.20 = 20% $ 320million
&Á
äÀº (C)
12. In a certain fund, 40 percent of the money is invested in stocks, and of that portion, 20 percent is invested in preferred stocks. If the fund has $576 invested in preferred stocks, what is the total amount of the fund? (A)
$960
(B) $1,440 (C) $2,880 (D) $4,608 (E) $7,200 Àüü fund¿¡ ¼- 40%°¡ stocks¿¡ ÅõÀڵưí , ÀÌ 40%Áß¿¡ 20%´  preferred stocks¿¡ ÅõÀڵǾú´ µ¥ ±× preferred stocksÀÇ ±Ý¾×Àº $576ÀÔ´ Ï ´ Ù. ¹ ®Á¦ ´  fundÀÇ ÃѾ×À» ±¸ ÇÏ ¶ó´  ¹ ®Á¦ ³ ׿ä . Àüü fund ±Ý¾×À» T ¶ó °¡ Á¤ÇÏ ¸ é, T× 0.4 ×0.2 = $576 ÀÌ ÁÒ. µû¶ó¼- T = $7,200 &Á
À±ÅÂÈ-
äÀº (E)
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13. A certain tax rate is $0.82 per $100.00. What is this rate, expressed as a percent? (A) 82% (B) 8.2% (C) 0.82% (D) 0.082% (E) 0.0082% tax rate = $0.82 = 0.0082 = 0.82%
$100
&Á
äÀº (C)
1 2
14. A mouse treated with a certain growth hormone weighs 1 ounces, and an untreated mouse weighs
3 ounce. The weight of the treated mouse is what percent of the weight of the 4
untreated mouse? (A)
50%
(B) (C)
112.5% 150%
(D)
200%
(E)
225%
Ç®ÀÌ : Percent =
treated untreated
, ÆÛ¼¾Æ® ¹ ®Á¦ ´  ¾î ´ À °Í ÀÌ º и ð¿¡ ÇØ´ çÇÏ ´  Áö¸ ¦ ÆǺ °Çؾß
ÇÕ´ Ï ´ Ù. “–ÀÇ ¸ î %À» ±¸ ÇÏ ”¶ó´  ¹ ®Á¦ ¿¡ ¼- “ –ÀÇ” °¡ º и ð°¡ µË´ Ï ´ Ù.
3 Áï % = 2 3 4
= 2 = 200
%
¹ ݵå½Ã Å« Áý´ÜÀÌ ³ ª ´ ë»óÀÌ º и ð¿¡ ¿À´  °Í ÀÌ ¾Æ´ Ï ¶ó º ñ±³ ´ ë»óÀÇ ÁÖü°¡ º и ð¿¡ ¿Â´ Ù´  °Í À» ÀØÁö ¸ ¶¼¼¿ä! &Á
À±ÅÂÈ-
äÀº (D)
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15. The graph above shows the percent of the people in a certain survey who belonged to each of four occupational categories. Of those surveyed, if 160 were in blue-collar occupations, how many were in occupations classified as “Other”? (A) (B)
15 24
(C)
60
(D)
70
(E)
240
40% + 27% + 18% + X(other) = 100, ÀÌ ½Ä¿¡ ¼- X(other) = 15% ´ ÙÀ½ ÀüüÀÇ ¼ö¸ ¦ T¶ó °¡ Á¤ÇÏ ¸ é, T × 0.4 (=40%) = 160¿¡ ¼- T = 400 ´ ٽà othersÀÇ ¹ ®Á¦ ¿¡ Àû¿ë ÇÏ ¸ é 400 × 15%(=0.15) = 60 &Á
äÀº (C)
16. An employee of Company X is entitled to a disability benefit equal to the sum of 60 percent of the first $2,000 of monthly salary and 40 percent of the amount of monthly salary in excess of $2,000. What is the monthly salary of an employee who receives $1,400 in disability benefits under this plan (A) $1,700 (B) $2,200 (C) $2,240 (D) $2,500 (E) $3,000 Çؼ³ : Disability benefit = 60%× $2,000 + 40%×($2,000 ÀÌ »óÀÇ monthly salary)ÀÇ ½ÄÀ» À¯µµÇÒ ¼ö ÀÖÁÒ. ´ ÙÀ½Àº ¾î ¶² employee °¡ $1,400ÀÇ disability benefits À» ¹ Þ¾Ò´ µ¥ ÀÌ »ç¶÷ÀÇ monthly salaryÀ» ±¸ÇÏ ¶ó´  ¹ ®Á¦ ³ ׿ä. ÀÌ »ç¶÷ÀÌ ¹ ÞÀº ¿ù±ÞÀ» S¶ó °¡ Á¤ÇÏ ¸ é, $1,400 = $1,200 (0.6 ×$2,000) + 0.4 × (S − $2,000), ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é S = $2,500À» ±¸ ÇÒ ¼ö ÀÖÁÒ. &Á
À±ÅÂÈ-
äÀº (D)
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17. In January 1981 the cost of dictating and transcribing a business letter was $6.60, a 10 percent increase over the cost in January 1980. If the percent increase from January 1979 to January
6 of a percentage point less than the percent increase from January 1980 to 10
1980 was
January 1981, approximately what was the cost of dictating and transcribing a business letter in January 1979? (A) $3.96
(B) $5.48
(C) $5.60
(D) $5.94
(E) $6.00
81³ âµµ 1¿ùÀÇ º ñ¿ë $6.60Àº 80³ âµµ 1¿ùÀÇ º ñ¿ë¿¡ ¼- 10%°¡ »ó½ÂÇÑ °¡ °ÝÀÌ ¶ó°í ÇÕ´ Ï´ Ù. µû¶ó¼- 80³ âµµ 1¿ùÀÇ º ñ¿ëÀº x × 1.1 = $6 .6 ⇒ x = $6.00ÀÌ °í , 79³ âµµ 1¿ùº Î ÅÍ 80³ âµµ 1¿ù »çÀÌ ÀÇ °¡ °Ý»ó½Â· üÀº percentage point)ÀÇ
80³ âµµ 1¿ù¿¡ ¼- 81³ âµµ 1¿ù »çÀÌ ÀÇ °¡ °Ý »ó½Â· ü 10%¿¡ ¼- 1%(a
6 6 ¸ ¸ Å- »©ÁÖ¾î ¾ß ÇÕ´ Ï ´ Ù. 1%ÀÇ Àº 0.6% (0.006)ÀÔ´ Ï ´ Ù. µû¶ó¼- 79³ âµµ 10 10
1¿ùº Î ÅÍ 80³ âµµ 1¿ù »çÀÌ ÀÇ °¡ °Ý»ó½Â· üÀº 10% − 0.6% = 9.4%ÀÔ´ Ï ´ Ù. 79³ âµµ 1¿ùÀÇ º ñ¿ë y × 1.094 = $6 ⇒ y ≈ $5.4844 ÿ Á¤´ äÀº
(B)
18. In 1986 the book value of a certain car was 2 of the original purchase price, and in 1988 its 3 book value was 1 of the original purchase price. By what percent did the book value of this 2
car decrease from 1986 to 1988?
2 16 % 3
(A)
%° ¨ ¼Ò=
(B) 25%
1 3
(C) 33 %
(D) 50%
(E) 75%
° ¨ ¼ÒµÈ °ª ( ó À½ °ª -- ³ ª Áß °ª ) ó À½ °ª
¿©±â¼- ´  %°¨ ¼Ò¸ ¦ ±¸ÇÏ ´  °ø½Ä¿¡ ´ ëÀÔÇÏ ¸ é ÈÎ ¾À ½±°Ô Ç® ¼ö ÀÖ½À´ Ï ´ Ù.
% °¨ ¼Ò =
2 1 − 3 2 = 1 = 25% 2 4 3
ÿ Á¤´ äÀº
(B)
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19. The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by 20 percent. What percent of the projected attendance was the actual attendance? (A)
45%
(B) 56%
part
Percent(%) =
whole
(C) 64%
, ÀÌ ¹ ®Á¦ ¿¡ ¼- whole¿¡
(D) 75%
(E) 80%
ÇØ´ çÇÏ ´  °Í Àº projected attendanceÀÌ ¸ ç part¿¡
ÇØ´ çÇÏ ´  °Í Àº actual attendanceÀÔ´ Ï ´ Ù. ¿ÃÇØÀÇ attendanceÀ» A¶ó ÇÏ ¸ é projected attendance´  A × 125%(=1.25) = 1.25A °¡ µÇ°í actual attendance´Â A¿¡ ¼- 20%°¡ °¨ ¼ÒµÇ¾úÀ¸ ¹ Ç· Î A×80%(=0.8)
= 0.8A°¡ µË´ Ï ´ Ù. ¸ ¶Áö¸ · À¸ · Î À§ÀÇ percentÀÇ ½Ä¿¡ ´ ëÀÔÇÏ ¸ é
ÿ Á¤´ äÀº
0.8 A = 0.64 = 64% 1.25 A
(C)
20. On the first business day of a certain week, the opening price of a stock was 27 1 and the 8
closing price was 32 3 ; on the second day, the opening price was 32 3 and the closing price 4
4
was 30 7 . The decrease in price on the second day was what percent of the increase in price 8
on the first day? (A) 25%
(B)
1 33 % 3
(C) 40%
(D) 50%
(E)
2 66 % 3
A (the decrease in price) is what percent of B (the increase in price)? ¶ó´  ¹ ®Á¦ ´  ¾Æ· ¡ ¿Í °°ÀÌ ° è»êÇÏ ¸ é Á» ´ õ È¿À² ÀûÀÔ´ Ï ´ Ù. ⇒
Percent (%) =
part whole
=
A B
1 8
¼¼ decimalÀ» ¸ ðµÎ º и ð 8· Î ÅëÀÏ ÇÏ ¸ é 27 =
217 3 262 7 247 , 32 = , 30 = 8 4 8 8 8
µû¶ó¼- À§ÀÇ ¼ýÀÚ217, 262, 247·Î °è»êÇÏ ´  °Í ÀÌ ÈÎ ¾À º ü¸ £°Ú³ ׿ä.
15( 262 − 247 ) 1 = 33 % 45(262 − 217 ) 3 ÿ Á¤´ äÀº
À±ÅÂÈ-
(B)
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21. A circle graph shows how the budget of a certain company was spent: 63 percent for salaries, 12 percent for research and development, 6 percent for utilities, 5 percent for equipment, 4 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation? (A)
10°
(B)
18°
(C) 36°
(D) 90°
(E) 324 °
¿©±â¼ the remainder for transportationÀÇ percent´ Â10%(= 100% − (63+12+6+5+4)) ¹ ®Á¦ ¿¡ ¼- percent´  circleÀÇ °¢µµ¿Í º ñ· Ê ÇÏ ¹ Ç· Î 100 : 10 = 360 : x . ¿ ©±â¼- x ´  36µµ. ÿ Á¤´ äÀº
(C)
22. Mr. Kranter, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 40 percent of all the votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast? (A) 10%
(B) 12%
(C) 15%
(D) 17%
(E) 20%
All the votes cast = V· Î °¡ Á¤ÇÏ ¸ é Mr. Kranter°¡ ¾òÀ¸ · Á´  ÅõÇ¥¼ö´  ÃÖ¼ÒÇÑ Àüü ÅõÇ¥¼öÀÇ ¹ ÝÀÔ´ Ï ´ Ù. µû¶ó¼-
ÀÌ
»ç¶÷Àº
0.5VÀÇ ÅõÇ¥¼ö¸ ¦
¾ò¾î ¾ß ÇÏ ¸ é Áö±Ý±î Áö
40%, 0.4V, À»
ȹ µæÇß½À´ Ï ´ Ù. ±×·¯¸ é 0.5VÀ» À§ÇØ ÇÊ¿äÇÑ ÅõÇ¥¼ö´  0.1V°¡ µÇÁÒ: 0.5V = 0.4V + 0.1V. ´ ٽà ¹ ®Á¦ ¿¡ ¼- 942,568 votes´  Àüü votes castÀÇ 40%¶ó ÇßÀ¸ ´ Ï ¾ÕÀ¸ · Î ³ ² ¾ÆÀÖ´  votes´  ÀüüÀÇ 60%ÀÌ °í ÀÌ 0.6VÁß¿¡ ¼- 0.1V´  ¸ î percentÀ» Â÷ÁöÇÏ ´ °¡ ¸ ¦ °áÁ¤ÇÏ ¸ é ¹ ®Á¦ ³ ¡ !
0.1V = 0.17 = 17% 0.6V ÿ Á¤´ äÀº
(D)
23. In year Y imported machine tools accounted for 25 percent of total machine-tool sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars? (A)
9 x 80
(B)
13 x 20
(C)
80 9 x
(D)
20 x 13
(E)
80 x 9
The total sales of all machine tools = T¶ó ÇÏ ¸ é imported machine tools´  0.25TÀÌ °í ´ ٽà Japanese imports´  0.25×0.45T = 0.1125T= x billion dollars, Áï 0.1125T = x ¿©±â¼- T°ª À» ±¸ ÇÏ ¸ é:
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° - ÁÂ Set 5 GRE Math
T=
x
0.1125
ÿ Á¤´ äÀº
= x × 8.8888 ⋅ ⋅ ⋅
(E)
24. Ann can have her bicycle repaired for $50, or she can trade it in, as is, and receive $22 credit toward the purchase of a new bicycle that sells for $107. If Ann trades in her current bicycle, the cost to her of purchasing the new bicycle is what percent greater than the cost of having her current bicycle repaired? (A)
44%
(B) (C)
60% 70%
(D)
114%
(E)
170% = $107 − $22 = $85
The purchasing of the new bicycle
The cost of having her current bicycle repaired = $50 µû¶ó¼- 85 = 1.7 = 170% , Áï ÀÚÀü°Å¸ ¦ 50
»õ·Î ±¸ ÀÔÇÏ ´  º ñ¿ëÀÌ °í Ä¡ ´  º ñ¿ëº ¸ ´ Ù 70%°¡ ´ õ
µç´ Ù´  ¸ »ÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(C)
25. The original retail price of an appliance was 60 percent more than its wholesale cost. If the appliance was actually sold for 20 percent less than the original retail price, then it was sold for what percent more than its wholesale cost? (A) 20% (B) 28% (C) 36% (D) 40% (E) 42% The original retail price = 1.6 × wholesale cost ½ÇÁ¦ Æȸ ®´ Âprice = 0.8 × ( the original retail price) = 0.8 × 1.6 × wholesale price ½ÇÁ¦ Æȸ ®´  price = 1.28 × wholesale price, Áï ½ÇÁ¦ °¡ °ÝÀº wholesale priceº ¸´Ù 28% ´ õ º ñ½Î °Ô Æȸ °´ Ù´  Àǹ Ì ¿Í µ¿ÀÏ ÇÕ´ Ï ´ Ù. ÿ Á¤´ äÀº
À±ÅÂÈ-
(B)
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° - ÁÂ Set 5 GRE Math
26.
The cost C of manufacturing a certain product can be estimated by the formula C =
0.03rst 2 , where
r and s are the amounts, in pounds, of the two major ingredients
and t is the production time, in hours. If r is increased by 50 percent, s is increased by 20 percent, and t is decreased by 30 percent, by approximately what percent will the estimated cost of manufacturing the product change? (A)
40% increase
(B) 12% increase (C) 4% increase (D)
12% decrease
(E)
24% decrease
C =
0.03rst 2 ↵ϒ r ´ ë½Å¿¡ 1.5 r , s ´ ë½Å¿¡ 1.2 s , t ´ ë½Å¿¡ 0.7 t À» ´ëÀÔÇÏ ¸ é »õ· Î ¿î
°ª 1.5 × 1.2 × 0.49 = 0.8820À» ±¸ ÇÒ ¼ö ÀÖ°í ÀÌ °ª Àº ±âÁ¸ ÀÇ C°ª ¿¡ ¼- ¾à 12% ° ¨ ¼ÒÇÑ °ª ÀÌ ³ ׿ä. ÿ Á¤´ äÀº
(D)
27. In a certain community, 39,285 more apartments were converted to condominiums and sold in 1981 than in 1980. If this was a 30 percent increase, how many apartments were converted and sold in 1981? (A) 11,786 (B) 51,070 (C) 91,665 (D) 130,950 (E) 170,235 1980³ â¿¡ Äܵµ¹ Ì ´ Ï ¾öÀ¸ · Î ¹ Ù² ï ÈÄ Æȸ ° ¾ÆÆÄÆ®ÀÇ ÃÑ ¼ö = A¶ó °¡ Á¤ 1981³ â¿¡ Äܵµ¹ Ì ´ Ï ¾öÀ¸ · Î ¹ Ù² ï ÈÄ Æȸ ° ¾ÆÆÄÆ®ÀÇ ÃÑ ¼ö = A + 39,285 ¿©±â¼- 39,285ÀÇ Áõ°¡ ´  30%ÀÇ Áõ°¡ ¶ó ÇßÀ¸ ¹ Ç· Î ÀÌ °Í À» ½ÄÀ¸ · Î ¹ Ù² Ù¸ é:
% Áõ°¡ =
Áõ° ¡ µÈ °ª ( ³ ª Áß °ª -- ó À½ °ª ) ó À½ °ª
30%(0.3) =
( A + 39, 285) − A A
⇒ 0.3 A = 39.285 ⇒ A = 130,950
A°ª (1980)À» ±¸ ÇßÀ¸ ¹ Ç· Î 1981 ÀÇ °ª Àº 130,950 + 39,285(Áõ°¡ º Ð) = 170,235 ÿ Á¤´ äÀº
À±ÅÂÈ-
(E)
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° - ÁÂ Set 5 GRE Math
28. If the length and width of a rectangular diagram 12 inches by 8 inches are to be reduced by the same percent so that the diagram will exactly fit into a rectangular space 4.5 inches by 3 inches, by what percent should the dimensions be reduced? (A) 25% (B) 37.5% (C) 62.5% (D) 75% (E) 87.5% ° ¡ · Î 12 inches ¼¼· Î 8 inches°¡ ¶È °° Àº percent· Î ÁÙ¾î ¼- °¢°¢ 4.5 inches¿Í 3 inches· Î ÁÙÀÌ · Á¸ é
¸î
percent¸¸Å-
°¨ ¼ÒÇß´ÂÁö¸¦
±¸ ÇÏ · Á¸ é
12 inches × x
= 4.5 inches
⇒ x =0.3750(37.5%)
Áï 12 inches¿¡ 37.5%À» °öÇÑ °ª ÀÌ 4.5 inches¶ó´Â °Í Àº 12¿¡ ¼- 62.5%¸¸Å- ÁÙÀÎ ´ Ù´  ¸»°ú °°ÁÒ. ¿¹ ¸ ¦ µé¾î 10,000¿ø ÇÏ ´  ¹ °° Ç°ª ÀÌ 60% ÇÒÀÎ À» ÇÒ ¶§ ÇÒÀÎ °¡ °ÝÀ» ±¸ ÇÏ · Á¸ é 10,000×0.4 = 4,000¿øÀÌ µÇ°í ÀÌ ¹ °°ÇÀ» 60%¸ ¸ Å- ÇÒÀÎ À» ¹ ÞÀº °Í ÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(C)
29. In a certain orchestra, 30 percent of the musicians can play the violin and 24 percent can play the piano. If
1 of those who can play the violin can also play the piano, what percent of the 3
orchestra musicians can play neither the violin nor the piano? (A)
36%
(B)
44%
(C)
46%
(D)
54%
(E)
56%
MusiciansÀÇ ÁýÇÕÀ» MÀÌ ¶ó Çϸé violinÀ» ´ Ù· ç´ Â »ç¶÷ÀÇ ¼ö´Â 0.3M, ÇǾƳ ë¸ ¦ Ä¡ ´  »ç¶÷ÀÇ ¼ö´  0.24M, µÎ ¾Ç±â¸ ¦ ÇÔ² ² ´ Ù· ç´ Â »ç¶÷Àº 1 × 30% = 10% = 0.1 M 3
ÀÏ ¹ ÝÀûÀ¸ · Î
n( A ∪ B ) = n( A) + n( B ) − n( A ∩ B ) ⇒ 0.3M + 0.24M − 0.1M = 0.44M
Áï Àüü musiciansÀÇ 44%°¡ ¾Ç±â ÇÏ ³ ª ´  ´ Ù· ê ÁÙ ¾È´ Ù´  ¸ »ÀÌ °í ³ ª ¸ ÓÁö 56%(100 − 44)´  ÇǾƳ ë¿ Í ¹ ÙÀÌ ¿Ã¸ ° µÑ ´ Ù ´ Ù· ê ÁÙ ¸ 𸠥´ Ù´  Àǹ Ì ³ ׿ä. ¾Æ· ¡ °ø½Ä Âü°í ! Aµµ ¾Æ´ Ï °í ÿ Á¤´ äÀº
À±ÅÂÈ-
Bµµ ¾Æ´ Ñ ÁýÇÕ = U – (A U B) = A c ∩ B c =( A ∪ B )
c
(E)
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° - ÁÂ Set 5 GRE Math
30. In an office, 40 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service? (A)
48
(B) (C)
64 80
(D)
144
(E)
160
90% of workers = 10³ â ¹ Ì ¸ ¸ ÀÇ ±Ù¹ «ÀÚ, 10%´  ÃÖ¼ÒÇÑ 10³ â ÀÌ »ó ±Ù¹ «ÀÚ ⇒ 16 workers ¿©±â¼- Àüü workersÀÇ ¼ö¸ ¦ ±¸ ÇÒ ¼ö ÀÖÁÒ: 0.1 ×the workers = 16 ⇒ ÃÑ ±Ù¹ «ÀÚ´  160¸ í ´ ٽà 40%°¡ Àû¾î µµ 5³ â ÀÌ »óÀÇ ±Ù¹ «ÀÚ ⇒ 160¸í × 0.4 = 64¸ í , ÀÌ 64¸ í ¼Ó¿¡ ´  10³ â ÀÌ »ó ±Ù¹ «ÀÚ 16¸ í ÀÌ Æ÷ÇԵǾúÀ¸ ¹ Ç· Î 16¸ í À» »©ÁÖ¾î ¾ß Á¤´ äÀ» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù.: 64 − 16 = 48¸í ÿ Á¤´ äÀº
(A)
31. A factory has 500 workers, 12 percent of whom are women. If 80 additional workers are to be hired and all of the present workers remain, what percent of the new workers must be women in order to raise the total percent of female workers to 20 percent? (A) 70% (B) 50% (C) 32% (D) 20% (E) 8%
500 workers
580 workers(80¸ í °í ¿ë)
12%(=60¸ í ) female
20%(=116¸ í ) female Female workers °¡ 56¸ í Áõ°¡
¹ ®Á¦ ´  »õ· Î °í ¿ëÇÑ 80¸ í Áß¿¡ 56¸ í ÀÇ female workers°¡ Â÷ÁöÇÏ ´  º ñÀ² À» ±¸ ÇÏ ´  °Í ÀÌ ¹ Ç· Î
56 = 0.7 = 70% 80 ÿ Á¤´ äÀº
À±ÅÂÈ-
(A)
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° - ÁÂ Set 5 GRE Math
Q
R
10%
40% P
30 %
S 20%
32. A rectangular parcel of land is divided into four lots, P , Q, R , and S , as shown above. If 25 percent of the entire parcel of land is plowed and this includes 20 percent of lot P , what percent of the plowed land is not in lot P ? (A) 5%
(B) 6%
(C) 10%
(D) 76%
(E) 80%
Àüü ¶¥ÀÇ 25%°¡ ¹ çÀÌ °¥¾ÆÁ³ °í ±× ¶¥ Áß¿¡ P´  20%°¡ Æ÷ÇԵǾú´ä´ Ï ´ Ù. ±×· ¯¸é ÀÌ ¶§ P°¡ Â÷ÁöÇÏ ´  ÆÛ¼¾Æ®´  0.3 × 0.2 = 0.06= 6% (plowed land 25%Áß¿¡ P° ¡ 6%À» Â÷ÁöÇÔ) ¹ ®Á¦ ´ Â
°æÀÛµÈ
¶¥
Áß¿¡
P° ¡
¾Æ´ Ñ
¶¥ÀÇ
ÆÛ¼¾Æ®¸ ¦
±¸ ÇÏ ´ Â
¹ ®Á¦ ÀÌ ¹ Ç· Î
19( 25% − 6%) = 76% 25% ÿ Á¤´ äÀº
(D)
33. In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? (A) 400 (B) 625 (C) 1,250 (D) 2,500 (E) 10,000
Àüü ¹ °° í ±â ¼ö¸¦ NÀÌ ¶ó ÇÏ ¸ é : ÿ Á¤´ äÀº
50 N
=
2 50
⇒
N = 1,250
(C)
STOP
À±ÅÂÈ-
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Category 6 Power and Root Test
1. If a 5
= 9( 25)(45)(75) , then a =
(A)
5
(B)
9
(C)
10
(D)
15
(E)
25
2. If (124) 2
answer
= 15,376 , what is (124)(248) ?
(A) (15,376) 3
answer
(B) (15,376 × 2) 2 (C) (15,376) 2 (D) 15,376 + 2 (E) 15,376 × 2
3. If 36.15 × 10 3 = n × 10 6 , then n = (A) 0.03615 (B)
0.3615
(C)
3.615
(D)
3,615
(E)
36,150
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answer
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12 4. 5
+ 513 = answer
(A) (B) (C) (D) (E)
25
5 10 25 6(512 ) 1012 + 5 2(512 ) + 5
2
5.
1 3 1 − = 2 (A) (B) (C) (D) (E)
answer
1 64 25 36 49 64 35 36 63 64
2 ( 0 . 01 ) ( 0.014 ) + (0.01)( 0.0026) = 6. answer
(A)
0.0000166
(B)
0.0000274
(C)
0.00004
(D)
0.000166
(E)
0.0004
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7. Which of the following is greatest? (A) 52 + 1
answer
(B) 54 + 1 (C) 56 −1 (D) 53 × 52 (E) 58 ÷ 52
x k x n− k = 8. For positive integers k and n , if k < n and x ≠ 0 , then x n (A)
0
(B)
1
(C)
x k x n −k x 2( n −k )
(D) (E)
6 2 2 4 9. 18 x y − 2 x y =
answer
(A) (3 x − y)(3 x + y) (B) 2(3 y − x)(3 y + x) (C) 2 x2 y2 (3 x2 − y)2 (D) 9 x4 y2 (3 x (E)
− y)2 2 x2 y2 (3 x2 + y) (3 x2 − y)
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answer
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10. If
x = −1, the
1 1 1 1 1 + + + − = x 4 x 3 x 2 x 5
answer
12 5 4 (B) 5 (A)
(C)
−1
15 1 (D) − 5 21 (E) − 5
11. Which of the following values of x will make the equation x40 + x39 I. II.
−1
III.
1
(A)
II only
(B)
I and II only
(C)
I and III only
(D)
II and III only
(E)
I, II, and III
answer
0
12. If 2 2 x +6 (A) 2 (B)
1
(C)
0
(D)
−1 −2
(E)
= 0 true?
= 4 , then x = answer
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13.
216 is (A)
2 more than 215
(B)
16 more than 215
answer
1 of 2 32 2 (D) 2 times 2 8 (E) 2 times 215 (C)
14.
40 2 + 2(5)(40) + 5 2 is the square of answer
(A)
35
(B)
37.5
(C)
41
(D)
42.5
(E)
45
15. What is the units digit of (13) 4 (17) 2 ( 29)3 ? (A)
9
(B)
7
(C)
5
(D)
3
(E)
1
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answer
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16. Four hours from now, the population of a colony of bacteria will reach 1.28 × 10 6 . If the population of the colony doubles every 4 hours, what was the population 12 hours ago?
answer
(A) 6.4 × 10 2 (B) 8.0 × 10 4 (C) 1.6 × 10 5 (D) 3.2 × 10 5 (E) 8.0 × 10 6
17. The volume of a box with a square base is 54 cubic centimeters. If the height of the box is
answer
twice the width of the base, what is the height, in centimeters?
18.
(A)
2
(B)
3
(C)
4
(D)
6
(E)
9
18 + 32 = (A)
25
(B)
5 2 7 2 13 2 25 2
(C) (D) (E)
answer
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19.
0.0016 = answer
(A) 0.08 (B) 0.04 (C) 0.004 (D) 0.0008 (E) 0.0004
20.
1 3 25 ⋅ ⋅ = 2 2 10 2
answer
12 25 3 (B) 20 (A)
2 6 2 (D) 10 2 (E) 100 (C)
21. Of the following, which is the closest approximation to
8.9(198 .7) ? 18
(A) 3 (B) 7 (C) 10 (D) 30 (E) 100
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answer
784 =
22.
23.
(A)
28
(B)
32
(C)
38
(D)
56
(E)
112
answer
( 3 + 2)( 3 − 2) = answer
3 − 4 6 − 4
(A) (B)
(C) − 1 (D) 1 (E) 2
24.
7 − 63 = answer
(A) (B) (C) (D) (E)
−8 7 −3 7 −2 7 2 7 3 7
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25. If p = 0.2 and n = 100, then (A)
p(1 − p ) = n
answer
− 0.002 0.02 − 0.02
(B) (C) 0
(D) 0.04 (E) 0.4
26. If y > 0 , which of the following is equal to
48 y 3 ?
answer
(A) 4 y 3 y (B) 3 y 4 y (C) 2 12 y (D) 3 8 y (E) 16 y 3 y
27. If x ≠ 0 and x = 4 xy − 4 y 2 , then, in terms of y, x =
(A) 2 y (B) y (C) (D) (E)
y 2
− 4 y 2 1 − 4 y − 2 y
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answer
28. Of the following numbers, which one is third greatest? answer
(A) 2 2
−1
2 + 1 (C) 1 − 2 (D) 2 − 1 (E) 2 (B)
q=3 3 r = 1 + 2 3 s = 3 + 3 29. If q, r , and s are the numbers shown above, which of the following shows their order from
answer
greatest to least? (A) q, r , s (B) q, s, r (C) r , q, s (D) s, q , r (E) s, r , q
30.
463 is between answer
(A)
21 and 22
(B)
22 and 23
(C)
23 and 24
(D)
24 and 25
(E)
25 and 26
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31. Of the following, which is most nearly equal to (A) 3.1 (B)
3.2
(C)
3.3
(D)
3.4
(E)
3.5
10 ? answer
32. In a certain set of weights, for each positive integer
n less than 10, there is one weight that
answer
n
weighs 2 grams. What is the least number of such weights with a combined weight of 108 grams? (A)
Three
(B)
Four
(C)
Five
(D)
Six
(E)
Seven
33. (2 2 (A) (B) (C) (D) (E)
− 1)(2 2 + 1)(2 4 + 1)(2 8 + 1) = ? 216 − 1 216 + 1 2 32 − 1 2128 − 1 216 (216 − 1)
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answer
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34. If s , true?
u , and v are positive integers and 2 s = 2 u + 2 v , which of the following must be
answer
s = u u ≠ v s > v
I. II. III. (A)
None
(B)
I only
(C)
II only
(D)
III only
(E)
II and III
35. If t = 2 x +1 , then in terms of t , 4 x is (A) t
answer
t 2 (C) t 2 t 2 (D) 2 t 2 (E) 4 (B)
36. If
x is a positive number and
1 the square root of x is equal to 2 x , then x = 2
1 16 1 (B) 4 1 (C) 2 (A)
(D) 2 (E) 8
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answer
37. If N = 2 3 ⋅ 5 7 ⋅ 9 3 , what is the sum of the different positive prime factors of (A) 17 (B)
16
(C)
15
(D)
10
(E)
7
N ?
38. If an integer raised to the fifth power is odd, then the integer must be which of the following? I.
Odd
II.
Even
III.
Positive
(A)
I only
(B)
II only
(C)
III only
(D)
I and III
(E)
II and III
39. A computer can perform 1,000,000 calculations per second. At this rate, how many hours will it take this computer to perform the 3.6×10 calculations required to solve a certain problem? 11
(A)
60
(B)
100
(C)
600
(D)
1,000
(E)
6,000
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answer
answer
answer
x = 4 and y = 16 , then
40. If
(A)
1 3
(B)
1 2
x + y is closest to which of the following? xy (C)
3 4
(D)
7 8
answer
(E) 1
41. Of the following sums, which is greatest? (A) (B) (C) (D) (E)
42.
1 1 1 1 + + + 2 3 4 5 1 1 1 1 + + + 2 2 32 4 2 5 2 1 1 1 1 + + + 2 2 23 24 25 1 1 1 1− + − 2 3 4 1 1 1 1 + + + 2 3 4 5
answer
74 − 1 =? 8(7 2 + 1) (A)
6
(B)
6.25
(C)
7
(D)
8
(E)
48
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answer
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¼öÇÐÇؼ³
1. If a 5
Category 6 Power and Root Test
= 9( 25)(45)(75) , then a =
(A)
5
(B)
9
(C)
10
(D)
15
(E)
25
a 5 = 9( 25)( 45)(75) = 32 (5 2 )(32 × 5)(32 × 52 ) = 35 × 55 &
´ äÀº (D)ÀÔ´ Ï ´ Ù.
2. If (124) 2
= 15,376 , what is (124)(248) ?
(A) (15,376) 3 (B) (15,376 × 2) 2 (C) (15,376) 2 (D) 15,376 + 2 (E) 15,376 × 2
(124)(248) = 2(124)2 = 2 × 15,376 ´ äÀº (D)ÀÔ´ Ï ´ Ù.
&
3. If 36.15 × 10 3 = n × 10 6 , then n = (A) 0.03615 (B)
0.3615
(C)
3.615
(D)
3,615
(E)
36,150
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36.15 × 103 = (0.03615 × 103 ) × 103 = 0.03615 × 103+3 &
´ äÀº (A)ÀÔ´ Ï ´ Ù.
12 4. 5
+ 513 =
(B)
5 25 10 25
(C)
6(512 )
(D) (E)
1012 + 5 2(512 ) + 5
(A)
512 + 513 = 512 (1 + 5 ) &
´ äÀº (C)ÀÔ´ Ï ´ Ù.
5.
1 3 1 − = 2
2
1 64 25 (B) 36 49 (C) 64 (A)
35 36 63 (E) 64 (D)
2
1 3 1 2 7 2 1 − = 1 − = 2 8 8 &
´ äÀº (C)ÀÔ´ Ï ´ Ù.
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6.
(0. 01) 2 ( 0.014 ) + (0.01)( 0.0026) = (A)
0.0000166
(B)
0.0000274
(C)
0.00004
(D)
0.000166
(E)
0.0004 2
1 14 1 26 (0.01) ( 0.014 ) + ( 0. 01)( 0.0026) = 2 3 + 2 4 10 10 10 10 2
´ äÀ äÀºº (B)À (B)ÀÔ Ô´ Ï ´ Ù.
&
7. Which of the following is greatest? (A) 52 + 1 (B) 54 + 1 (C) 56 −1 (D) 53 × 52 (E) 58 ÷ 52
53 × 52 = 53+2 = 55 , 58 ÷ 52 = 58−2 = 56 ´ äÀ äÀºº (E)À (E)ÀÔ Ô´ Ï ´ Ù.
&
x k x n− k < n and x ≠ 0 , then = 8. For positive integers k and n , if k < x n (A)
0
(B)
1
(C)
x k x n −k x 2( n −k )
(D) (E)
x k x n−k = x k +n−k −n = x 0 n x &
´ äÀ äÀºº (B)À (B)ÀÔ Ô´ Ï ´ Ù.
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6 2 2 4 9. 18 x y − 2 x y =
(A) (3 x − y)(3 x + y) (B) 2(3 y − x)(3 y + x) (C) 2 x2 y2 (3 x2 − y)2 (D) 9 x4 y2 (3 x
− y)2
(E) 2 x2 y2 (3 x2 + y) (3 x2 − y)
18 x6 y 2 − 2 x2 y4 = 2 x2 y 2 (9 x4 − y2 ) = 2 x2 y 2 (3 x2 + y)(3 x2 − y) ´ äÀ äÀºº (E)À (E)ÀÔ Ô´ Ï ´ Ù.
&
10. If
x = −1, the 12 5
(A)
1 1 1 1 1 + + + − = x 4 x 3 x 2 x 5 4 1 (B) (C) − 5 15
(D)
−1 5
(E)
−
21 5
´ äÀ äÀºº (D)À (D)ÀÔ Ô´ Ï ´ Ù.
&
11. Which of the following values of x will make the equation x40 + x39 I. II.
−1
III.
1
= 0 true?
0
(A) (A) II only onl y (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III ¾ç ¼ö ¶Ç ¶ Ç´  À½¼öÀ öÀÇ Ç Â¦ ¼ö ½ÂÀº ¾ðÁ ðÁ¦¦ ³ ª ¾ç ¼öÀ öÀÔ Ô´ Ï ´ Ù. ex. 2 2
= 4, (−2)2 = 4
ÇÏ Áö¸ ¸ À½¼öÀÇ È¦ ¼ö ½Â ½ÂÀº ¾ðÁ¦ ³ ª À½¼öÀÓÀ» ±â ¾ï ÇØ¾ß ÇÕ´ Ï ´ Ù. ex. (−2)3 &
= −8, (−3)3 = −27
´ äÀ äÀºº (B)À (B)ÀÔ Ô´ Ï ´ Ù.
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12. If 2 2 x +6 (A) (A) 2
= 4 , then x = (B)
1
(C)
0
(D)
− 1
−2
(E)
úÀ¸¸ ¹ Ç· Î exponen exponent¸ t¸ ¸ ° ° ¾ÆÁö¸ é µË´ µË´ Ï ´ Ù. 2 x + 6 = 2 2 2 x+6 = 2 2 base¸ ¦ ° ° ° Ô ÇØÁÖ¾úÀ ´ äÀ äÀºº (E)À (E)ÀÔ Ô´ Ï ´ Ù.
&
13.
216 i s (A) (A)
2 more than 215
(B)
16 more than 215
1 of 2 32 2 (D) 2 times 2 8 (E) 2 times 215 (C)
base°¡ ase° ¡ ° ° Àº ¼öÀÇ ° ö¼ÀÀº exponen exponent° t° £¿¡ µ¡ ¼À° ú ° ° ½À´ Ï ´ Ù.
2 × 215 = 2 1+15 = 216 ´ äÀ äÀºº (E)À (E)ÀÔ Ô´ Ï ´ Ù.
&
14.
40 2 + 2(5)(40) + 5 2 is the square of (A) (A)
35
(B)
37.5
(C)
41
(D)
42.5
(E)
45
40 2 + 2(5)( 40) + 5 2 °ϒ ¾î ¶² ¼öÀÇ Á¦ ° öÀÎ Áö¸ ¦ (square) ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ´ äÀ äÀ»» ° è»ê è»êÇ ÇÏ ´  ¹ æ¹ ý¿ ý¿¡¡ ´  ´ ÙÀ½ÀÇ µÎ ° ¡ Áö° ö°¡¡ ÀÖ½À´ Ï ´ Ù. 2 2 + + 40 2 ( 5 )( 40 ) 5 ℵ≈° è»ê ÇÏ ¿© 2,02 i) ½Ç ½ÇÁ¦ · Î 2,025¸ 5¸ ¦ ¼ÒÀÎ ¼ö º ÐÇØÇÏ ¿© ´ äÀ äÀ»» ã´  ¹ æ¹ ýÀÔ´ Ï ´ Ù. 2 ii) 40
2 + 2(5)(40) + 5 2 ℵ∩ÀÏ ÀÇ ÀÚ¸ ® ¼ýÀ ýÀÚ Ú° ¡ 5 ¿¡ ÀÇÇؼ-
2 µû¶ó¼-- 40 µû¶ó¼
° á Á¤µÇ ¤µÇ´´  °Í ° Í À» ¾Ë ¾Ë ¼ö ÀÖ ÀÖ½À´ Ï ´ Ù.
+ 2(5)(40) + 5 2 ℵ∩ÀÏ ÀÇ ÀÚ¸ ® ¼ö´  5À 5ÀÔ Ô´ Ï ´ Ù. º ¸ ±â¿¡
ÁÖ¾î Áø ¼ýÀÚµé Áß Á¦ Á¦ ° öÇ öÇÏÏ
2 2 2 + + 40 2 ( 5 )( 40 ) 5 40 ℵ≡ ÀÌ ¿ © ÀÏ ÀÇ ÀÚ¸ ® ¼ö°¡ ö° ¡ 5ÀÎ º ¸ ±â´  (A), (E)° ¡ ÀÖ½À´ Ï ´ Ù. ÀÌ Á¦ 2 ÇÏ ³ ª ÀÇ Ç×ÀÌ ±â ¶§¹ ¶ §¹ ®¿¡ 35 º ¸ ´ ÙÅ« ¼ö¶ ¼ö¶ó´ ó´  ° Í À» ¾Ë ¾Ë ¼ö ÀÖ ÀÖ½À´ Ï ´ Ù.
&
´ äÀ äÀºº (E)À (E)ÀÔ Ô´ Ï ´ Ù.
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15. What is the units digit of (13) 4 (17) 2 ( 29)3 ? (A)
9
(B)
7
(C)
5
(D)
3
(E)
1
“ units digit” digit”À ÀÌ ¶ õ ÀÏ ÀÏ ÀÚ¸ ®ÀÇ ¼ýÀÚ¸ ¦ Àǹ Ì ÇÕ´ Ï ´ Ù. (13) 4 (17) 2 ( 29)3 ÀÇ ÀÏ ÀÚ¸ ® ¼ýÀ ýÀÚ Ú¸ ¦ ¾Ë±â À§ÇØ À§ÇØ ¼- ´  Àüà üü ¼ ¼ýÀÚ° £ÀÇ °è»êÀ °è»ê Àº »ý· «Ç «ÇÏÏ ° í ´ ÜÁö ° ¢ ¼ýÀÚÀÇ ÀÏ ÀÏ ÀÚ¸ ® ¼ýÀÚ¸ ¸ À» ° è »ê »êÇ ÇÏ ¸ é µË´ Ï ´ Ù. Áï Áï , 4 ½ÂÇÑ ¼ýÀÚÀÇ ÀÏ ÀÏ ÀÚ¸ ® ¼ö´  1 , 17 4 ÀÇ ÀÏ ÀÚ¸ ® ¼öÀÎ 7À» Á¦ Á¦ ° öÇ öÇÏÏ ¸ é 13 4 ÀÇ ÀÏ ÀÚ¸ ® ¼öÀÎ 3À» 4½ 3 ÀÏ ÀÚ¸ ® ¼ö´ ö´Â  9, 29 ÀÇ ÀÏ ÀÚ¸ ® ¼öÀ öÀÎÎ 9¸ ¦ 3½ÂÇÑ ¼ýÀ ýÀÚ ÚÀÇ ÀÏ ÀÚ¸ ® ¼ö´ ö´Â  9ÀÔ´ Ï ´ Ù. ÀÌ ÀÌ · ¸ ÄÉ ±¸ ±¸Ç ÇØÁø ÀÏ ÀÚÀÇ ¼ýÀ ýÀÚ Ú¸ ¦ ° öÇ öÇÏÏ ¸ é ¹ ®Á¦ ¿ ¡ ´ ë ÇÑ ´ ä À» ÇÒ ÇÒ ¼ö ÀÖ ÀÖ½À´ Ï ´ Ù. &
´ äÀ äÀºº (E)À (E)ÀÔ Ô´ Ï ´ Ù.
16. Four hours from now, the population of a colony of bacteria will reach 1.28 × 10 6 . If the population of the colony doubles every 4 hours, what was the population 12 hours ago? (A) 6.4 × 10 2 (B) 8.0 × 10 4 (C) 1.6 × 10 5 (D) 3.2 × 10 5 (E) 8.0 × 10 6 bacteriaÀÇ ¼ö° ¼ö°¡¡ 4½Ã° £ ÈÄ¿¡ 1.28 × 10 6 ∝∪×∧° ÇÕ´ Ï ´ Ù. Bacteria BacteriaÀ ÀÇ ¼ö´  4½Ã° £ ¸ ¶´ Ù µÎ ¹ è°¡ µÈ ´ Ù° í ÇÕ´ Ï ´ Ù. ÀÌ ÀÌ · ¯Ç ¯ÇÑ Ñ Á¶° ¶°Ç Ç ÇÏ ÇÏ ¿¡ ¼- 12½Ã° £ÀÌ ÀüÀÇ bacter bacteria ia ¼ö¸ ¼ö¸ ¦ ¹ ° ¾î º ¸ ° í ÀÖ½À´ Ï ´ Ù. 4½Ã° £ ÈÄ ÈÄ ¿¡ bacter bacteria ia ¼ö°¡ 1.28 × 10 6 ℵ⊂∂⌠° Ç߱⠶§¹ ®¿ ¡ ÇöÀ öÀçç ÀÇ ¼ö´ ö´Â  6.4 ×10 5 ℵ™×∉×∧ .4½Ã .4½ ð £ ¸ ¶´ Ù ¼ö ° ¡ 2¹ è ¾¿ Áõ° Áõ° ¡ ÇÑ´ Ù° í Ç߱⠶§¹ ¶ §¹ ®¿ ¡ ´ ÙÀ½ÀÇ ½ÄÀ» °è ° è »ê »êÇ ÇØ ÁÖ¸ é µË´ µË´ Ï ´ Ù.
6.4 × 105 = 8.0 × 104 3 2 &
´ äÀ äÀºº (B)À (B)ÀÔ Ô´ Ï ´ Ù.
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17. The volume of a box with a square base is 54 cubic centimeters. If the height of the box is twice the width of the base, what is the height, in centimeters? (A) (A)
2
(B)
3
(C)
4
(D)
6
(E) 9
Á¤» ¤»çç° ¢Ç ¢ÇüÀ üÀÇ ¹ Ù´ Ú¸ é À» ° ¡ Áö° ö°íí ÀÖ´  »óÀÚÀÇ(a box b ox with w ith a squar sq uaree base) ba se) üÀûÀ ûÀÌÌ 54cm 54cm3 (54 cubic centimeters)À centimeters) ÀÏ ¶§ »óÀ »óÀÚ ÚÀÇ ³ ôÀÌ ´  ¹ Ù´ Ú¸ é Æø ±æÀ ±æÀÌ ÀÇ 2¹ è¶ è¶ó° ó°íí ÇÕ´ Ï ´ Ù. ÀÌ ÀÌ · ² ¶§ ³ ôÀ ôÀÌÌ ÀÇ ±æÀÌ ¸ ¦
ÀÔ´ Ï ´ Ù ¹ ° ¾î º ¸ ° í ÀÖ½À´ Ï ´ Ù. ¿ì ¿ ì ¼± Á÷À° ¸ é üÀÇ Ã¼ÀûÀ ûÀ»» ±¸ ÇÏ ´  ° ø½ ø½Ä ÄÀº v = l × h × w ÀÔ . ¹ ®Á¦ ¿¡ ÁÖ
= w ) ³ ôÀ ¾î Áø Á÷À Á÷À° ¸ éà éü ¼´  ¹ Ù´ Ú¸ é ÀÇ Æø° ú ³ ÐÀÌ ° ¡ ° ° ° í ( l = ôÀÌÌ ° ¡ ÆøÀÇ µÎ µÎ ¹ è ÀÌ ±â( h = 2l ) ¶§¹ ®¿¡ ´ ÙÀ½ ½ÄÀ» Ç®¸ é ³ ôÀ ôÀÌÌ ¸ ¦ ¾Ë ¼ö ÀÖ ÀÖ½À´ Ï ´ Ù.
54 = 2l 3 ´ äÀ äÀºº (D)À (D)ÀÔ Ô´ Ï ´ Ù.
&
18.
18 + 32 = (A)
25
(B)
5 2
(C)
7 2
(D)
13 2 25 2
(E)
18 + 32 = 3 2 + 4 2 = 7 2 ´ äÀ äÀºº (C)À (C)ÀÔ Ô´ Ï ´ Ù.
:
19.
0.0016 = (A)
0.8
(B)
0.4
(C)
0.04
(D)
0.008
(E)
0.004
0.0016 = &
:
16 = 4 10000 100
´ äÀ äÀºº (C)À (C)ÀÔ Ô´ Ï ´ Ù.
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20.
1 3 25 ⋅ ⋅ 2 = 2 2 10 (A)
12 25
(B)
3 20
2 6 2 (D) 10 2 (E) 100 (C)
1 3 25 3 × 2 5 3 × 2 5−1 3 × 2 4 −2 12 ⋅ ⋅ 2 = = 2 = = 2 25 25 × × 10 2 10 2 25 2 2 &
´ äÀ äÀºº (A)À (A)ÀÔ Ô´ Ï ´ Ù.
8.9(198 .7) ? 18
21. Of the following, following, which is the closest approximation to (A) (A)
3
(B)
7
(C)
10
(D)
30
(E)
100
8.9(198.7 ) ≅ 9 × 200 18 18 &
´ äÀ äÀºº (C)ÀÔ´ Ï ´ Ù.
784 =
22. (A)
28
(B)
32
(C)
38
(D)
56
(E)
112
, 784 = 2 2 × 7 = 28 784 = 2 4 × 7 2 ℵ⊂≠∩•∈ &
´ äÀ äÀºº (A (A)À )ÀÔ Ô´ Ï ´ Ù.
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23.
( 3 + 2)( 3 − 2) = 3 − 4
(A)
(B)
6 − 4
(C)
−1
(D) 1
(E) 2
( 3 + 2)( 3 − 2) = ( 3 ) 2 − 4 = −1 ´ äÀº (C)ÀÔ´ Ï ´ Ù.
&
24.
7 − 63 =
(B)
−8 7 −3 7
(C)
−2 7
(D)
2 7 3 7
(A)
(E)
7 − 3 2 × 7 = 7 − 3 7 = −2 7 ´ äÀº (C)ÀÔ´ Ï ´ Ù.
&
25. If p = 0.2 and n = 100, then (A)
p(1 − p ) = n
− 0.002 0.02 − 0.02
(B) (C) 0
(D) 0.04 (E) 0.4
p(1 − p ) = 0.2 × 0.8 = 0.16 = 0.4 n 100 100 10 &
´ äÀº (D)ÀÔ´ Ï ´ Ù.
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48 y 3 ?
26. If y > 0 , which of the following is equal to (A) 4 y 3 y (B) 3 y 4 y (C) 2 12 y (D) 3 8 y (E) 16 y 3 y
48 y 3 = 2 4 × 3 × y 3 = 22 y 3 y = ´ äÀº ( A)ÀÔ´ Ï ´ Ù.
&
27. If x ≠ 0 and x = 4 xy − 4 y 2 , then, in terms of y, x = (A) 2 y (B) y (C) (D) (E)
y 2
− 4 y 2 1 − 4 y − 2 y
¾ç º ¯À» Á¦ °öÇÑ ÈÄ¿¡ Á¤¸ ®ÇÏ ¸ é ´ ÙÀ½°ú ° °½À´ Ï ´ Ù.
( x )2 = ( 4 xy − 4 y 2 )
2
&
x 2 = 4 xy − 4 y 2
x 2 − 4 xy + 4 y 2 = 0
( x − 2 y )2 = 0
´ äÀº (A)ÀÔ´ Ï ´ Ù.
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28. Of the following numbers, which one is third greatest? (A) 2 2
−1
2 + 1 (C) 1 − 2 (D) 2 − 1 (B)
(E)
2
2 + 1 > 2 2 −1 > 2 > 2 −1 > 1 − 2 ´ äÀº (E)ÀÔ´ Ï ´ Ù.
::
::
q=3 3 r = 1 + 2 3 s = 3 + 3 29. If q, r , and s are the numbers shown above, which of the following shows their order from greatest to least? (A) q, r , s (B) q, s, r (C) r , q, s (D) s, q , r (E) s, r , q
q ¿Í r ÀÇ Å©±â¸ ¦ º ñ±³ ÇÏ ±â À§Çؼ- µÎ ¼ö¸¦ Â÷°¨ ÇÑ °á°ú°¡ ¾ç¼öÀÎ Áö À½¼öÀÎ Áö¸ ¦ º ñ±³ ÇØ º ¸ ¸ é ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù.
q − r = 3 3 − (1 + 2 3 ) = 3 − 1 ,
3 Àº 1º ¸´ Ù Å« ¼ö ÀÔ´ Ï ´ Ù. µû¶ó¼- q − r Àº ¾ç¼öÀÌ ¹ Ç· Î
q > r ÀÔ´ Ï ´ Ù. . µû¶ó¼- r − s ´  À½¼öÀÌ ¹ Ç· Î s > r r − s = 1 + 2 3 − (3 + 3 ) = 3 − 2 , 2´  4 ÀÔ´ Ï ´ Ù
q − s = 3 3 − (3 + 3 ) = 2 3 − 3 , 2 3 Àº
12 , 3 ˼
9 ÀÌ ¹ Ç· Î q − s ´  ¾ç¼öÀÌ ¹ Ç· Î
q > r ÀÔ´ Ï ´ Ù. µû¶ó¼- q > s > r ÀÔ´ Ï ´ Ù. &
´ äÀº (B)ÀÔ´ Ï ´ Ù.
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463 is between
30.
(A)
21 and 22
(B)
22 and 23
(C)
23 and 24
(D)
24 and 25
(E)
25 and 26
463 À» Á¦ °öÇÏ ¸ é 463ÀÔ´ Ï ´ Ù. µû¶ó¼- º ¸ ±â¿¡ ÁÖ¾î Áø ¼ýÀÚ¸ ¦ Á¦ °öÇÏ ¿© 463ÀÌ ¼ÓÇÏ ´  ±¸ °£À» °¡ Áö°í ÀÖ´  º ¸ ±â° ¡ ´ äÀÌ µË´ Ï ´ Ù.
212 = 441 , 22 2 = 484 ℵ™×∉×∧ µû¶ó¼- 21 463 < 22 . ´ äÀº (A)ÀÔ´ Ï ´ Ù.
&
31. Of the following, which is most nearly equal to (A) 3.1 (B) 3.2 (C) 3.3
10 ? (D)
3.4
(E)
3.5
º¸±â¿¡ ÁÖ¾î Áø ¼öµéÀ» Á¦ °öÇÏ ¿© 10¿¡ °¡ Àå ° ¡ ±î ¿î °Í À» °í ¸ £¸ é µË´ Ï ´ Ù. (Å©±â ´ ë¼Ò¿Í °°Àº ¹ ®Á¦ ¸ ¦ Ç® ¶§ º ¸ ±â¿¡ ¼- º Î ÅÍ ´äÀ» ã´  °æ¿ì ¶ó¸é º ¸ ±â(C)º Î ÅÍ ´ ëÀÔÇØ º ¸ ´  °Í ÀÌ ÁÁ½À´ Ï ´ Ù.)
3.3 2 = 10.89 , 3.2 2 = 10.24 , 3.12 = 9.61 ´ äÀº (B)ÀÔ´ Ï ´ Ù.
&
32. In a certain set of weights, for each positive integer
n less than 10, there is one weight that
n
weighs 2 grams. What is the least number of such weights with a combined weight of 108 grams? (A) Three
(B) Four
(C) Five
(D) Six
(E) Seven
n
Ãß(weight) ¼¼Æ® ³ »¿¡ °¢°¢ÀÇ Ãß ¹ «°Ô´  2 gram ÀÌ °í n Àº 10º ¸ ´ Ù ÀÛÀº ¾çÀÇ Á¤¼öÀÔ´ Ï ´ Ù ( 1,2.3,…9). Áï 21, 2 2 ,2 3 ,⋅ ⋅ ⋅,2 9 ℵ∩¹ «°Ô°¡ ³ ª °¡ ´  ÃßµéÀ» ÇÏ ³ ª ¾¿ Á¶ÇÕÇÏ ¿© 108 gramÀÌ µÇµµ· Ï ÇÏ ´  ÃßÀÇ ÃÖ¼Ò °³ ¼ö¸ ¦
¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.
Ãß ¼¼Æ® ³ »¿¡ ÀÖ´  °³ º ° ÃßÀÇ ¹ «° Ô´  2,2 2 ,2 3 ,...2 9 gramÀÔ´ Ï ´ Ù. µû¶ó¼- , ´ ÙÀ½ÀÇ 4° ³ ÀÇ Ã߸ ¦ °¡ Áö°í 108gramÀ» ¸ ¸ µé ¼ö ÀÖ½À´ Ï ´ Ù. ´ Ü 2 7
= 128 ° 2 8 ,2 9 µéÀº
108º ¸ ´ Ù °ª ÀÌ Å©¹ Ç· Î ÀÏ
´ Ü Á¦ ¿Ü½ÃÄÑ¾ß ÇÏ ÁÒ: ( 22
= 4 ) + ( 2 3 = 8 ) + ( 2 5 = 32 ) +( 2 6 = 64 ) = 108
ÿ ´ äÀº
(B)ÀÔ´ Ï ´ Ù.
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33. (2 2 (A) (B) (C) (D) (E)
− 1)(2 2 + 1)(2 4 + 1)(2 8 + 1) = ? 216 − 1 216 + 1 2 32 − 1 2128 − 1 216 (216 − 1)
− b 2 ⇒ (2 2 − 1)(2 2 + 1) = 2 4 − 1 ⇒ (2 4 − 1)(2 4 + 1) = 2 8 − 1 ⇒ (2 8 − 1)(2 8 + 1) = 216 − 1
°ø½Ä: (a + b)( a − b ) = a 2
ÿ Á¤´ äÀº
34. If s , true?
(A)
u , and v are positive integers and 2 s = 2 u + 2 v , which of the following must be s = u u ≠ v s > v
I. II. III. (A)
None
(B)
I only
(C)
II only
(D)
III only
(E)
II and III
ÀÌ · ± ¹ ®Á¦ ÀÇ ÇÔÁ¤Àº s , u , and v °¡ 0ÀÌ ¾Æ´ Ï ¶ó´  °Í ÀÔ´ Ï ´ Ù. µû¶ó¼¾çÀÇ Á¤¼öÀÌ ¹ Ç· Î s > v ´  Ç×»ó trueÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
s , u , and v °¡ Ç×»ó
(D)
35. If t = 2 x +1 , then in terms of t , 4 x is
t (B) 2
(A) t
2
(C) t
t 2 (D) 2
t 2 (E) 4
2
t 2 t t = 2 × 2 ⇒ 2 = ⇒ 4 x = , ÇÑ °¡ Áö À¯ÀÇÇÒ »çÇ×Àº (2 x ) = 2 2 x ⇒ 4 x •∈ ¹ Ù² î ´  ° Í 2 2 x
x
2
ÀÌ Áö 2 x · Î ¹ Ù² î ´  °Í ÀÌ ¾Æ´ Õ´ Ï ´ Ù. ÁÖÀÇÇÏ ¼¼¿ä! ÿ Á¤´ äÀº (E)
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36. If
x is a positive number and
(A)
1 16
(B)
1 4
1 the square root of x is equal to 2 x , then x = 2 1 (C) (D) 2 (E) 8 2
2 °¡ µÇ¹ Ç· Î the square root of x ´  x ° ¡ µË´ Ï ´ Ù. µû¶ó¼1 1 x = 2 x ⇒ x = 2 16
square root of 2 =
ÿ Á¤´ äÀº
(A)
37. If N = 2 3 ⋅ 5 7 ⋅ 9 3 , what is the sum of the different positive prime factors of (A) 17 (B) 16 (C) 15 (D) 10 (E) 7
N ?
N = 2 3 ⋅ 5 7 ⋅ 9 3 , ¿©±â¼- ¼ÒÀÎ ¼ö( prime factors)ÀÇ ÇÕÀ» ±¸ ÇÏ ¸ é 9 3 = 36 ¿©±â¼- ¼ÒÀÎ ¼ö´ Â2, 3, 5ÀÌ °í ÀÌ µéÀÇ ÇÕÀº 10. ÿ Á¤´ äÀº
(D)
38. If an integer raised to the fifth power is odd, then the integer must be which of the following? (I)
Odd
(II)
Even
(III)
Positive
(A)
I only
(B) II only
(C) III only
(D) I and III
(E) II and III
ÇÑ Á¤¼öÀÇ 5Á¦ °öÀÌ È¦ ¼öÀÌ ¸ é ÀÌ Á¤¼ö´  Ç×»ó Ȧ ¼öÀÌ °í À½ÀÇ Á¤¼öµµ °¡ ´ ÉÇÏ ÁÒ. µû¶ó¼- Ç×»ó ÂüÀÎ °Í Àº Ȧ ¼öÀÏ ¶§ ÀÌ È¦ ¼öÀÇ 5Á¦ °öµµ Ç×»ó Ȧ ¼öÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(A)
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39. A computer can perform 1,000,000 calculations per second. At this rate, how many hours will it take this computer to perform the 3.6×1011 calculations required to solve a certain problem? (A)
60
(B) 100
(C) 600
(D) 1,000
(E) 6,000
1ÃÊ¿¡ 1,000,000 = 10 6 ÀÇ °è»êÀ» ó ¸ ®ÇÏ ´  ÄÄÇ»ÅÍ °¡ 3.6×1011 ℵ∩°è»êÀ» ó ¸ ®ÇÏ ´ µ¥ °É¸ ®´ Â
3.6 × 1011 = 3.6 × 10 5 per 6 10
½Ã°£Àº
second.
´ Ù½Ã
3.6 × 10 5 ℵ≈ hours·Î
¹ Ù² ãÁÖ¸ é
3.6 × 10 5 = 100 hours × 60 60 ÿ Á¤´ äÀº
40. If
(B)
x + y is closest to which of the following? xy
x = 4 and y = 16 , then 1 3
(A) ÀÏ´ Ü x
(B)
1 2
(D)
= 4 ¿Í y = 16 À» ´ ëÀÔÇÏ ¸ é
5 ¿¡ ´ ëÀÔÇÏ ¸ é ±Ù»çÄ¡ ´  4
ÿ Á¤´ äÀº
3 4
7 8
(E) 1
+ y ≠ x + y
x + y 1 1 , ¿©±â¿¡ x = + xy x y ÀÌ °Í À»
(C)
5 °¡ 4
µË´ Ï ´ Ù.
5 ≈2.24
1 2
(B)
41. Of the following sums, which is greatest? (A) (B) (C) (D) (E)
1 + 1 + 1 + 1 2 3 4 5 1 1 1 1 + + + 2 2 32 4 2 5 2 1 1 1 1 + + + 2 2 23 24 25 1 1 1 1− + − 2 3 4 1 1 1 1 + + + 2 3 4 5
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º и ðÀÇ ÇÕÀÌ °¡ Àå ÀÛÀº °Í ÀÌ °á°úÀûÀ¸ · Î ´  °¡ Àå Å« °ª ÀÌ µË´ Ï ´ Ù. µû¶ó¼- º и ðÀÇ ÇÕÀÌ °¡ Àå ÀÛÀº (A)°¡ Á¤´ äÀÌ µÇÁÒ. ÿ Á¤´ äÀº
(A)
74 − 1 = 2 + 8 ( 7 1 ) 42. (A)
6
(B)
6.25
(C)
7
(D)
8
(E)
48
7 4 − 1 = 7 2 − 1) 7 2 + 1) = (7 + 1)( 7 − 1)(7 2 + 1) ℵ≈À§¿¡ ½Ä¿¡ ´ ëÀÔÇÏ ¸ é ³ ² ´  °Í Àº 6ÀÌ ³ ׿ä. ÿ Á¤´ äÀº
(A)
ø½ Ä m
l
x
l
m
l
x
= x
x • • • x (X°¡ m°³ )
a m b = m ab
m
×
m l
×⋅
x
a b
m
n
m+ n
=x =
a b
m
x m−n , m > n x = = 1 , m n x n 1 x − , m < n m
l
n m
m n
l
l
( n a)m np
l
l
(x
m n
0
l
x
l
m an
a
= n am
amp = n a m
)
(xy)
l
n m
a = mn a =
m
= 1,
=x
m•n
= x m y m (´ Ü x
≠
0) ; x
−n
= 1n x
= n am
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GRE M ath
Set 7-1
Category 7 A l gebra 1.
If (a − 1)(b − 2) = 0, which of the following must be true? I. II. III. (A) (B) (C) (D) (E)
2.
answer
a = 1 and b = 2. If a ≠ 1 , then b = 2 If a = 1 , then b ≠ 2 . I only II only III only I and II II and III
If ( x − 5)( y + 2) = 0 , which of the following must be true? answer
(A) x = y (B) x > y (C) x < y (D) xy = −10 (A) None of the above
3. If r and s are the two roots of the equation x 2 value of s − r ? (A) -8 (B) –2 (C) 2 (D) 7 (E) 8
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+ 8 x + 15 = 0 ,
and r < s , what is the
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4. If (−2, k ) is a point on the graph of y = 2 x 2 (A) -13 (B) -1 (C) 3 (D) 11 (E) 15
− 3 x + 1 , then
k =
5.
The product of two positive integers m and n is twice their sum. If n is 6, what is the value of m ? (A) 8 (B) 6 (C) 4 (D) 3 (E) 2
6.
If x : y = 2 : 3 , y : z = 3 : 4 , and x = 8 , then z − y (A) 1 (B) 4 (C) 6 (D) 8 (E) 12
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answer
answer
=
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7.
If S is the set of all numbers x such that 1 − 2 x ≤ 3, which of the following is true about
answer
S ? (A) (B) (C) (D) (E)
8.
9.
The least number in S is − 1 . The least number in S is 0. The least number in S is 3. The greatest number in S is − 2 . The greatest number in S is − 1 .
If rt > st and r > s , then which of the following must be true? (A) t > 0 (B) s > 0 (C) r > 0 (D) t < 0 (E) rs > 0
If − 3 ≤ x ≤ 7 and (A) –15 (B) –9 (C) –7 (D) 0 (E) 9
−6≤
y ≤ 2 , what is the smallest possible value of x − 2 y ?
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10. For any integer x , x is defined by the equation x = x + 1. Which of the following is equal to ( x) (A) 0 (B) 2 (C) (D)
2 x 2 x
(E)
2 x
2
−
answer
2
x for all integers x ?
11. An operation * defined on whole numbers gives results such as the following: answer
2*3 = 7 3 * 4 = 13 1* 5 = 6 0 * 6 =1 According to the equations above, which of the following could define the operation * ? (A) x * y = x + y (B) x * y = 2 x + y (C) x * y = y 2
− x
(D) x * y = x 2
+ y
(E) x * y = xy + 1
12. If r s = rs + r + s , then for what value of s is r s equal to r for all values of r ? (A) –1 (B) 0 (C) 1 o
(D) (E)
o
1 r + 1 r
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13. Marie’s monthly salary is determined by the formula s = 850 +
x , were s is her salary 10
answer
and x is the total amount of her monthly sales, both expressed in dollars. If the total of Marie’ s sales for July was $22,000, then her salary for July was (A) $2,115 (B) $3,050 (C) $5,620 (D) $6,410 (E) $10,700
14. The total cost C , in dollars, of manufacturing x items of a certain type is given by
answer
1 C = x 2 + 5,000 . When the total cost is $10,000, exactly how many such items are 2 manufactured? (A) 100 (B) 140 (C) 200 (D) 30,000 (E) 50,000,000
15. A loaf of bread and 2 one-pound containers of butter cost a total of $4.95. If a pound of butter costs $0.90 more than a loaf of bread, how much does a pound of butter cost? (A) $1.05 (B) $1.58 (C) $1.95 (D) $2.03 (E) $2.93
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16. Pat bought n apples at a cost of 3 for $0.20 and then sold the n apples at a price of 4 for $0.35. If Pat’s revenue from the sale of the apples was $2.50 more than the cost of the apples, what is the value of n ? (A) 150 (B) 120 (C) 90 (D) 80 (E) 60
17. The total cost of 3 pounds of hamburger and 4 pounds of hot dogs is $12.39. At the same rates, if the cost of 5 pounds of hamburger is $9.45, what is the cost per pound of hot dogs? (A) $1.59 (B) $1.68 (C) $1.77 (D) $1.89 (E) $2.03
18. At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $1.25 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11
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answer
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19. A mother and her child have a combined weight of 150 pounds. If the mother’s weight is 5 times her child’ s weight, what is the weight, in pounds, of the child? (A) 32 (B) 30 (C) 28 (D) 25 (E) 24
20. Jim multiplied a number by 5 when he should have divided it by 4. If the result he got was 10, what would have been the result if he had not made the error? (A) (B) (C) (D) (E)
answer
answer
1 20 1 10 1 5 1 4 1 2
21. An instructor scored a student’s test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers. If the student answered all of the questions and received a score of 38, how many questions did that student answer correctly? (A) 19 (B) 38 (C) 41 (D) 44 (E) 46
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22. The area of a rectangular region with length 2 x +1 and width x − 3 is 2
(A) 2 x
answer
−3
(B) 2 x2 + x − 3 (C) 2 x2 − 5x − 3 (D) 2 x2 − 6x − 3 (E) 2 x2 + 7x + 3
23. The total price of n ( n
>
1) equally priced copies of a certain book is $50. In terms of n ,
n − 1 of these copies?
which of the following gives the total price of (A) 50 ( n
answer
− 1)
50 n −1 50 ( n − 1) (C) n 50 n (D) n −1 50 (E) n ( n − 1) (B)
24. The supply of a certain commodity is given by the formula S = 9 x + x 2 and the demand for the commodity is given by the formula D
=
2 ,475 − x , where x is the price of the
commodity in dollars. At which of the following values of commodity equal the demand for the commodity? (A) 9 (B) 45 (C) 55 (D) 275 (E) 2,475
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x will the supply of the
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3v 2 2d d = and t = , where 20 v d is the distance traveled, in meters, after the brakes are applied v is the velocity, in meters pet second, before the brakes are applied t is the time, in seconds, it takes to stop after the brakes are applied.
25. The formulas above are used to compute the distance a car travels after the brakes are applied. If the driver of a car applied the brakes just as a traffic light turned yellow and stopped exactly 6 seconds later, what is the value of v ? (A) 20 (B)
80 3
(C) (D) (E)
30 40 60
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¼öÇÐ
Çؼ³
Category 7 Algebra
1. If (a − 1)(b − 2) = 0, which of the following must be true?
(A) (B) (C) (D) (E)
a = 1 and b = 2. I. II. If a ≠ 1 , then b = 2 III. If a = 1 , then b ≠ 2 . I only II only III only I and II II and III
a = 1 ¶Ç´  b = 2ÀÌ ¸ é (a − 1)(b − 2) =0ÀÌ µË´ Ï ´ Ù. µû¶ó¼- a ≠ 1 À̸é b ´  ¹ ݵå½Ã 2° ¡ µË ´ Ï ´ Ù. a = 1 À̸é b =2 ÀÌ °Å³ ª b ≠ 2 ÀÔ´ Ï ´ Ù . ¢Ñ
´ äÀº (B)ÀÔ´ Ï ´ Ù.
2. If ( x − 5)( y + 2) = 0 , which of the following must be true? (A) x = y (B) x > y (C) x
<
y
(D) xy = −10 (E) None of the above
x = 5 ¶Ç´  y = −2 À̸é ( x − 5)( y + 2) = 0 ÀÌ µË´ Ï ´ Ù. ¢Ñ
´ äÀº (E)ÀÔ´ Ï ´ Ù.
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3. If r and s are the two roots of the equation x 2 value of s − r ? (A) -8 (B) –2 (C) 2 (D) 7 (E) 8
+ 8 x + 15 = 0 ,
and r < s , what is the
x 2 + 8 x + 15 = 0 ÀÇ µÎ °³ ÀÇ ±ÙÀÌ (two roots) r , s ÀÏ ¶§ s − r ÀÇ °ª À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. x 2 + 8 x + 15 = ( x + 3)( x + 5) = 0 , r = −5 , s = −3 ¢Ñ
´ äÀº (C)ÀÔ´ Ï ´ Ù.
4. If (−2, k ) is a point on the graph of y = 2 x 2 (A) -13 (B) -1 (C) 3 (D) 11 (E) 15
− 3 x + 1 , then
k =
(−2, k ) °¡ ±×·¡ ÇÁ y = 2 x 2 − 3 x + 1 ÀÇ Á¡ ÀÏ ¶§ k ÀÇ ° ª À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¢Ñ
´ äÀº (E)ÀÔ´ Ï ´ Ù.
5. The product of two positive integers m and n is twice their sum. If n is 6, what is the value of m ? (A) 8 (B) 6 (C) 4 (D) 3 (E) 2 ¾çÀÇ Á¤¼ö m , n À» °öÇÏ ¿© ÁØ °ª ÀÌ À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¢Ñ ´ äÀº (D)ÀÔ´ Ï ´ Ù.
( m + n ) °ª ÀÇ µÎ ¹ è¶ó° í ÇÕ´ Ï ´ Ù. n ÀÌ 6ÀÏ ¶§ m ÀÇ °ª
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6. If x : y = 2 : 3 , y : z = 3 : 4 , and x = 8 , then z − y (A) 1 (B) 4 (C) 6 (D) 8 (E) 12
=
. µû¶ó¼- , y : z = 3 : 4 = 12 : 16 x = 8 ÀÌ ¹ Ç· Î y = 12 ÀÔ´ Ï ´ Ù ¢Ñ
´ äÀº (B)ÀÔ´ Ï ´ Ù.
7. If S is the set of all numbers x such that 1 − 2 x ≤ 3, which of the following is true about
S ? (A) (B) (C) (D) (E)
The least number in S is − 1 . The least number in S is 0. The least number in S is 3. The greatest number in S is − 2 . The greatest number in S is − 1 .
1 − 2 x ≤ 3 ⇒ x ≥ −1 ¢Ñ
´ äÀº (A)ÀÔ´ Ï ´ Ù.
8. If rt > st and r > s , then which of the following must be true? (A) t > 0 (B) (C) (D) (E)
s > 0 r > 0 t < 0 rs > 0
º εî È£ÀÇ ¾çº ¯À» ¾ç¼ö· Î ³ ª ´ ©¾î Áְų ª °öÇØÁÙ º Î µî È£ÀÇ ¹ æÇâÀÌ ¹ Ù² î Áö ¾Ê½À´ Ï ´ Ù. ¢Ñ
´ äÀº (A)ÀÔ´ Ï ´ Ù.
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9. If − 3 ≤ x ≤ 7 and − 6 ≤ y ≤ 2 , what is the smallest possible value of x − 2 y ? (A) –15 (B) –9 (C) –7 (D) 0 (E) 9
x = −3 , y = 2 ÀÏ ¶§ ° ¡ Àå ÀÛÀº °ª À» °®°Ô µË´ Ï ´ Ù. ¢Ñ
´ äÀº (C)ÀÔ´ Ï ´ Ù.
10. For any integer x , x is defined by the equation x = x + 1. Which of the following is equal to ( x) 2 (A) 0 (B) 2 (C) (D) (E)
−
x 2 for all integers x ?
2 x 2 x 2 x
2 ( x) 2 − x 2 = ( x + 1) − x 2 − 1 = 2 x
¢Ñ
´ äÀº (D)ÀÔ´ Ï ´ Ù.
11. An operation * defined on whole numbers gives results such as the following:
2*3 = 7 3 * 4 = 13 1* 5 = 6 0 * 6 =1 According to the equations above, which of the following could define the operation * ? (A) x * y = x + y (B) x * y = 2 x + y (C) x * y = y 2
− x
(D) x * y = x 2
+ y
(E) x * y = xy + 1 ÁÖ¾î Áø ¿¹ ¸ ¸ À» °¡ Áö°í ´ äÀ» »ý°¢ÇÏ ±â ¾î · Æ´ Ù¸ é º ¸ ±â· Î º Î ÅÍ ´ äÀ» ãÀ¸ ¸ é µË´ Ï ´ Ù. ¢Ñ
´ äÀº (E)ÀÔ´ Ï ´ Ù.
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12. If r s = rs + r + s , then for what value of s is r s equal to r for all values of r ? o
(A)
–1
o
(B)
0
(C)
1
(D)
1 r + 1
(E)
r
r s = r ÀÌ µÇµµ· Ï ÇÏ ´  s ÀÇ °ª À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. o
¢Ñ
´ ä Àº (B)ÀÔ´ Ï ´ Ù.
13. Marie’s monthly salary is determined by the formula s = 850 +
x , were s is her salary 10
and x is the total amount of her monthly sales, both expressed in dollars. If the total of Marie’ s sales for July was $22,000, then her salary for July was (A) $2,115 (B) $3,050 (C) $5,620 (D) $6,410 (E) $10,700 MarieÀÇ ±Þ¿©°¡ °ø½Ä s = 850 +
x ( s : ±Þ¿©, x : ÇÑ ´ Þ µ¿¾ÈÀÇ ÆǸ ž×) ÀÇÇؼ- °áÁ¤ µÈ ↵ϒ 10
´ Ù°í ÇÕ´ Ï ´ Ù. 7¿ùÀÇ ÆǸ Å· ®ÀÌ $22,000ÀÌ ¾úÀ» ¶§ 7¿ùÀÇ ±Þ¿©¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¢Ñ
14.
´ äÀº (B)ÀÔ´ Ï ´ Ù.
The total cost C , in dollars, of manufacturing x items of a certain type is given by
1 C = x 2 + 5,000 . When the total cost is $10,000, exactly how many such items are 2 manufactured? (A) 100 (B) 140 (C) 200 (D) 30,000 (E) 50,000,000
1 x ° ³ ¸ ¦ »ý»êÇÒ ¶§ÀÇ ÃѺ ñ¿ëÀº ½Ä C = x 2 + 5,000 ¿¡ ÀÇÇؼ- »êÃâµÈ´ Ù°í ÇÕ´ Ï ´ Ù. ÃѺ ñ¿ëÀÌ 2 $10,000ÀÌ ¾úÀ» ¶§ »ý»êÇÑ Á¦ Ç°ÀÇ °³ ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¢Ñ
´ äÀº (A)ÀÔ´ Ï ´ Ù.
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15. A loaf of bread and 2 one-pound containers of butter cost a total of $4.95. If a pound of butter costs $0.90 more than a loaf of bread, how much does a pound of butter cost? (A) $1.05 (B) $1.58 (C) $1.95 (D) $2.03 (E) $2.93 »§ ( x) °ú 1ÆÄ¿î µå ¹ öÅÍ ( y ) 2°³ ÀÇ °¡ °ÝÀÌ $4.95ÀÔ´ Ï ´ Ù.( x + 2 y = 4.95 ) ¹ öÅÍ ÀÇ °¡ °ÝÀÌ »§ÀÇ °¡ °Ý º ¸ ´ Ù $0.90 ³ ôÀ» ¶§( y − 0.90 = x ) 1 ÆÄ¿î µå ¹ öÅÍ ÀÇ °¡ °ÝÀ» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¢Ñ
´ äÀº (C)ÀÔ´ Ï ´ Ù.
16. Pat bought n apples at a cost of 3 for $0.20 and then sold the n apples at a price of 4 for $0.35. If Pat’s revenue from the sale of the apples was $2.50 more than the cost of the apples, what is the value of n ? (A) 150 (B) 120 (C) 90 (D) 80 (E) 60
n °³ ÀÇ »ç°ú¸ ¦ 3° ³ ¿¡ $0.20¾¿ ÁÖ°í ±¸ÀÔÇÏ ¿© 4°³ ¿¡ $0.35¿¡ ÆǸ ÅÇÏ ¿© »ç°úÆǸ żҵæÀÌ »ç°ú±¸ ÀÔº ñ¿ëº ¸ ´ Ù $2.50 ¸ ¹ ¾ÒÀ» ¶§ n ÀÇ °ª À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÀÌ ¹ ®Á¦ ¸ ¦ Ç®±â À§ÇÏ ¿© µÎ °¡ Áö ÀÇ ¹ æ¹ ýÀ» »ç¿ëÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. ¥° ) ¿¬¸ ³ ½ÄÀ» ¼¼¿öÁÖ°í n ÀÇ °ª À» ã´  °Í ÀÔ´ Ï ´ Ù.
n n (0.35) − (0.20) = 2.50 4 3 ¥±) 3° ú 4ÀÇ ÃÖ¼Ò°ø¹ è¼ö°¡ 12¶ó´  »ç½ÇÀ» ÀÌ ¿ëÇÏ ¿© 12°³ ¾¿ ÆǸ ÅÇÏ °í 12° ³ ¾¿ ±¸ÀÔÇßÀ» ¶§ÀÇ ±Ý¾× Â÷ÀÌ ¸ ¦ ±¸ÇÏ ±â´  ½±ÁÒ( 1.05 − 0.8 = 0.25 ). ÀÌ Â÷ÀÌ ¸ ¦ ÀÌ ¿ëÇÏ ¿© ¹ ®Á¦ ¸ ¦ Ç®¸ é µË´Ï ´ Ù.( 2.50 ÷ 0.25 = 10 , 12° ³ ¾¿ 10¹ øÀ» ÆǸ ÅÇÑ °Í °ú ° °ÁÒ.) ¢Ñ
´ äÀº (B)ÀÔ´ Ï ´ Ù.
17. The total cost of 3 pounds of hamburger and 4 pounds of hot dogs is $12.39. At the same rates, if the cost of 5 pounds of hamburger is $9.45, what is the cost per pound of hot dogs? (A) $1.59 (B) $1.68 (C) $1.77 (D) $1.89 (E) $2.03
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the cost of 5 pounds of hamburger°¡ $ 9.45¶ó°í Ç߱⠶§¹ ®¿¡ the cost of 3 pound of hamburger ´  $5.67ÀÔ´ Ï ´ Ù (
3 × 9.45 = 5.67 ). ÀÌ °ª À» the cost of 3 pounds of hamburger + the cost of 4 pounds 5
of hot dogs = $12.39¿¡ ´ ëÀÔÇÏ ¿© °è»êÇÏ ¸ é the cost per pound of hot dogs¸ ¦ ±¸ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. ¢Ñ
´ äÀº (B)ÀÔ´ Ï ´ Ù.
18. At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $1.25 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 ½Å¹ ß´ ë¿©º ñ¿ëÀº $0.50, °ÔÀÓº ñ´  $1.25ÀÏ ¶§, ½Å¹ ß´ ë¿©¸ ¦ ÇØ¾ß ÇÏ ´  »ç¶÷ÀÌ $12.80¸ ¦ °¡ Áö°í ÇÒ ¼ö ÀÖ´  ÃÖ´ ëÀÇ °ÔÀÓ ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. °¡ Áø µ· $12.80¿¡ ¼- ½Å¹ ßÀ» ´ ë¿©ÇÏ °í ³ ² Àº µ· À¸ · Î ÇÒ ¼ö ÀÖ´  °ÔÀÓ ¼ö¸ ¦ ±¸ÇÏ ¸ é µË´ Ï ´ Ù. ( (12.80 − 0.50) ÷ 1.25 ) ¢Ñ
´ äÀº (C)ÀÔ´ Ï ´ Ù.
19. A mother and her child have a combined weight of 150 pounds. If the mother’s weight is 5 times her child’ s weight, what is the weight, in pounds, of the child? (A) 32 (B) 30 (C) 28 (D) 25 (E) 24 ¾ö¸ ¶¿Í ¾ÆÀÌ ÀÇ ¸ ö¹ «°ÔÀÇ ÇÕÀÌ 150 poundsÀÌ °í ¾ö¸ ¶ÀÇ ¸ ö¹ «°Ô°¡ ¾ÆÀÌ ¸ ö¹ «° ÔÀÇ 5¹ èÀÏ ¶§, ¾ÆÀÌ ÀÇ ¸ ö¹ «°Ô¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. Mother’ s weight + child’ s weight = 150 Mother’ s weight = 5 Child’ s weight ¢Ñ
´ äÀº (D)ÀÔ´ Ï ´ Ù.
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- ÁÂ Set 7-1 GRE M ath °
20. Jim multiplied a number by 5 when he should have divided it by 4. If the result he got was 10, what would have been the result if he had not made the error? (A)
1 20
(B)
1 10
(C)
1 5
(D)
1 4
(E)
1 2
4· Î ³ ª ´ ©¾î ¾ß ÇÒ ¶§ 5¸ ¦ °öÇØÁÖ¾ú°í ±× °á° ú´  10À̾ú ´ Ù°í ÇÕ´ Ï ´ Ù. ½Ç¼ö¸¦ ÇÏ Áö ¾Ê¾ÒÀ» ¶§ ¾ò¾î Á³ À» ¼ýÀÚ¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 10Àº 5° ¡ °öÇØÁø ¼ýÀÚÀÔ´ Ï ´ Ù. µû¶ó¼- 5° ¡ °öÇØÁø ¼ýÀÚ ´  2¿´ ½À´ Ï ´ Ù. ¢Ñ
´ äÀº (E)ÀÔ´ Ï ´ Ù.
21. An instructor scored a student’s test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers. If the student answered all of the questions and received a score of 38, how many questions did that student answer correctly? (A) 19 (B) 38 (C) 41 (D) 44 (E) 46 ¸ ÂÀº ¹ ®Á¦ ÀÇ °³ ¼ö¿¡ ¼- Ʋ¸° ¹ ®Á¦ ÀÇ °³ ¼ö¿¡ 2¸ ¦ °öÇÑ °ª À» »©¾î ÁÖ¾î Á¡ ¼ö¸¦ °è»ê ÇÑ´ Ù°í ÇÕ ´ Ï ´ Ù. ¸ ðµç ¹ ®Á¦ ¿¡ ´ äÀ» ÇÏ°í 38Á¡À» ¹ Þ¾Ò´ Ù°í ÇÕ´ Ï ´ Ù. À̶§ ¸ ÂÀº ¹ ®Á¦ ÀÇ °³ ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¸ ÂÀº ¹ ®Á¦ ÀÇ °³ ¼ö¸¦ x ÇÏ ¸ é Ʋ¸° ¹ ®Á¦ ÀÇ °³ ¼ö´  50 − x ÀÔ´ Ï ´ Ù . µû¶ó¼- ´ ÙÀ½ÀÇ ½Ä À» Ç®¸ é ´ äÀ» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù.
x − 2(50 − x) = 38 ¢Ñ
´ äÀº (E)ÀÔ´ Ï ´ Ù.
22 . The area of a rectangular region with length 2 x +1 and width x − 3 is (A) 2 x2 − 3 (B) 2 x2 + x − 3 (C) 2 x2 − 5x − 3 (D) 2 x2 − 6x − 3 (E) 2 x2 + 7x + 3 Á÷»ç°¢ÇüÀÇ ¼¼· Î °¡ 2 x +1 , ° ¡ · Î ° ¡ x − 3 ÀÏ ¶§ ³ ÐÀÌ ¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.
(2 x + 1)( x − 3) = 2 x 2 − 5 x − 3 ¢Ñ
´ äÀº (C)ÀÔ´ Ï ´ Ù.
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23. The total price of n ( n
>
1) equally priced copies of a certain book is $50. In terms of n ,
which of the following gives the total price of (A) 50 ( n
n − 1 of these copies?
− 1)
50 n −1 50 ( n − 1) (C) n 50 n (D) n −1 50 (E) n ( n − 1) (B)
n − 1 ±ÇÀÇ Ã¥°ª À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 50 . µû¶ó¼- n − 1 ±ÇÀÇ Ã¥°ª Àº n ±ÇÀÇ Ã¥° ª ÀÌ $50ÀÌ ¹ Ç· Î ÇÑ ±ÇÀÇ Ã¥° ª Àº $ ÀÔ´ Ï ´ Ù n 50 . $ ( n − 1) ÀÔ´ Ï ´ Ù n
±Çº ° ° ¡ °ÝÀÌ µ¿ÀÏ ÇÑ n ±ÇÀÇ Ã¥° ª ÀÌ $50ÀÏ ¶§
¢Ñ
´ äÀº (C)ÀÔ´ Ï ´ Ù.
24. The supply of a certain commodity is given by the formula S = 9 x + x 2 and the demand for the commodity is given by the formula D
=
2 ,475 − x , where x is the price of the
commodity in dollars. At which of the following values of commodity equal the demand for the commodity? (A) 9 (B) 45 (C) 55 (D) 275 (E) 2,475
x °¡ ÀçÈ- ÀÇ °¡ °ÝÀÏ ¶§ ° ø±ÞÀº ½Ä S = 9 x + x 2
↵ϒ ÀÇÇؼ-
x will the supply of the
¼ö¿ä´  ½Ä D
=
2 ,475 − x ¿¡
ÀÇÇؼ- °áÁ¤ µÉ ¶§, ¼ö¿ä¿Í °ø±ÞÀÌ ÀÏ Ä¡ ÇÏ ´  °¡ °Ý x ¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. µû¶ó¼- ´ ÙÀ½ÀÇ ½ÄÀ» °è»êÇÏ ¸ é ° ¡ °ÝÀ» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù.
9 x + x 2
=
¢Ñ
´ äÀº (B)ÀÔ´ Ï ´ Ù.
2, 457 − x
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3v 2 2d d = and t = , where 20 v d is the distance traveled, in meters, after the brakes are applied v is the velocity, in meters pet second, before the brakes are applied t is the time, in seconds, it takes to stop after the brakes are applied.
25. The formulas above are used to compute the distance a car travels after the brakes are applied. If the driver of a car applied the brakes just as a traffic light turned yellow and stopped exactly 6 seconds later, what is the value of v ? (A) 20 (B)
80 3
(C) (D) (E)
30 40 60
d ´  º ê· ¹ ÀÌ Å©¸ ¦ ¹ âÀº ÈÄ ÀÚµ¿Â÷°¡ ¿òÁ÷ÀÎ °Å¸ ®, v ´  º ê· ¹ ÀÌ Å©¸ ¦ ¹ â±â Àü ¼Óµµ, t ´  º ê · ¹ ÀÌ Å©¸ ¦ ¹ âÀº ÈÄ ÀÚµ¿Â÷°¡ ¸ ØÃß´ µ¥ ¼Ò¿äµÈ ½Ã°£À» ³ ª Ÿ ³ »°í ÀÖ½À´ Ï ´ Ù. ¿î ÀüÀÚ°¡ º ê· ¹ ÀÌ Å©¸ ¦ ¹ â°í 6ÃÊ ÈÄ¿¡ Â÷°¡ ¸ ØÃß¾úÀ» ¶§ ÀÚµ¿Â÷ÀÇ ¼Óµµ¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.
2d 3v 2 . ½Ä d = t = ℵ⊂≠∩•∈ d = 3v ÀÔ´ Ï ´ Ù v 20
↵ϒ
d = 3v À» ´ëÀÔÇÏ ¿© v °ª À» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï
´ Ù. ¢Ñ
´ äÀº (A)ÀÔ´ Ï ´ Ù.
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GRE Math ° - ÁÂ Set 7-2
Category 7 Algebra Set 7-2 1.
Three musical tones have frequencies positive, 2 x
(B)
( 2 ) x
(D) (E)
2.
answer
x y = , and 2 x = z , what is y in terms of x ? y z
(A)
(C)
x , y , and z , respectively. If x , y , and z are
1 x 2 1 x 2 2 x 3
2 . If the numerator of the fraction is increased by 4 and 5 1 the denominator is doubled, the new fraction is equivalent to . What is the sum of the 3 A certain fraction is equivalent to
answer
numerator and denominator of the original fraction?
3.
(A)
49
(B)
35
(C)
28
(D)
26
(E)
21
If a total of x identical disks can be arranged in 8 stacks of equal height or in 12 stacks of equal height, the least possible value of x is (A)
96
(B)
48
(C)
36
(D)
24
(E)
12
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answer
GRE Math ° - ÁÂ Set 7-2
4.
The total price of n ( n
> 1) equally priced copies of a certain book is $50.
In terms of
n,
n − 1 of these copies? 50 50 ( n − 1) (B) (C) n −1 n 50 (E) n ( n − 1)
answer
which of the following gives the total price of (A) 50 ( n (D)
5.
− 1)
50 n n −1
x feet when it ascended 2,000 feet and then 1 descended 5,000 feet. If the plane’ s altitude after these two changes was its original 3 A plane was originally flying at an altitude of
answer
altitude, then the solution of which of the following equations gives the plane’ s original altitude, in feet? (A) (B) (C) (D) (E)
6.
1 x + 2, 000 = ( x − 3,000 ) 3 1 ( x − 3, 000 ) = x 3 1 x + 3,000 = x 3 1 x − 7,000 = x 3 1 x − 3, 000 = x 3
There are how many hours between
x minutes past 12 noon and 8:10 p.m. of the same day, answer
x < 60 ? 490 − x 60 480 − x 60 470 − x 60 60 (60 − x + 7 ) 60 (60 − x + 17 )
where (A) (B) (C) (D) (E)
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GRE Math ° - ÁÂ Set 7-2
7.
8.
x minutes past 3 p.m. and y minutes past 4 p.m. of the same day? ( 0 < x < 60 and 0 < y < 60 ) (A) 3,600 + 60( y − x ) (B) 3,600 + 60( x − y ) (C) 60 + 60( x − y) (D) 60 + ( y − x) (E) 60( x − y ) 2 There are how many seconds between
answer
A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat answer
above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360?
9.
(A)
$12
(B)
$14
(C)
$16
(D)
$17
(E)
$18
A certain used-book dealer sells paperback books at 3 times dealer’ s cost and hardback books at 4 times dealer’ s cost. Last week the dealer sold a total of 120 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus dealer’ s cost) on the sale of all of these books was $300, how many of the books sold were paperbacks? (A)
40
(B)
60
(C)
75
(D)
90
(E)
100
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answer
GRE Math ° - ÁÂ Set 7-2
10. On a legislative committee, the number of males is 3 fewer than twice the number of females.
answer
If one male were replaced by a female, there would be an equal number of males and females on the committee. How many members are on the committee? (A)
14
(B)
12
(C)
10
(D)
9
(E)
7
11. An investor has stocks, bonds, and government securities currently worth a total of $100,000,
answer
as well as a real estate investment. If the stocks and the bonds are worth a total of $2,500 more than the value of the real estate investment, and if the government securities are worth $7,500 more than twice the value of the real estate investment, how much are the government securities worth? (A)
$67,500
(B)
$62,500
(C)
$37,500
(D)
$32,500
(E)
$30,000
12. Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an answer
equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought? (A)
5
(B)
10
(C)
15
(D)
20
(E)
25
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GRE Math ° - ÁÂ Set 7-2
13. A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. answer
Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour? (A)
140
(B)
200
(C)
250
(D)
300
(E)
360
14. The cost of registration at a professional association meeting was $50 per person; a lunch for answer
registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 100 more than the number who did not, and if receipts for registration and lunch totaled $92,600, how many people paid just for registration at the meeting? (A)
700
(B)
800
(C)
1,300
(D)
1,500
(E)
1,800
15. In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term of the sequence? (A) (B) (C) (D) (E)
À±ÅÂÈ-
3 5 5 8 8 5 3 5 9 2
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GRE Math ° - ÁÂ Set 7-2
16. A kennel sold 3 puppies of breed X and 2 puppies of breed Y for a total of $690. If each
answer
breed Y puppy was sold for 20 percent less than each breed X puppy, how much did each breed X puppy sell for? (A)
$120.00
(B)
$127.70
(C)
$138.00
(D)
$150.00
(E)
$156.70
17. In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 75 bricks in the wall, how many bricks does the bottom row contain? (A)
14
(B)
15
(C)
16
(D)
17
(E)
18
STOP
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GRE Math ° - ÁÂ Set 7-2
¼öÇÐÇؼ³ Category 7 Algebra 1. Three musical tones have frequencies
x , y , and z , respectively. If x , y , and z are
x y = , and 2 x = z , what is y in terms of x ? y z 1 1 2 x (B) ( 2 ) x (C) (D) x x 2 2
positive, (A)
(E)
2 x 3
x y = . 2 x = z À» ´ ëÀÔÇÏ ¸ é 2 x 2 = y 2 ℵ™×∉×∧ . x , y ´  ¾ç¼öÀÌ ±â ¶§¹ ® ´  xz = y 2 ℵ™×∉×∧ y z ¿¡ y =
2 x ℵ™×∉×∧ .
´ äÀº (B)ÀÔ´ Ï ´ Ù.
::
::
2 . If the numerator of the fraction is increased by 4 and 5 1 the denominator is doubled, the new fraction is equivalent to . What is the sum of the 3
2. A certain fraction is equivalent to
numerator and denominator of the original fraction? (A)
49
(B)
35
(C)
28
(D)
26
º ÐÀÚ°¡ 4¸¸ Å Áõ°¡ ÇÏ °í º и ð°¡ µÎ ¹ è°¡ µÇ¾úÀ» ¶§, »õ· Î ¿î º мö °ª ÀÌ
(E)
21
1 ÀÌ ¶ó°í ÇÕ´ Ï ´ Ù. º ¯ 3
È ¸ ¦ ÁÖ±â Àü º мöÀÇ º ÐÀÚ¿Í º и 𸠦 ÇÕÇÏ ¸ é ±× °ª ÀÌ ¾ó¸ ¶ÀÎ Áö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ´ ÙÀ½ÀÇ µÎ ½ÄÀ» ¿¬¸ ³ ÇÏ ¿© °è»êÇÏ ¸ é µË´ Ï ´ Ù.
n 2 = d 5
¥¡)
¥¢)
´ äÀº (E)ÀÔ´ Ï ´ Ù.
::
À±ÅÂÈ-
n+ 4 1 = 2d 3 ::
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GRE Math ° - ÁÂ Set 7-2
3. If a total of x identical disks can be arranged in 8 stacks of equal height or in 12 stacks of equal height, the least possible value of x is (A)
96
(B)
48
(C)
36
(D)
24
(E)
12
x °³ ÀÇ µð½º Å©¸ ¦ ³ ôÀÌ °¡ µ¿ÀÏ ÇÑ 8° ³ ´ õ¹Ì ¶Ç´  ³ ôÀÌ °¡ µ¿ÀÏ ÇÑ 12°³ ´ õ¹ Ì · Î ½×À» ¼ö ÀÖÀ» ¶§, x ÀÇ ÃÖ¼Ò °ª À» ¹ °¾î º ¸°í ÀÖ½À´ Ï ´ Ù. x ´  8°ú 12· Î ³ ª ´ ©¾î ¶³ ¾î Áö´  ¼ýÀÚÀÔ´ Ï ´ Ù. ¹ ®Á¦ ¿¡ ¼ x ÀÇ ÃÖ¼Ò °ª À» ¹ °¾î º ¸ °í Àֱ⠶ §¹ ®¿¡ °á±¹ 8°ú 12ÀÇ ÃÖ¼Ò°ø¹ è¼ö¸¦ ¹ °¾î º ¸ ´  °Í °ú °°½À´ Ï ´ Ù. ´ äÀº (D)ÀÔ´ Ï ´ Ù.
::
::
4. The total price of n ( n
> 1) equally priced copies of a certain book is $50.
which of the following gives the total price of (A) (B) (C) (D) (E)
n − 1 of these copies?
50 n −1 50 ( n − 1) n 50 n n −1 50 n ( n − 1) n ±ÇÀÇ Ã¥ ° ¡ °ÝÀÌ $50ÀÏ ¶§, n − 1 ±ÇÀÇ ° ¡ °ÝÀ» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù.
±Çº ° Ã¥ °¡ °ÝÀÌ µ¿ÀÏ ÇÏ ´ Ù°í ÇßÀ¸ ¹ Ç· Î ÇÑ ±ÇÀÇ Ã¥ °¡ °ÝÀº $
À±ÅÂÈ-
50 . µû¶ó¼ n − 1 ±ÇÀÇ Ã¥ ÀÔ´ Ï ´ Ù n
50(n − 1) . ÀÔ´ Ï ´ Ù n
´ äÀº (C)ÀÔ´ Ï ´ Ù.
::
n,
50 ( n − 1)
¸ Å ±ÇÀÇ °¡ °ÝÀÌ µ¿ÀÏ ÇÑ
°¡ °ÝÀº $
In terms of
::
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GRE Math ° - ÁÂ Set 7-2
x feet when it ascended 2,000 feet and then 1 descended 5,000 feet. If the plane’ s altitude after these two changes was its original 3
5. A plane was originally flying at an altitude of
altitude, then the solution of which of the following equations gives the plane’ s original altitude, in feet?
1 x + 2,000 = ( x − 3,000 ) 3 1 ( x − 3,000 ) = x 3 1 x + 3,000 = x 3 1 x − 7,000 = x 3 1 x − 3,000 = x 3
(A) (B) (C) (D) (E)
x feetÀÇ °í µµ¿¡ ¼ 2,000 feet¸ ¦ »ó½ÂÇß´ Ù°¡ ( x feet + 2,000 feet) 5,000 feet¸ ¦ ÇÏ ° ÇßÀ» ¶§( x feet + 1 1 2,000 feet - 5,000 feet) ó À½ °í µµÀÇ ÁöÁ¡ ¿¡( x ) ÀÖ´ Ù°í ÇÕ´ Ï ´ Ù. 3 3 ´ äÀº (E)ÀÔ´ Ï ´ Ù.
::
::
6. There are how many hours between where (A) (B) (C) (D) (E)
x minutes past 12 noon and 8:10 p.m. of the same day,
x < 60 ? 490 − x 60 480 − x 60 470 − x 60 60 (60 − x + 7 ) 60 (60 − x + 17 )
Á¤¿À12½Ã¿¡ ¼ ¿ÀÈÄ8½Ã±î Áö´  8½Ã°£ÀÇ °£° ÝÀÌ ÀÖ½À´ Ï ´ Ù. 12½Ã¿¡ ¼
x º Ð ¸ ¸ Å ÀÌ Áö³ µÀ¸ ¹ Ç· Î
x ¸ ¸ Å »©ÁÖ¾î ¾ß µÇ¸ ç ¿ÀÈÄ 8½Ã¿¡ ¼ 10º и ¸ Å ÃÊ°úµÇ¾úÀ¸ ¹ Ç· Î ´ õÇØÁÖ¾î ¾ß ÇÕ´ Ï ´ Ù. ´ äÀº (A)ÀÔ´ Ï ´ Ù.
::
À±ÅÂÈ-
::
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GRE Math ° - ÁÂ Set 7-2
7. There are how many seconds between the same day? ( 0 < x < 60 and 0 < y (A)
3,600 + 60( y − x )
(B)
3,600 + 60( x − y )
(C)
60 + 60( x − y)
(D)
60 + ( y − x)
(E)
60( x − y ) 2
x minutes past 3 p.m. and y minutes past 4 p.m. of
< 60 )
15½Ã x º ÐÀ¸ · Î º Î ÅÍ 16½Ã y º бî ÁöÀÇ »çÀÌ °¡ ¸ î ÃÊ Â÷ÀÌ ÀÎ Áö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 1½Ã°£¿¡ y º Ð ¸¸ Å ´õÇÏ°í ´ äÀº (A)ÀÔ´ Ï ´ Ù.
::
x º Ð ¸ ¸ Å »©ÁÖ¾î ¾ß ÇÕ´ Ï ´ Ù.
::
8. A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360? (A)
$12
(B)
$14
(C)
$16
(D)
$17
(E)
$18
100°³ ÀÇ ¹ ßÄÚ´ Ï Á¼®ÀÌ ÀÖ°í ¹ ßÄÚ´ Ï Á¼®ÀÇ °¡ °ÝÀÌ $10º ¸´Ù ³ ôÀ» ¶§ Á¼®ÀÇ ° ¡ °ÝÀÌ $2ÀÎ »ó µÇ¸ é ÆǸ ŵǴ  Á¼®ÀÇ ¼ö´  5°³ ¾¿ ÁÙ¾î µç´ Ù°í ÇÕ´ Ï ´ Ù. Á¼®ÀÇ °¡ °ÝÀÌ $10ÀÏ ¶§ ¸ ðµç Á¼® ÀÌ ÆǸ Å µÈ´ Ù°í ÇÏ ¸ é Á¼® ÆǸ żöÀÍ ÀÌ $1,360ÀÏ ¶§ ÆǸ ÅµÈ Á¼®ÀÇ °³ ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖÁÒ. Á¼®ÀÇ °¡ °ÝÀÌ $2¾¿ ÀÎ »óµÉ ¶§ ÆǸ ŵǴ  Á¼®ÀÇ ¼ö°¡ 5°³ ¾¿ ÁÙ¾î µé¹ Ç· Î ´ ÙÀ½ÀÇ ½ÄÀ» ¼¼¿ï ¼ö ÀÖ½À´ Ï ´ Ù.
(10 + 2n)(100 − 5n) = 1,360 ´ äÀº (C)ÀÔ´ Ï ´ Ù.
::
À±ÅÂÈ-
::
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GRE Math ° - ÁÂ Set 7-2
9. A certain used-book dealer sells paperback books at 3 times dealer’ s cost and hardback books at 4 times dealer’ s cost. Last week the dealer sold a total of 120 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus dealer’ s cost) on the sale of all of these books was $300, how many of the books sold were paperbacks? (A)
40
(B)
60
(C)
75
(D)
90
(E)
100
dealer’s cost°¡ $1ÀÌ ¸ ç paperback bookÀÇ °¡ °ÝÀÌ dealer costÀÇ 3¹ è¶ó°í Ç߱⠶§¹ ®¿¡ paperback bookÀ» ÇÑ ±Ç ÆǸ ÅÇßÀ» ¶§ profitÀº $2ÀÔ´ Ï ´ Ù. Hardback bookÀº $3ÀÇ profitÀÌ ¹ ß»ýÇÕ´ Ï ´ Ù. ´ÙÀ½ ÀÇ µÎ ½ÄÀ» ° ¡ Áö° í ¹ ®Á¦ ¿¡ ´ ëÇÑ ´ äÀ» ãÀ» ¼ö ÀÖ½À´ Ï ´ Ù. ¥¡) P + H = 120
::
¥¢) 2 P + 3H = 300
´ äÀº (B)ÀÔ´ Ï ´ Ù ::
10. On a legislative committee, the number of males is 3 fewer than twice the number of females. If one male were replaced by a female, there would be an equal number of males and females on the committee. How many members are on the committee? (A)
14
(B)
ÀÔ¹ ýÀ§¿øȸ¿¡ ¼Ò¼ÓµÇ¾î
12
(C)
10
ÀÖ´  ³ ² ¼º ÀÇ ¼ö´  ¿©¼º
(D)
9
¼öÀÇ 2¹ è¿¡
(E) 7
3¸ ¸ Å ÀÌ
ÀÛ´ Ù°í
ÇÕ´Ï
´ Ù. (m = 2 f − 3) ³ ² ¼º ÇÑ ¸ í ÀÌ ¿©¼º À¸ · Î ´ ëüµÇ¸ é( m − 1 = f + 1 ; ´ ëüµÇ´  °Í Àº ³ ² ¼º ÀÇ ¼ý ÀÚ´  ÇÑ ¸ í ÀÌ ÁÙ¾î µå´ Â °Í ÀÌ ¸ ç ¿©¼º ÀÇ ¼ýÀÚ´  ÇÑ ¸ í ÀÌ ´ Ã¾î ³ ª ´  °Í ÀÔ´ Ï ´ Ù.) À§¿øȸ ¿¡ ³ ² ¼º °ú ¿©¼º ÀÇ ¼ýÀÚ°¡ °°¾ÆÁø´ Ù°í ÇÕ´ Ï ´ Ù. µÎ ½ÄÀ»( m = 2 f − 3 , m − 1 = f + 1 ) ¿¬¸ ³ ÇÏ ¿© °è»êÇÏ ¸ é µË´ Ï ´ Ù. À§¿øȸÀÇ ÀÇ¿ø¼ö¸¦ ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. ::
´ äÀº (B)ÀÔ´ Ï ´ Ù.
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GRE Math ° - ÁÂ Set 7-2
11. An investor has stocks, bonds, and government securities currently worth a total of $100,000, as well as a real estate investment. If the stocks and the bonds are worth a total of $2,500 more than the value of the real estate investment, and if the government securities are worth $7,500 more than twice the value of the real estate investment, how much are the government securities worth? (A)
$67,500
(B)
$62,500
(C)
$37,500
(D)
$32,500
(E)
$30,000
¥¡ ) stock + bond + government security = $ 100,000 ¥¢) “stock & bond”ÀÇ °¡ Ä¡ - $2,500 = º Î µ¿»êÀÇ °¡ Ä¡ ¥£) “government security”ÀÇ °¡ Ä¡ - $7,500 = 2(º Î µ¿»êÀÇ °¡ Ä¡ ) ´ äÀº (A)ÀÔ´ Ï ´ Ù. ::
::
12. Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought? (A)
5
(B)
10
(C)
15
(D)
20
(E)
25
¿ì Ç¥¸ ¦ ±¸ÀÔÇÑ ÃÑ ±Ý¾×Àº $2.65ÀÌ ¸ ç 5 cent, 25cent ¿ì Ç¥´Â °° Àº °³ ¼ö¸¦ 10 cent ¿ì Ç¥´Â 5 cent ¿ì Ç¥º ¸ ´ Ù 2¹ è ¸ ¹ ÀÌ ±¸ ÀÔÇß´ Ù°í ÇÕ´ Ï ´ Ù. ÀÌ ¶§ ±¸ ÀÔÇÒ ¼ö ÀÖ´  1centÂ¥¸ ® ¿ì Ç¥ÀÇ °¡ °ÝÀ» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ±¸ÀÔÇÑ 5 cent ¿ì Ç¥ÀÇ °³ ¼ö¸ ¦ n ÀÌ ¶ó ÇÏ ¸ é À§ÀÇ ³ »¿ëÀ» ´ ÙÀ½ ½ÄÀ¸ · Î Á¤¸ ®ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. ($0.01 × x ) + ($0.05 × n ) + ($0.10 × 2 n ) + ($0.25 × n ) = $2.65
⇒ 0.01 x + 0.5 n = 2.65
n ÀÌ 5ÀÏ ¶§ x ´  ÃÖ¼Ò°ª À» °¡ Áö°Ô µË´ Ï ´ Ù.
´ äÀº (C)ÀÔ´ Ï ´ Ù.
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GRE Math ° - ÁÂ Set 7-2
13. A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour? (A)
140
(B)
200
(C)
250
(D) 300
(E)
360
55 mileÀÇ ¼Óµµ· Î ¿î Çà ÇÒ ¶§´  1 °¶· ± ´ ç 4.5mile, 60 mileÀÇ ¼Óµµ· Î ¿î Çà ÇÒ ¶§´  1°¶· ± ´ ç 3.5mileÀ» °¡´Â Æ®· °ÀÌ 500mileÀÇ °Å¸ ®¸ ¦ ¶§· Î ´  55mile, 60mileÀÇ ¼Óµµ· Î °¡ ¸ é¼ 120gallonÀÇ ¿¬·á¸ ¦ ¼Òº ñÇß´ Ù°í ÇÕ´ Ï ´ Ù.ÀÌ ¶§ 55mile· Î ¿î ÇàÇÑ °Å¸ ®¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 55mile· Î ¿î ÇàÇÑ °Å¸ ®¸ ¦ d ¶ó ÇÏ ¸ é ´ ÙÀ½ÀÇ ½ÄÀ» ¸ ¸ µé ¼ö ÀÖ½À´ Ï ´ Ù.
d 500 − d + = 120 4 .5 3 .5 ´ äÀº (E)ÀÔ´ Ï ´ Ù.
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::
14. The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 100 more than the number who did not, and if receipts for registration and lunch totaled $92,600, how many people paid just for registration at the meeting? (A)
700
(B)
800
(C)
1,300
(D)
1,500
(E)
1,800
µî·Ïºñ´Â $50, ½Ä»ç°ª Àº $22 ÀÏ ¶§ ½Ä»ç° ª À» Áöº ÒÇÑ »ç¶÷ÀÌ ³ »Áö ¾ÊÀº »ç¶÷º ¸ ´ Ù 100¸ í ÀÌ ¸ ¹ ´ Ù°í ÇÕ´ Ï ´ Ù. ÀÌ ¶§ µî · Ï º ñ¸ ¸ À» ³ ½ »ç¶÷ÀÌ ¸ î ¸ í ÀÎ Áö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. µî · Ï ÇÑ Àüü ÀÎ ¿øÀ» T ¶ó ÇÏ ¸ é ½Ä»ç° ª À» ÁöºÒÇÑ »ç¶÷Àº
T − 50 ÀÔ´ Ï ´ Ù . µû¶ó¼ ´ ÙÀ½ÀÇ ½ÄÀÌ 2
¼º ¸ ³ ÇÕ´ Ï ´ Ù.
T 50T + 22 × − 50 = 92,600 2 ´ äÀº (A)ÀÔ´ Ï ´ Ù.
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GRE Math ° - ÁÂ Set 7-2
15. In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term of the sequence? (A)
3 5
(B)
5 8
(C)
8 5
(D)
3 5
(E)
9 2
¼ýÀÚÀÇ ¿¬¼Ó¿¡ ¼ ù ¹ ø° ¼ýÀÚ°¡ 1ÀÌ ¸ ç ±× ´ ÙÀ½ÀÇ ¼öµéÀº ¹ Ù· Î ¾ÕÀÇ ¼ýÀÚÀÇ ¿ª ¼ö¿¡ 1À» ´ õ ÇÑ °ª ÀÌ ¶ó°í ÇÒ ¶§, ´ Ù¼¸ ¹ ø° ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÁÖ¾î Áø Á¶° Ç¿¡ µû¶ó ¼ýÀÚ¸ ¦ ³ ª ¿ ÇØ º ¸ ¸ é ´ ÙÀ½°ú ° °½À´ Ï ´ Ù. 1, 2,
´ äÀº (C)ÀÔ´ Ï ´ Ù.
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1 2 3 +1, +1, +1 2 3 5
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16. A kennel sold 3 puppies of breed X and 2 puppies of breed Y for a total of $690. If each breed Y puppy was sold for 20 percent less than each breed X puppy, how much did each breed X puppy sell for? (A)
$120.00
(B)
$127.70
(C)
$138.00
(D)
$150.00
(E)
$156.70
X Á¾ÀÚ ° ¾ÆÁö 3¸ ¶¸ ®¿Í Y Á¾ÀÚ ° ¾ÆÁö 2¸ ¶¸ ®¸ ¦ $690¿¡ ÆȾҴ Ù°í ÇßÀ¸ ¹ Ç· Î ÀÌ ¸ ¦ ½ÄÀ¸ · Î ³ ª Ÿ ³ »¸é 3 X + 2Y = 690 ÀÔ´ Ï ´ Ù . Y Á¾ÀÚ ° ¾ÆÁöÀÇ °¡ °ÝÀÌ X Á¾ÀÚ ° ¾ÆÁöÀÇ °¡ °Ýº ¸ ´ Ù 20%°¡ ÀÛ´ Ù°í ÇßÀ¸ ¹ Ç· Î ÀÌ ¸ ¦ ½ÄÀ¸ · Î ³ ª Ÿ ³ »¸ é Y = 0.8 X ÀÔ´ Ï ´ Ù .
´ äÀº (D)ÀÔ´ Ï ´ Ù.
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À±ÅÂÈ-
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GRE Math ° - ÁÂ Set 7-2
17. In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 75 bricks in the wall, how many bricks does the bottom row contain? (A)
14
(B)
15
(C)
16
(D)
17
(E)
18
º ®ÀÇ Á¦ ÀÏ ¾Æ· ¡ ÂÊ ÁÙ¿¡¼ º Î ÅÍ À§· Î ÇÑ ÁÙ ¾¿ ¿Ã¶ó° ¡ ¸ é¼ º ®µ¹ ÀÇ °³ ¼ö°¡ ÇÑ °³ ¾¿ ÁÙ¾î µç´ Ù °í ÇÕ´ Ï ´ Ù. ÃÑ5ÁÙ¿¡ 75° ³ ÀÇ º ®µ¹ · Î ¸ ¸ µé¾î Áø º ®¿¡ ¼ Á¦ ÀÏ ¾Æ·¡ ÂÊ ÁÙÀÇ º ®µ¹ °³ ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. Á¦ ÀÏ ¾Æ· ¡ ÂÊ¿¡ À§Ä¡ ÇÑ º ®µ¹ ÀÇ °³ ¼ö¸ ¦ b ¶ó ÇÏ ¸ é 5n − 10 = 75 ÀÔ´ Ï ´ Ù .
´ äÀº (D)ÀÔ´ Ï ´ Ù.
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GRE Math °- ÁÂ Set 8-1
Category 8 Wor d Problem 1 2
1. Water has been pouring into a tank for 12 minutes at the constant rate of 1 gallon per second. If the tank was initially empty and is now
answer
1 full, what is the total capacity of the 3
tank, in gallons? (A)
375
(B)
1,125
(C)
1,500
(D)
2,160
(E)
2,250
2. During a sale, Pam paid the regular price for one quart of oil and paid $0.01 for a second quart.
answer
If she paid a total of $1.20 for the two quarts, the amount paid for the second quart was what fraction of the amount paid for the first quart? (A)
1 118
(B)
1 119
(C)
1 120
(D)
1 121
(E)
1 122
3. A carpenter purchases a hammer costing $8.03, a bag of nails costing $5.16, and a tape measure costing $2.81 with a twenty-dollar bill. How much change does the carpenter receive if a sales tax of 5 percent is charged on the entire purchase? (A)
$3.20
(B)
$3.29
(C)
$3.80
(D)
$4.00
(E)
$4.80
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answer
GRE Math °- ÁÂ Set 8-1
4. A certain property doubl ed in value from 1950 to 1960 and tripled in value from 1960 to 1980.
answer
The value of the property in 1980 was how many times the value in 1950? (A)
3
(B)
5
(C)
6
(D)
8
(E)
9
5. Of the final grades received by the students in a certain math course,
B ’s,
1 1 are A ’s, are 5 4
answer
1 are C ’ s and the remaining 10 grades are D ’ s. What is the number of students 2
in the course? (A)
80
(B)
110
(C)
160
(D)
200
(E)
400
6. If 50 tomatoes weigh a total of 30 pounds and cost 35 cents per pound, what is the cost per tomato? (A)
17 cents
(B)
21 cents
(C)
24 cents
(D)
28 cents
(E)
35 cents
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answer
GRE Math °- ÁÂ Set 8-1
7. On a new job Alice earned $198 the first week and $220 the second week. If she worked 4
answer
more hours the second week than the first week and was paid at the same hourly rate, how much did she earn per hour? (A)
$4.00
(B)
$4.50
(C)
$5.00
(D)
$5.50
(E)
$6.00
8. If a store purchased 6 dozen items at a cost of $1.80 per dozen and later sold them all for $0.20
answer
apiece, what was the store’ s profit on these items? (A)
$2.16
(B)
$2.40
(C)
$2.84
(D)
$3.20
(E)
$3.60
9. A mail clerk put 1 or 2 stamps on each of 20 envelopes, using a total of 36 stamps. On how many of the envelopes did the clerk put 2 stamps? (A)
4
(B)
6
(C)
8
(D)
12
(E)
16
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answer
GRE Math °- ÁÂ Set 8-1
10. In 1984 the production costs of Company X totaled $719,000 and nonproduction costs totaled $15,000. In 1985 robots were introduced, and production costs dropped to $600,000,
answer
but nonproduction costs rose to $65,000 for the year. What was the decrease in total costs for Company X from 1984 to 1985? (A) $50,000 (B)
$69,000
(C)
$119,000
(D)
$134,000
(E)
$169,000
11. In traveling from a dormitory to a certain city, a student went
1 2 of the way by foot, of 5 3
answer
the way by bus, and the remaining 8 kilometers by car. What is the distance, in kilometers, from the dormitory to the city? (A)
30
(B)
45
(C)
60
(D)
90
(E)
120
12. A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $10.00? (A)
40
(B)
60
(C)
90
(D)
120
(E)
240
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answer
GRE Math °- ÁÂ Set 8-1
13. A man who died left an estate valued at $111,000. His will stipulated that his estate was to be
answer
distributed so that each of his three children received from the estate and his previous gifts, combined, the same total amount. If he had previously given his oldest child $15,000, his middle child $10,000, and his youngest $2,000, how much did the youngest child receive from the estate? (A)
$50,000
(B)
$48,000
(C)
$46,000
(D)
$44,000
(E)
$39,000
14. On a 3-day fishing trip, 4 adults consumed food costing $60. For the same food costs per
answer
person per day, what would be the cost of food consumed by 7 adults during a 5-day fishing trip? (A)
$300
(B)
$175
(C)
$105
(D)
$100
(E)
$84
15. Joe went on a diet 6 months ago when he weighed 222 pounds. If he now weighs 198 pounds and continues to lose at the same average monthly rate, in approximately how many months will he weigh 180 pounds? (A)
3
(B)
3.5
(C)
4
(D)
4.5
(E)
5
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GRE Math °- ÁÂ Set 8-1
16. Mr. Hernandez, who was a resident of State X for only 8 months last year, had a taxable income of $22,500 for the year. If the state tax rate were 4 percent of the year’ s taxable
answer
income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’ s State X tax for last year? (A) $900 (B)
$720
(C)
$600
(D)
$300
(E)
$60
17. If a 50-pound food package consists of individual 4-ounce packets, how many individual
answer
packets are contained in 4 tons of 50-pound packages? (Assume that all weights given exclude the weight of packaging material. 1 ton = 2,000 pounds; 1 pound = 16 ounces) (A)
32,000
(B)
8,000
(C)
800
(D)
200
(E)
160
18. The cost of sending a package is 30 cents per ounce in addition to a basic fee of 5 dollars. If integer x represents the weight in ounces of a certain package, which of the following represents the cost, in dollars, of sending the package? (A) 5 x + 0.30 (B) (5 + x )0.30 (C) 5 − 0.30 x (D) 0.30 x + 5 (E) 0.70 x + 5
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GRE Math °- ÁÂ Set 8-1
19. An empty oil tanker was filled with oil at a uniform rate in t hours. What proportion of
answer
the tanker was filled during the first x hours if x < t ? (A)
x t
(B)
t x
(C)
x t − x
(D)
t − x t
(E)
t − x x
20. If a basketball team scores an average (arithmetic mean) of x points per game for n games and then scores y points in its next game, what is the team’ s average score for the
answer
n + 1 games? nx + y (A) n +1 y (B) x + n +1 y (C) x + n n( x + y ) (D) n +1 x + ny (E) n +1
21. If a train travels at a speed of k meters per second, how many kilometers will it travel in t answer
minutes? (1 kilometer = 1,000 meters) (A) (B) (C) (D) (E)
60kt 1,000 60kt 100 1,000kt 60 6.000kt 60, 000kt
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GRE Math °- ÁÂ Set 8-1
< H igh L evel ¹®Á¦ > 22. Mason and Kathy, who both work in the evening wish to arrange for an evening off together.
answer
Each evening that Mason is off is followed by 3 evenings that he is a work, and each evening that Kathy is off is followed by 5 evenings that she is at work. If Mason will be off this evening, and Kathy will be off tomorrow evening, how many evenings must pass before they have an evening off together? (A)
10
(B)
12
(C)
24
(D)
28
(E)
So long as they continue this working pattern, they will never have the same evening off.
23. On a certain 10-question test, each question after the first question is worth 2 points more
answer
than the previous question. If the greatest number of points that can be scored on the test is 100, how many points is the eighth question worth? (A)
9
(B)
14
(C)
15
(D)
19
(E)
33
24. A certain car dealership sells only full-size and mid-size cars. One of its sales representatives receives an annual salary of $15,000. He also receives a commission of $800 for each full-size car he sells and $500 for each midsize car he sells. What is the least number of cars he must sell in a year to receive total annual earnings of exactly $25,000? (A)
7
(B)
12
(C)
13
(D)
14
(E)
17
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GRE Math °- ÁÂ Set 8-1
25. A school supply store sells only one kind of desk and one kind of chair, at a uniform cost per
answer
desk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs then the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs? (A)
5
(B)
3
(C)
8 3
(D)
5 2
(E)
7 3
26. A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of
answer
the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment? (A)
24
(B)
25
(C)
26
(D)
28
(E)
30
27. A manufacturer can save x dollars per unit in production costs by overproducing in certain seasons. If storage costs for the excess are y dollars per unit per day ( x > y ) , which of the following expresses the maximum number of days that n excess units can be stored before the storage costs exceed the savings on the excess units? (A) x − y (B) ( x − y )n
x y xn (D) y x (E) yn (C)
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GRE Math °- ÁÂ Set 8-1
28. A certain disability plan pays monthly benefits of 60 percent of the first $2,000 of monthly
answer
salary plus 40 percent of any portion in excess of $2,000 —the total monthly benefit not to exceed $2,500. What is the smallest monthly salary that will yield the maximum monthly benefit under this plan? (A)
$5,750
(B)
$5,250
(C)
$4,500
(D)
$3,250
(E)
$2,200
29. One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and
answer
1 of the nondefective switches are rejected by mistake. 20
If all the switches not rejected are sold, what percent of the switches sold by the factory are defective? (A)
4%
(B)
5%
(C)
6.25%
(D)
11%
(E)
16%
30. In Company X , 30 percent of the employees live over ten miles from work and 60 percent of the employees who live over ten miles from work are in car pools. If 40 percent of the employees of Company X are in car pools, what percent of the employees of Company X live ten miles or less from work and are in car pools ? (A)
12%
(B)
20%
(C)
22%
(D)
28%
(E)
32%
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GRE Math °- ÁÂ Set 8-1
31. A garment order consists of jackets costing $36 each and shirts costing $26 each. If the total
answer
cost of the order is $1,200, and if the average (arithmetic mean) cost per garment is $30, how many more shirts than jackets are in the order? (A)
32
(B)
22
(C)
18
(D)
13
(E)
8
32. The front wheels of a toy truck are 4 inches in circumference. The back wheels are 7 inches
answer
in circumference. If the truck travels in a straight line without slippage, how many inches will the truck have traveled when the front wheels have made 12 more revolutions than the back wheels? (A)
112
(B)
64
(C)
48
(D)
36
(E)
28
33. A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, the average number sold was 84, and among the male members, the average number sold was 96. What was the ratio of the number of male members to the number of female members i n the club? (A)
1:1
(B)
1:2
(C)
1:3
(D)
2:1
(E)
3:1
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answer
GRE Math °- ÁÂ Set 8-1
34. A team won 40 percent of the 15 games it has already played. If the team were to win 75
answer
percent of its remaining games, it will have won 60 percent of all its games. How many remaining games are there? (A)
12
(B)
20
(C)
24
(D)
30
(E)
45
35. In a quality control process it has been determined that all of the engines that fail inspection are faulty, but approximately
answer
1 of the faulty engines pass inspection. If, in a group of 1,000 6
engines, 100 fail inspection, approximately how many faulty engines pass inspection? (A)
16
(B)
20
(C)
50
(D)
70
(E)
120
36. If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production? (A)
4%
(B)
10%
(C)
14%
(D)
15%
(E)
18%
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answer
GRE Math °- ÁÂ Set 8-1
37. Jeff drove to work from his home averaging 40 miles per hour, and was 12 minutes late. The
answer
next day he left home for work at the same time, took the same route, averaging 48 miles per hour, and was 7 minutes late. How far in miles is it from Jeff’ s home to his work? (A)
20.0
(B)
24.5
(C)
30.0
(D)
37.5
(E)
40.0
38. If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per
answer
hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day? (A)
100
(B)
120
(C)
140
(D)
150
(E)
160
39. When a certain stretch of highway was rebuilt and straightened, the distance along the stretch answer
was decreased by 20 percent and the speed limit was increased by 25 percent. By what percent was the driving time along this stretch reduced for a person who always drives at the speed limit? (A) 16% (B) 36%
1 2
(C) 37 % (D) 45%
1 4
(E) 56 %
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GRE Math °- ÁÂ Set 8-1
40.
Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water
answer
evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X ? (A) 30% (B) (C)
1 33 % 3 1 37 % 2
(D)
40%
(E)
50%
41. How many gallons of water must be mixed with 1 gallon of a 15-percent salt solution to obtain
answer
a 10-percent salt solution? (A) 0.50 (B) 0.67 (C) 1.00 (D) 1.50 (E) 2.00
42. The seating chart of an airplane shown 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window seat. The view from the window seats in 5 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and the window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view? (A) (B) (C) (D) (E)
1 6 1 3 2 3 5 6 17 18
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GRE Math °- ÁÂ Set 8-1
43. One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot
answer
Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week? (A)
18
(B)
16
(C)
12
(D)
8
(E)
4
44. A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of
answer
gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city? (A)
14
(B)
16
(C)
21
(D)
22
(E)
27
45. On a 20-mile course Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and, without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course? (A)
75
(B)
105
(C)
117
(D)
150
(E)
162
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GRE Math °- ÁÂ Set 8-1
46. An investor bought n shares of Company X stock at $75 per share. She sold 60 percent
answer
of the shares for $120 per share and the rest at a later date for $70 per share. If her gross profit on the sale of the n shares of stock was $7,500, how many shares did she buy? (A)
375
(B)
300
(C)
100
(D)
95
(E)
75
47. In 1982 a certain company had losses of $10,000 per month. In the first three months of 1983,
answer
this company had gains of $4,000 per month. On the average, what would the company need to gain per month in the remainder of 1983 in order to break even over this two-year period? (A)
$9,000
(B)
$10,800
(C)
$12,000
(D)
$13,500
(E)
$18,000
48. An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.60 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold? (A)
130,000
(B)
300,000
(C)
380,000
(D)
400,000
(E)
420,000
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GRE Math °- ÁÂ Set 8-1
1 2
49. For each hour worked in excess of 40 hours per week, a mechanic is paid 1 times her
answer
regular rate of $12 per hour. Her gross pay for a week in which she works 52 hours is equal to her pay at the regular rate for how many hours? (A)
58
(B)
64
(C)
66
(D)
70
(E)
78
50. Fifty percent of the subscribers to newspaper X are corporate managers and of these, 30 percent are in the financial field. If 40 percent of the subscribers who are corporate
answer
managers in the financial field are money managers, how many of the newspaper’s 25,000 subscribers are corporate money managers in the financial field? (A)
1,500
(B)
3,000
(C)
3,750
(D)
7,500
(E)
8,750
51. Reggie had to type 90 letters. During the first day he typed second day he typed
1 of the letters, and during the 3
2 of the remaining letters. How many letters were still untyped at the 5
end of the second day? (A)
36
(B)
32
(C)
24
(D)
18
(E)
12
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GRE Math °- ÁÂ Set 8-1
52. One karat signifies that
1 of an alloy is pure gold. If a certain ring is 14-karat gold, 24
answer
approximately what percent of the alloy composing the ring is not gold? (A)
14%
(B)
24%
(C)
42%
(D)
55%
(E)
58%
1 1 of the pizzas sold in one week were mushroom and of the 8 3 remaining pizzas sold were pepperoni. If n of the pizzas sold were pepperoni, how many
53. At a certain pizzeria,
answer
were mushroom? (A) (B) (C) (D) (E)
3 n 8 3 n 7 7 n 16 7 n 8 3n
3 of the votes cast in a certain election. What fraction of the other votes 10 1 cast would she have needed in order to have received of the votes cast? 2 1 (A) 5 2 (B) 7 3 (C) 10 7 (D) 20 1 (E) 2
54. Beth received
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GRE Math °- ÁÂ Set 8-1
55. From January 1, 1980, to January 1, 1984, the number of employees of Company X
answer
declined by 700 per year. If the number of employees on January 1, 1984, was 80 percent of the number on January 1, 1980, how many employees did the company have on January 1, 1984? (A)
2,800
(B)
3,500
(C)
11,200
(D)
16,800
(E)
17,500
56. Both marble tiles and terra-cotta tiles are available in squares with 12-centimeter sides, but
answer
marble tiles cost x cents more per tile than terra-cotta tiles. How much more would it cost, in cents, to tile a rectangular floor 240 centimeters by 120 centimeters with marble tiles than with terra-cotta tiles? (A) (B) (C) (D) (E)
200 x 360 x 720 x 2,400 x 28,800−144 x
57. If 6 machines ran at the same constant rate, they can complete a certain job in 8 hours. If only 5 of these machines run at this rate, how many more minutes will be required to complete the same job? (A) 38 (B) 72 (C) 80 (D) 90 (E) 96
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GRE Math °- ÁÂ Set 8-1
58. An inlet pipe can fill an empty pool with water in 3 hours, and the pool’ s outlet pipe can empty
answer
a full pool in 4 hours. The water flows at constant rates through both pipes regardless of the water level in the pool. If both pipes were inadvertently left open, what fraction of the pool would be filled exactly 2 hours after water began to flow into the empty pool? (A)
1 12
(B)
1 6
(C)
1 4
(D)
1 3
(E)
1 2
59. Working alone, R can complete a certain kind of job in 9 hours. R and S , working
answer
together at their respective rates, can complete one of these jobs in 6 hours. In how many hours can S , working alone, complete one of these jobs? (A)
18
(B)
12
(C)
9
(D)
6
(E)
3
60. Machines A, B, and C working together, but independently, at their respective constant
1 hours. If A alone can do the job in 5 hours, and B 2 alone can do the job in 3 hours, in how many hours can C alone do the job? 1 (A) 1 3 1 (B) 2 7 rates can do a certain job in 1
(C)
3
(D)
5
(E) 7
1 2
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GRE Math °- ÁÂ Set 8-1
61. Bell X rings once every 12 minutes, bell Y once every 14 minutes, and bell Z once every 15 minutes. If, during a given day, the three bells ring at exactly the same instant, how many
answer
minutes will elapse before the three bells next ring simultaneously?
62.
(A)
60
(B)
210
(C)
420
(D)
840
(E)
2,520
How many bits of computer memory will be required to store the integer
x , were
answer
x = − 810 , 000 , if each digit requires 4 bits of memory and the sign of x requires 1 bit? (A)
25
(B)
24
(C)
17
(D)
13
(E)
12
63. Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? (A)
81
(B)
159
(C)
166
(D)
285
(E)
324
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answer
GRE Math °- ÁÂ Set 8-1
64. In a certain game, a player can accumulate points only by scoring either an X , which counts
answer
3 points, or a Y , which counts 2 points. If a player scored 24 points in the game and t points were made by scoring X ’ s how many different values could t have? (A)
Four
(B)
Five
(C)
Six
(D)
Seven
(E)
Eight
65. An apartment building has 9 floors with 2 n apartments per floor. If
1 of the apartments 3
answer
are to have walls removed to form, in each case, one bigger apartment from two smaller ones, how many apartments will there be after the remodeling? (A) (B) (C) (D)
(E)
3n 5n 6n 12n 4 15n
66. One-fourth of a solution that was 10 percent sugar by weight was replaced by a second solution, resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight? (A)
34%
(B)
24%
(C)
22%
(D)
18%
(E)
8.5%
STOP
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GRE Math °- ÁÂ Set 8-1
Categor y 8-1 Wor d Probl ems
¼öÇÐÇؼ³
1 2
1. Water has been pouring into a tank for 12 minutes at the constant rate of 1 gallon per second. If the tank was initially empty and is now
1 full, what is the total capacity of the 3
tank, in gallons? (A)
375
(B)
1,125
(C)
1,500
(D)
2,160
(E)
2,250
12(1/2)minutes´  12º Ð 30ÃÊ, ´ ٽà second·Î °í Ä¡ ¸ é 12×60 + 30 = 750 seconds. À§¿¡ ¼ per second ´ ç 1 gallonÀÇ ¼Óµµ· Î Áõ°¡ ÇÑ´ Ù°í ÇßÀ¸ ´ Ï 750ÃÊ µÚ¿¡ ´  750 gallonÀÌ Áõ°¡ ÇßÁÒ. ÀÌ ¾çÀº Àüü ÅÊÅ©ÀÇ capacityÀÇ 1/3À» ä¿ î ´ Ù. µû¶ó¼ ÿ Á¤´ äÀº
capacity = 750 3
(E)
2. During a sale, Pam paid the regular price for one quart of oil and paid $0.01 for a second quart. If she paid a total of $1.20 for the two quarts, the amount paid for the second quart was what fraction of the amount paid for the first quart?
1 118
(A)
(B)
1 119
(C)
1 120
(D)
1 121
(E)
1 122
$ 0 . 01 = 1 Tip : fractions À¯ÇüÀÇ ¹ ®Á¦ ¸ ¦ Ç® ¶§ ÁÖÀÇÇÒ Á¡ Àº º и ð¿Í º ÐÀÚ $ 1 . 19 ( 1 . 20 − 0 . 01 ) 119
¸ ¦ È¥µ¿ÇÏ Áö ¸ »¾Æ¾ß ÇÑ´ Ù´  Á¡ ÀÔ´ Ï ´ Ù. ¿©±â¼ ´ Â
the amount paid for the first quartÀÇ what
fractionÀ» ¹ ¯´  °Í ÀÌ ´ Ï ±î ÀÌ °Í ÀÌ º и ð°¡ µÇ¾î ¾ß ÇÕ´ Ï ´ Ù. ÿ Á¤´ äÀº
Tips:
(B)
Fractions ÀÇ Á¤ÀÇ
d = numerator = part = dividend n deno min ator whole divisor
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GRE Math °- ÁÂ Set 8-1
3. A carpenter purchases a hammer costing $8.03, a bag of nails costing $5.16, and a tape measure costing $2.81 with a twenty-dollar bill. How much change does the carpenter receive if a sales tax of 5 percent is charged on the entire purchase? (A)
$3.20
(B)
$3.29
(C)
$3.80
(D)
$4.00
(E)
$4.80
$ 20 – 1.05($8.03 + $5.16 + $2.81) = $3.20 ÿ
<Àüü ¹ °°Ç °ª ¿¡ 105%À» °öÇÏ ¸ é µÇÁÒ>
Á¤´ äÀº (A)
4. A certain property doubled in value from 1950 to 1960 and tripled in value from 1960 to 1980. The value of the property in 1980 was how many times the value in 1950? (A)
3
(B)
5
(C)
6
(D)
8
(E)
9 2¹ è
1950
3¹ è
1960
1980 , µû¶ó¼ 1980³ âÀº 1950³ âÀ» ±âÁØÀ¸ · Î 6¹ è° ¡ Áõ°¡
ÇßÁÒ. ÿ Á¤´ äÀº
(C)
5. Of the final grades received by the students in a certain math course,
B ’s,
1 1 are A ’s, are 5 4
1 are C ’ s and the remaining 10 grades are D ’ s. What is the number of students 2
in the course? (A)
80
1− (1/5+1/4+1/2) =
(B)
110
(C)
160
(D)
200
(E) 400
1 (the number of students in the course) = 10 ¸ í 20
µû¶ó¼ Àüü Çлý¼ö´  200¸ í ÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(D)
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GRE Math °- ÁÂ Set 8-1
6.
If 50 tomatoes weigh a total of 30 pounds and cost 35 cents per pound, what is the cost per tomato? (A)
17 cents
(B)
21 cents
(C)
24 cents
(D)
28 cents
(E)
35 cents
Åä¸ ¶Åä 50°³ ÀÇ ¹ «°Ô°¡ 30 poundsÀÌ ¸ ç 1 pound´ ç °¡ °ÝÀº 35centÀÏ ¶§ Åä¸ ¶Åä ° ³ ´ ç ° ¡ °ÝÀ» ¹ ° ¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¼ö½Ä: ( 30 pounds × 35(cents) ) / 50 (°³ ) = 21 cents ÿ Á¤´ äÀº
(B)
7. On a new job Alice earned $198 the first week and $220 the second week. If she worked 4 more hours the second week than the first week and was paid at the same hourly rate, how much did she earn per hour? (A)
$4.00
(B)
$4.50
(C)
$5.00
(D)
$5.50
(E)
$6.00
½Ã°£´ ç ±Þ·á° ¡ ÀÏ Á¤ÇÑ Á¶° Ç ÇÏ ¿¡ ¼ ù ÁÖ´  $198À» µÎ ¹ ø° ÁÖ¿¡ ´  $220À» ¹ ú¾úÀ¸ ¸ ç, µÎ ¹ ø ° ÁÖ¿¡ ´  4½Ã°£À» ´ õ ÀÏ Çß´ Ù°í ÇÕ´ Ï ´ Ù. ½Ã°£´ ç ±Þ· Ḡ¦ ¾Ë°í ½Í À¸ ¸ é µÎ ÁÖ°£ÀÇ ±Þ· áÀÇ Â÷ÀÌ ¸ ¦ 4½Ã°£À¸ · Î ³ ª ´ ©¸ é µÇ°Ú±º ¿ä. ¼ö½Ä) 22(dollars) / 4 (hours) = 5. 5 (dollar/hour) ÿ
´ äÀº (D)ÀÔ´ Ï ´ Ù.
8. If a store purchased 6 dozen items at a cost of $1.80 per dozen and later sold them all for $0.20 apiece, what was the store’ s profit on these items? (A)
$2.16
(B)
$2.40
(C)
$2.84
(D)
$3.20
(E)
$3.60
12°³ ¿¡ $1.8ÇÏ ´  ¹ °°ÇÀ» 72° ³ ±¸ÀÔ(6 dozen items)ÇÏ°í ÀÌ ¸ ¦ °³ ´ ç $0.20¿¡ ÆǸ ÅÇÒ ¶§ÀÇ ¼öÀÍ À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. °³ ´ ç ±¸ÀÔ°¡ °ÝÀ» ¸ ÕÀú ±¸ ÇÏ °í ( 1.8 (dollars) / 12(°³ ) = 0.15 ) ÆǸ Å°¡ °Ý¿¡ ¼ ±¸ ÀÔ°¡ °ÝÀ» »« ±Ý ¾×¿¡ ( 0.2(dollar) – 0.15(dollar) = 0.05(dollar) ) ¼ö· ®À» °öÇÏ ¿© ÁÖ¸ é µÇ°Ú½À´ Ï ´ Ù. ÿ ´ äÀº
(E)ÀÔ´ Ï ´ Ù.
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GRE Math °- ÁÂ Set 8-1
9. A mail clerk put 1 or 2 stamps on each of 20 envelopes, using a total of 36 stamps. On how many of the envelopes did the clerk put 2 stamps? (A)
4
(B)
6
(C)
8
(D)
12
(E) 16
20°³ ÀÇ º ÀÅõ¿¡ ÇÑ °³ ¶Ç´  µÎ °³ ÀÇ ¿ì Ç¥¸ ¦ º Î Ä¡ ´ µ¥ 36°³ ÀÇ ¿ì Ç¥¸ ¦ »ç¿ëÇß´Ù. µÎ °³ ÀÇ ¿ì Ç¥ ¸ ¦ º Πģ º ÀÅõ´Â ¸ î °³ ÀÎ °¡ ¸ ¦ º Ñ°í ÀÖ½À´ Ï ´ Ù. ±âº »ÀûÀ¸ · Î 20°³ÀÇ º ÀÅõ¿¡ ÇÑ °³ ¾¿ ¿ì Ç¥¸ ¦ º Î Ä¡ °í µµ 16°³ ¸¦ ´ õ »ç¿ëÇßÀ¸ ¹ Ç· Î µÎ °³ ÀÇ ¿ì Ç¥ ¸ ¦ º Πģ º ÀÅõ´  16°³ ÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(E)
10. In 1984 the production costs of Company X totaled $719,000 and nonproduction costs totaled $15,000. In 1985 robots were introduced, and production costs dropped to $600,000, but nonproduction costs rose to $65,000 for the year. What was the decrease in total costs for Company X from 1984 to 1985? (A) $50,000 (B) $69,000
(C) $119,000
(D) $134,000
(E) $169,000
production cost´Â $719,000, nonproduction cost´  $15,000¿´ ´ µ¥ ÀÛ¾÷°øÁ¤¿¡ · Î º ¸ Æ®°¡ µµÀÔµÈ ÈÄ production cost´  $600,000À¸ · Î °¨ ¼ÒÇÏ °í nonproduction cost $65,000· Î º ¯ÇßÀ» ¶§ º ñ¿ëÀüü °¨ ¼Ò¸ ¦ ±¸ÇÏ ¶ó´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. Áï $719,000 µÎ °ª À» ÇÕÄ¡ ¸ é $734,000 ÿ Á¤´ äÀº
e
e
$600,000À¸ · Î °¨ ¼Ò : $15,000 e 65,000Áõ°¡
$665,000 °¨ ¼ÒµË´ Ï ´ Ù. ÀÌ µÎ °ª ÀÇ Â÷ÀÌ °¡ Á¤´ äÀÌ ³ ׿ä.
(B)
11. In traveling from a dormitory to a certain city, a student went
1 2 of the way by foot, of 5 3
the way by bus, and the remaining 8 kilometers by car. What is the distance, in kilometers, from the dormitory to the city? (A)
30
(B)
45
(C)
60
(D)
90
(E)
120
1/5¸ ¦ µµº ¸ · Î 2/3´  ¹ ö½º · Î ±×¸ ®°í ³ ª ¸ ÓÁö 8Km´  ÀÚµ¿Â÷¸ ¦ ÀÌ ¿ëÇÑ´ Ù°í ÇÒ ¶§ ±â¼÷»ç¿¡¼ µµ½Ã±î ÁöÀÇ °Å¸ ®¸ ¦ ¹ °¾î º ¸ °í ÀÖ´ Ù. Àüü°Å¸ ®¸ ¦ D¶ó °¡ Á¤ÇÏ °í Ç®¸ é : D – (1/5D+2/3D)= 8 (Km) ÿ Á¤´ äÀº
(C)
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GRE Math °- ÁÂ Set 8-1
12. A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $10.00? (A)
40
(B)
60
(C)
90
(D)
120
(E)
240
3 pounds ÀÇ ¹ Ù³ ª ³ ª ¸ ¦ $0.5¿¡ ±¸ ÀÔÇÏ ¿© 4 poundsÀÇ ¹ Ù³ ª ³ ª ¸ ¦ $1¿¡ ÆǸ ÅÇÒ ¶§ ¾ó¸ ¶¸ ¸ Å ÀÇ ¹ Ù ³ ª ³ ª ¸ ¦ ÆǸ ÅÇØ¾ß $10.00ÀÇ ¼öÀÍ À» ° ÅµÑ ¼ö ÀÖ´ ÂÁö¸ ¦ ¹ °¾î º ¸ °í ÀÖ´ Ù. ÆÄ¿î µå ´ ç ±¸ÀÔ°¡ °Ý ¹ × ÆǸ Å°¡ °ÝÀ» ±¸ ÇÏ ¿© $10À» ³ ª ´ ©¾î µµ µÇ°ÚÁö¸¸ , ´ äÀ» »¡ ¸ ® ±¸ ÇÏ ±â À§ Çؼ ´  3° ú 4ÀÇ ÃÖ¼Ò°ø¹ è¼öÀÎ 12¸ ¦ ±¸ ÇÏ ¿© Ç®¸ é º ü¸ £°Ô Ç® ¼ö ÀÖ´ Ù. ±¸ ÀԽà : 12 pounds $ 2 ÆǸ Žà : 12 pounds $ 3 ±×· ¯¹ Ç· Î 12 pound¸ ¦ ÆǸ ÅÇÒ ¶§ ¸ ¶´ Ù $1¸ ¸ Å ¼öÀÍ À» ¿Ã¸ °´ Ù. 12 pounds: $1 = x : $10 ÿ Á¤´ äÀº
(D)
13. A man who died left an estate valued at $111,000. His will stipulated that his estate was to be distributed so that each of his three children received from the estate and his previous gifts, combined, the same total amount. If he had previously given his oldest child $15,000, his middle child $10,000, and his youngest $2,000, how much did the youngest child receive from the estate? (A)
$50,000
(B)
$48,000
(C)
$46,000
(D)
$44,000
(E)
$39,000
$111,000ÀÇ Àç»êÀ» ¼¼ ¾Æµéµé¿¡ °Ô ³ ª ´ ©¾î ÁÙ ¶§, Å« ¾ÆµéÀÌ $15,000, µÑ°°¡ $10,000, ±×¸ ®°í ¸ · ³ »°¡ $2,000À» ±× Àü¿¡ ¹ Þ¾Ò½À´ Ï ´ Ù. $111,000ÀÇ ³ ª ´ ©µÇ ±× Àü¿¡ ¹ ÞÀº µ· °ú »õ·Î ¹ ÞÀº µ· À» ÇÕÃÄ ¸ ðµÎ ¶È°°Àº ±Ý¾×À» ¹ Þ¾Ò´ Ù¸ é , $111,000 Áß¿¡ ¼ ¸ · ³ » ¾ÆµéÀÇ ¸ òÀÌ ¾ó¸¶ÀÎ °¡ ¸ ¦ ±¸ ÇÏ ´  ¹ ®Á¦ ³ ׿ä. $111,000+$15,000+$10,000+$2,000 ÷3 = $46,000( °¢°¢ÀÌ ¹ ÞÀº ÃÑ ¾×¼ö) ¸ · ³ »´  ±× Àü¿¡ $2,000À» ¹ Þ¾ÒÀ¸ ¹ Ç· Î $46,000 - $2,000 = $44,000À» estate¿¡ ¼ ¹ Þ¾Ò½À´ Ï ´ Ù. ÿ Á¤´ äÀº
(D)
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14. On a 3-day fishing trip, 4 adults consumed food costing $60. For the same food costs per person per day, what would be the cost of food consumed by 7 adults during a 5-day fishing trip? (A) 4¸ í ÀÌ
$300 3ÀÏ
$175
µ¿¾È $60À» food¿¡
$60 = $5 , 3 − day × 4adults ÿ Á¤´ äÀº
(B)
(C)
$105
ÁöÃâÇß´Ù¸ é
(D) 1¸ í ÀÌ
$100
(E)
ÇÏ · 絿¾È À½½Ä¿¡
$84 ¾² ´  °æº ñ´Â
7¸í ÀÌ 5ÀÏ µ¿¾È À½½Ä¿¡ ÁöÃâÇÏ ´  µ· Àº $5 ×7 adults ×5-day = $175
(B)
15. Joe went on a diet 6 months ago when he weighed 222 pounds. If he now weighs 198 pounds and continues to lose at the same average monthly rate, in approximately how many months will he weigh 180 pounds? (A)
3
(B)
3.5
(C)
4
(D)
4.5
(E)
5
6 months: 24 pounds (222 pounds − 198 pounds) = X : 18 pounds(198 pounds – 180 pounds) X = 4.5 ÿ Á¤´ äÀº
(D)
16. Mr. Hernandez, who was a resident of State X for only 8 months last year, had a taxable income of $22,500 for the year. If the state tax rate were 4 percent of the year’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of Mr. Hernandez’ s State X tax for last year? (A) $900 (B) $720 (C) $600 (D) $300
(E) $60
$ 22,500 × 0.04 × (8/12) = $ 600; ¹ ®Á¦ ¿¡ ¼ »¡°£ ÁÙÀÌ ÀÖ´Â ºÎ º ÐÀÇ Àǹ Ì ´  ¼¼±Ý³ ³ ¼¼ÀÚ°¡ Àϳ â Áß resident·Î¼ ±× ÁÖ¿¡ ¼ »ê ±â°£¸ ¸ Å ¼¼±ÝÀ» ° è»êÇÑ´ Ù´  Àǹ Ì ÁÒ. Àϳ â Áß 8°³ ¿ùÀ» ¾î ¶² ÁÖ¿¡ ¼ »ì ¾Ò´ Ù¸ é Àüü ¼¼±ÝÀÇ
8 ¸ ¸ Å ¸ ¸ ³ ³ ¼¼ÇÏ ¿© µÈ´ Ù´  ¶æÀÔ´ Ï ´ Ù. 12 ÿ Á¤´ äÀº
(C)
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17. If a 50-pound food package consists of individual 4-ounce packets, how many individual packets are contai ned in 4 tons of 50-pound packages? (Assume that all weights given exclude the weight of packaging material. 1 ton = 2,000 pounds; 1 pound = 16 ounces) (A)
32,000
(B) 8,000
(C) 800
(D) 200
(E) 160
4tons ×2000 pounds ×16 ounces = 128,000 ounces ÀÌ °Í À» 4-ounce· Î ³ ª ´ ©¸ é ±× °ª ÀÌ packetsÀÇ ÃÑ ¼öÀÔ´ Ï ´ Ù. 128,000 ÷ 4 = 32,000 ÿ
Á¤´ äÀº (A)
18. The cost of sending a package is 30 cents per ounce in addition to a basic fee of 5 dollars. If integer x represents the weight in ounces of a certain package, which of the following represents the cost, in dollars, of sending the package? (A) 5 x + 0.30 (B) (5 + x )0.30 (C) 5 − 0.30 x (D) 0.30 x + 5 (E) 0.70 x + 5 ¹ °°ÇÀ» º ¸ ³ »´ µ¥ ±âº »¿ä±ÝÀÌ $5¿¡ ounce´ ç 30cent¾¿ Ãß°¡ µÈ´ Ù´  ³ »¿ëÀÔ´ Ï ´ Ù.´ ÜÀ§¸ ¦ ÁÖÀÇÇÏ ¿© ¹ ®Á¦ ¸ ¦ ÇØ°áÇØ¾ß ÇÕ´ Ï ´ Ù. Cent¸ ¦ $´ ÜÀ§· Î °í Ä¡ ¸ é 30cent´  $0.3ÀÌ µÇÁÒ… ÿ
´ äÀº (D)ÀÔ´ Ï ´ Ù.
19. An empty oil tanker was filled with oil at a uniform rate in t hours. What proportion of the tanker was filled during the first x hours if x < t ? (A)
x t
(B)
t x
(C)
x t − x
(D)
t − x t
(E)
t − x x
¼®À¯ÅÊÅ©°¡ ÀÏ Á¤ÇÑ ¼Óµµ· Î t ½Ã°£ ¸ ¸ ¿¡ ä¿ ö Áú ¶§ ù x½Ã°£ µ¿¾È¿¡ ä¿ì Áö´  ÅÊÅ©ÀÇ º ñÀ² À» ±¸ÇÏ ¶ó´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. ÅÊÅ©´  ÇÑ ½Ã°£´ ç ¾ó¸ ¶ ¸ ¸ Å½Ä Ã¤¿öÁú±î ¿ä.
1 ¸ ¸ Å ¾¿ ä¿öÁöÁÒ.±×· ¡ ¾ß¸ ¸ ÀÌ t½Ã°£ÀÌ Áö³ ª ¾ß t
Áö Àüü°¡ ä¿öÁö°ÚÁÒ. ÿ
Á¤´ äÀº (A)
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20. If a basketball team scores an average (arithmetic mean) of x points per game for n games and then scores y points in its next game, what is the team’ s average score for the
n + 1 games? nx + y (A) n +1 y n +1 y (C) x + n n( x + y ) (D) n +1 x + ny (E) n +1 (B)
x +
N°ÔÀÓ¿¡ ¼ ´  X points Æò±ÕµæÁ¡ ; N°ÔÀÓ ´ ÙÀ½ °æ±â µæÁ¡ Àº y. ¾Æ· ¡ °ø½ÄÀ» ÀÌ ¿ë ÇÏ ¸ é: <
°í , N 2 ÀÇÆò±ÕÀº A ÀÏ Average Probl em > ±×·ì N 1 ÀÇaverage´  A ÀÌ 1 2
Combin ed Aver age = ÿ
¶§,
N 1 ⋅ A1 + N 2 ⋅ A2 , ℵ♣ℵ∩ ≠→ℑƒ÷ƒ↵⇒ℜ⊇ℵ∩ °⊗↵ϒ×ℵ™∩∉÷ N 1 + N 2
Á¤´ äÀº (A)
21. If a train travels at a speed of k meters per second, how many kilometers will it travel in t minutes? (1 kilometer = 1,000 meters) (A) (B) (C) (D) (E)
60kt 1,000 60kt 100 1,000kt 60 6.000kt 60, 000kt Distance(° Ÿ ®) = Rate(¼Óµµ) × Time(½Ã° £)
ÃÊ´ ç k metersÀ» °¡ ´  ±âÂ÷°¡ t minutes ÈÄ ¸ î kilometersÀ» °¡ ´ ÂÁö¸ ¦ ±¸ ÇÏ ´  ¹ ®Á¦ ³ ׿ä. K metersÀ» 1,000À¸ · Î ³ ª ´ « ÈÄ ´ ٽà 60À» ° öÇØÁÖ¸ é Á¤´ äÀ» ±¸ ÇÒ ¼ö ÀÖ³ ׿ä. ÿ
Á¤´ äÀº (A)
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GRE Math °- ÁÂ Set 8-1
22. Mason and Kathy, who both work in the evening wish to arrange for an evening off together. Each evening that Mason is off is followed by 3 evenings that he is a work, and each evening that Kathy is off is followed by 5 evenings that she is at work. If Mason will be off this evening, and Kathy will be off tomorrow evening, how many evenings must pass before they have an evening off together? (A)
10
(B)
12
(C)
24
(D)
28
(E) So long as they continue this working pattern, they will never have the same evening off. Mason Àº 4ÀÏ ¿¡ ÇÑ ¹ ø, Kathy´  5¿¡ ÇÑ ¹ ø¾¿ ½®´ Ù´  Àǹ Ì ÀÔ´ Ï ´ Ù. ÀÌ ¹ ®Á¦ ´  ½ÇÁ¦ · Î ±×¸ ² À» ±×· Á °¡ ¸ ç µûÁ®¾ß ÇÏ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. °¡ ² û ÀÌ · ¯ÇÑ ¹ ®Á¦ µµ ÃâÁ¦ µË´ Ï ´ Ù. ÿ Á¤´ äÀº
(E)
23. On a certain 10-question test, each question after the first question is worth 2 points more than the previous question. If the greatest number of points that can be scored on the test is 100, how many points is the eighth question worth? (A)
9
(B) 14
(C) 15
(D) 19
(E) 33
10¹ ®Á¦ · Î ÀÌ · ç¾î Áø test¿¡ ¼ °¢ ¹ ®Á¦ ¿¡ ´ëÇÑ Á¡ ¼ö´  1¹ ø ¹ ®Á¦ ÀÌ ÈÄ· Î ´  ¾ÕÀÇ ¹ ®Á¦ º ¸´Ù 2Á¡ ¾¿ ¿Ã¶ó °¡ ¸ ç ¹ ®Á¦ ¸ ¦ Ç®¾î ¼ ÃÖ°í · Î ¾òÀ» ¼ö ÀÖ´Â Á¡ ¼ö°¡ 100Á¡ÀÏ ¶§ 8¹ ø ¹ ®Á¦ ÀÇ Á¡ ¼ö¸¦ ¹ ° ¾î º ¸ °í ÀÖ´ Ù. 10S(ó À½ °ª ) + (2 + 4 + 6 + ⋅⋅⋅ + 18) = 100 ⇒ S = 1(ÃʱⰠª )¿¡ 2×7 = 14À» ´ õÇÏ ¸ é 15. ÿ Á¤´ äÀº
(C)
24. A certain car dealership sells only full-size and mid-size cars. One of its sales representatives receives an annual salary of $15,000. He also receives a commission of $800 for each full-size car he sells and $500 for each midsize car he sells. What is the least number of cars he must sell in a year to receive total annual earnings of exactly $25,000?
(A)
7
(B) 12
(C) 13
(D) 14
(E) 17
$ 15,000Àº ÆǸ Å· ®°ú »ó° ü ¾øÀÌ ¹ Þ´Â ¿¬º ÀÀÌ ±â ¶§¹ ®¿¡ ¿ì ¼± $25,000¿¡ ¼ »©¾î ÁÖ°í ³ ² °Ô µÇ´Â $10,000¸ ¸ Å À» commissionÀ¸ · Î ¹ ÞÀ¸ ¸ é µË´ Ï ´ Ù. ÀÌ Á¦ ÀÚµ¿Â÷ ÆǸ Å· ®À» °¡Àå ÀÛ°Ô ÇÏ · Á¸ é µÉ ¼ö· Ï ´ ë´ ç commissionÀÌ ³ ôÀº a full size carÀ» ¸ ¹ ÀÌ ÆǸ ÅÇÏ ¸ é µÇ°ÚÁÒ. $ 800x + $ 500y = $10,000 À» ¸¸ Á· ÇÏ ´  °ª À» ±¸ ÇÏ ¸ é X°¡ 12ÀÏ ¶§°¡ $9,600ÀÌ µÇ¹ Ç· Î Á¤´ äÀÔ´ Ï ´ Ù. . ÿ
Á¤´ äÀº (D)
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25. A school supply store sells only one kind of desk and one kind of chair, at a uniform cost per desk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs then the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs? (A)
5
(B)
3
(C)
8 3
(D)
5 2
(E)
7 3
3Desk + Chair = 2(D+3C) ⇒ D = 5C 4D + C = x (D+4C) ⇒ ¿©±â¿¡ D = 5CÀ» ´ ëÀÔÇÏ ¸ é 21C = x ( 9C ) ⇒ x = 7/3 ÿ Á¤´ äÀº
(E)
26. A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment? (A)
24
(B) 25
(C) 26
(D) 28
(E) 30
Total revenue ( x -2° ³ ÀÇ ÆǸ Å revenues¿¡ ¼- 2° ³ ´  demonstrators· Î »ç¿ëÇ߱⠶§¹ ®¿¡ »©ÁÜ) = $120 + the cost of shipment ($300) ⇒
300 + $5) × ( x − 2 ) − 300 × 2 − the cost of shipment ($300) = $120 x x À§ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é x 2 − 26 x − 240 ⇒ x = 30 Total Revenue (
ÿ Á¤´ äÀº
(E)
27. A manufacturer can save x dollars per unit in production costs by overproducing in certain seasons. If storage costs for the excess are y dollars per unit per day ( x > y ) , which of the following expresses the maximum number of days that n excess units can be stored before the storage costs exceed the savings on the excess units? (A) x − y
(B) ( x − y )n
(C)
x y
(D)
xn y
(E)
x yn
D¸ ¦ º ¸ °üÇÏ ´  ³ ¯ÀÌ ¶ó°í ÇÏ ¸ é,
nx = ynD ⇒ D = ÿ
x y
Á¤´ äÀº (C)
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28. A certain disability plan pays monthly benefits of 60 percent of the first $2,000 of monthly salary plus 40 percent of any portion in excess of $2,000 —the total monthly be nefit not to exceed $2,500. What is the smallest monthly salary that will yield the maximum monthly benefit under this plan? (A)
$5,750
(B) $5,250
(C) $4,500
(D) $3,250
(E) $2,200
$2,000ÀÌ ÇÏ ÀÎ ±Þ¿©¿¡ ´ ëÇؼ ´  60%°¡ Áö±ÞµÇ±â ¶§¹ ®¿¡ $2,500¿¡ ¼ $1,200À» Á¦ ¿ÜÇÑ $1,300À» ¹ Þ±â À§ÇÑ ÃÖ¼Ò±Þ¿©°¡ ¾ó¸ ¶ÀÎ Áö¸ ¦ °è»êÇÏ ¸ é µË´ Ï ´ Ù. $ 1,300 ×(5/2)= $ 3,250 °á±¹ , $2,000 + $ 3,250 = $ 5,250 (ÇÔÁ¤) $3,250¿¡ $2,000À» ´ õÇÏ ¿© ÁÖ´  °Í À» ÀØÀ¸ ¸ é ¾ÈµË´ Ï ´ Ù. ÿ Á¤´ äÀº
(B)
29. One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and
1 of the nondefective switches are rejected by mistake. 20
If all the switches not rejected are sold, what percent of the switches sold by the factory are defective? (A)
4%
Àüü »ý»ê· ®ÀÇ
(B)
5%
(C) 6.25%
(D) 11%
(E) 16%
1 4 1 °¡ º Ò· ®Ç°ÀÌ ¸ ç , º Ò· ®Ç°ÀÇ °¡ Á¦ °Å µÇ¾î Áö³ ª º Ò· ®Ç°ÀÌ ¾Æ´ Ñ Á¦ Ç°ÀÇ 20 5 5
ÀÌ ¶ÇÇÑ ½Ç¼ö· Î Á¦ °Å µÇ¾î Áø´ Ù°í ÇÕ´ Ï ´ Ù.ÀÌ · ² ¶§ ÆǸ Å µÇ¾î Áö´  Á¦ Ç° Áß º Ò· ®Ç°ÀÇ º ñÀ² À» ±¸ÇÏ ¶ó´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù.
• º Ò· ®Ç°ÀÌ ¸ ç Á¦ °ÅµÇ¾î Áö´  Á¦ Ç°ÀÇ º ñÀ² (defective and rejected) : 1 4 × = 0.16 (16%), Àüü »ý»ê· ® Áß 20%( 1 )°¡ º Ò· ®Ç°ÀÌ ¶ó°í Ç߱⠶§¹®¿¡ 20% - 16% =4% 5 5 5 ÀÇ º Ò· ®Ç°ÀÌ Á¦ °ÅµÇÁö ¾Ê´Â´ Ù´  Àǹ Ì ÀÔ´ Ï ´ Ù.
• º Ò· ®Ç°ÀÌ ¾Æ´ Ï Áö¸ ¸ Á¦ °ÅµÇ¾î Áö´  Á¦ Ç°ÀÇ º ñÀ² (not defective and rejected) : 4 1 × = 0.04 , Àüü »ý»ê· ® Áß º Ò· ®Ç°ÀÌ ¾Æ´ Ñ 4%ÀÇ Á¦ Ç°ÀÌ º Ò· ®Ç°À¸ · Î ¿ÀÀÎ µÇ¾î ÆǸ ÅµÇ 5 20 Áö ¾Ê½À´ Ï ´ Ù. µÎ °á°ú¸¦ ÇÕÄ¡ ¸ é Àüü »ý»ê· ® Áß º Ò· ®Ç° 16%, Á¤»óÁ¦ Ç° 4%° ¡ Á¦ °Å µÇ¾î ÃÑ»ý»ê· ®ÀÇ 80%°¡ ÆǸ ŵǾî Áö° í ÀÌ Áß º Ò· ®Ç° 4%°¡ ¼¯ÀÌ ¾î µé¾î °©´ Ï ´ Ù. Æ÷ÀÎ Æ®´  Æȸ ° ¹ °°Ç Áß¿¡ ¸ î percent °¡ defective ÀÎ °¡ ¸ ¦ ¹ ¯´  ¹ ®Á¦ ÁÒ. °ø½ÄÀ» Á¤¸ ®ÇÏ ¸ é:
part 4%(defective & sold ) = = 5% whole (80% − 4%) + 4% ÿ Á¤´ äÀº
(B)ÀÔ´ Ï ´ Ù.
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30. In Company X , 30 percent of the employees live over ten miles from work and 60 percent of the employees who live over ten miles from work are in car pools. If 40 percent of the employees of Company X are in car pools, what percent of the employees of Company X live ten miles or less from work and are in car pools ? (A)
12%
(B) 20%
(C) 22% 10 miles ÀÌ»ó
Car pool
(D) 28% 10 miles ÀÌ ÇÏ 40 – 18 = 22%
30% × 60%
(E) 32% Total 40%
Not Car pool 30% ¹ ®Á¦ ´  10milesÀÌ ÇÏ ÀÌ °í car poolÀ» ÇÏ ´  »ç¶÷ÀÇ percentÀ» ±¸ ÇÏ ´  °Í ÀÔ´ Ï ´ Ù. À§ÀÇ ±×¸ ² Âü°í ! ÿ Á¤´ äÀº
(C)
31. A garment order consists of jackets costing $36 each and shirts costing $26 each. If the total cost of the order is $1,200, and if the average (arithmetic mean) cost per garment is $30, how many more shirts than jackets are in the order? (A)
32
(B) 22
(C) 18
(D) 13
(E) 8
jacketÀÇ °¡ °ÝÀº $36, shirtÀÇ °¡ °ÝÀº $26ÀÌ ¸ ç Æò±Õº ñ¿ëÀº $30ÀÌ ¶ó¸ é, jacketÀ» 2¹ ú ±¸ ÀÔÇÒ ¶§ shirt¸ ¦ 3¹ ú ±¸ ÀÔÇß´ Ù´  °Í ÀÌ ´ Ù. ±×· ¡ ¾ß °¡ Áß Æò±ÕÀ» ±¸ ÇÒ ¶§ Æò±Õº ñ¿ëÀÌ $30ÀÌ µÇ¾î Áø´ Ù. ÀÌ · ¯ÇÑ »ç½ÇÀ» ÀÌ ¿ë ÇÏ ¿© ´ ÙÀ½°ú ° °ÀÌ ¹ ®Á¦ ¸ ¦ ÇØ°áÇÒ ¼ö ÀÖ´ Ù. $36 × N + $26 ×1.5N= $1,200 ⇒ N(jackets) = 16°³ , µû¶ó¼ shirts´  16×1.5 =24° ³ ÀÔ´ Ï ´ Ù. 24°³ – 16°³ = 8°³ ÿ Á¤´ äÀº
(E)
32. The front wheels of a toy truck are 4 inches in circumference. The back wheels are 7 inches in circumference. If the truck travels in a straight line without slippage, how many inches will the truck have traveled when the front wheels have made 12 more revolutions than the back wheels? (A) 112
(B) 64
(C) 48
(D) 36
(E) 28
¾Õ ¹ ÙÄûÀÇ ¿øÁÖ°¡ 4 inches, µÚ ¹ ÙÄûÀÇ ¿øÁÖ°¡ 7inches ÀÏ ¶§ ¾Õ ¹ ÙÄû°¡ µÚ ¹ ÙÄûº ¸ ´ Ù 12¹ ÙÄû ´ õ ȸ Àü ÇßÀ» ¶§ ¿òÁ÷ÀÎ °Å¸ ®¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÀÌ ¹ ø ¹ ®Á¦ ´  ¸ ¶Ä¡ °ø¹ è¼ö¸¦ ±¸ÇØ ÁÖ´Â ¹ ®Á¦ ¿Í °°Àº ³ í ¸ ®· Î ÇØ°áÇÏ ¸ é µË´ Ï ´ Ù. µÎ ¹ ÙÄûÀÇ ¿ø ÁÖ°¡ ¼·Î ´ Ù¸ £Áö¸ ¸ ¿òÁ÷ÀÎ °Å¸ ®´  °°°Ô µË´ Ï ´ Ù. ¿òÁ÷ÀÎ °Å¸ ®°¡ ÀÏ Ä¡ ÇÏ · Á¸ é µÚ ¹ ÙÄû°¡ 4¹ Ù Äû (28inches) µ¹ ¶§ ¾Õ ¹ ÙÄû´  7¹ ÙÄû(28inches) µ¹ ¾Æ¾ß ÇÕ´ Ï ´ Ù. °á±¹ 3¹ ÙÄû¸¦ ´ õ µ¹ ¾Æ¾ß µË´Ï
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GRE Math °- ÁÂ Set 8-1
´ Ù. ÀÌ · ¯ÇÑ °á° ú· Î 28 inches¾¿ ° ¥ ¶§ ¾Õ ¹ ÙÄû´  µÚ ¹ ÙÄû º ¸ ´ Ù 3 ¹ ÙÄû¸ ¦ ´ õ µ¹ ¾Æ¾ß ÇÑ´ Ù´  »ç½ÇÀ» ¾Ë¾Ò½À´ Ï ´ Ù. ¹ ®Á¦ ´  ¾Õ ¹ ÙÄû°¡ 12 ¹ ÙÄû¸ ¦ ´ õ µ¹ ¸ é, Áï 3 revolution : 28 inches = 12 revolution : X ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é X = 112 ÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(A)ÀÔ´ Ï ´ Ù.
33. A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, the average number sold was 84, and among the male members, the average number sold was 96. What was the ratio of the number of male members to the number of female members in the club? (A)
1:1
(B) 1 : 2
(C) 1 : 3
(D) 2 : 1
(E) 3 : 1
Àüü Æò±ÕÀ¸ · Πȸ¿ø 1¸ í ÀÌ 92°³ ÀÇ ticketÀ» ÆȾҰí , ȸ ¿ø Áß ³ ² ¼º Àº 96Àå ¿©¼º Àº 84Àå ÆȾҴ Ù ¸ é ³ ² ¼º Àº 1¸ í ´ ç Æò±Õº ¸ ´ Ù 4À徿 ´ õ ÆÈ¾Ò°í ¿©¼º Àº 8¾¿À» ´ ú ÆȾҴ Ù. ÀÌ · ¯ÇÑ »óȲ ¿¡ ¼ Æò±Õ À» ¸ ÂÃß¾î ÁÖ±â À§Çؼ ´  ¿©¼º 1¸ í ´ ç ³ ² ¼º 2¸ í ÀÌ ticketÀ» ÆÈ¾Æ¾ß Æò±Õ°ú ÀÏ Ä¡ ÇÏ °Ô µË´ Ï ´ Ù. ÿ Á¤´ äÀº
(D)
34. A team won 40 percent of the 15 games it has already played. If the team were to win 75 percent of its remaining games, it will have won 60 percent of all its games. How many remaining games are there? (A)
12
(B) 20
(C) 24
(D) 30
(E) 45
ÀÌ ¹ Ì 15 °æ±â Áß¿¡ ¼6°æ±â¸ ¦ ½Â¸ ®ÇÏ ¿© 40%ÀÇ ½Â· üÀ» ±â· Ï ÇÏ °í ÀÖÀ¸ ¸ ç , ³ ª ¸ ÓÁö °æ±â¿¡ ¼ 75%ÀÇ ½Â· üÀ» ±â· Ï ÇÒ ¶§ Àüü °æ±âÀÇ ½Â· üÀÌ 60%°¡ µÈ´ Ù°í ÇÕ´ Ï ´ Ù. 40%ÀÇ ½Â· üÀ» ±â· Ï ÇÏ °í ÀÖ´  15° æ±â¿¡ ¼ ½Â· üÀÌ Æò±ÕÀÎ 60%°¡ µÇ±â À§Çؼ ´  3°æ±â¸ ¦ ´ õ ÀÌ °å¾î ¾ß µË´ Ï ´ Ù. °á±¹ 15° æ±â ÀÌ ¿ÜÀÇ °æ±â¿¡ ¼( n ) ½Â· üÀÌ 75%°¡ µÇ¸ é ÀÌ ´  ÃÑ°æ±â¿¡ ´ ëÇÑ Æò±Õ ½Â· ü 60%º ¸ ´ Ù 15%¸ ¸ Å »óȸ ÇÏ °í ÀÖ´  °Í ÀÌ ¸ ç 15%´  3°æ±â¿¡ ¼ ÀÇ ½Â¸ ®¸ ¦ Àǹ Ì ÇÏ ´  °Í ÀÌ ´ Ù.
n×
15 = 3 (°æ±â) 100
e
n = 20
Çؼ³ 2 ¶Ç ´ Ù¸ ¥ ¹ æ¹ ýÀº nÀ» ³ ² Àº °æ±â¼ö¶ó ° ¡ Á¤ÇÏ °í ´ ÙÀ½°ú ° °ÀÌ ½ÄÀ» ¸ ¸ µé ¼ö ÀÖÁÒ: 6 games + 0.75( n ) = (15 + n )0.6 , ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é n = 20 ÿ Á¤´ äÀº
(B)ÀÔ´ Ï ´ Ù.
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35. In a quality control process it has been determined that all of the engines that fail inspection are faulty, but approximately
1 of the faulty engines pass inspection. If, in a group of 1,000 6
engines, 100 fail inspection, approximately how many faulty engines pass inspection? (A)
16
(B)
20
(C) 50
(D) 70
(E) 120
º Ò· ® ¿£ÁøÀÇ 5/6ÀÌ °Ë»ç¸ ¦ Åë° úÇÏ Áö ¸ øÇßÀ¸ ¸ ç ±× °³ ¼ö´  100° ³ ÀÌ ´ Ù. º Ò· ®¿£Áø°³ ¼ö°¡ F°³ ¶ó¸ é, F × (5/6) = 100 , Àüü º Ò· ® ¿£Áø °³ ¼ö´  120°³ ÀÌ ´ Ù. ÿ Á¤´ äÀº
(B)
36. If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production? (A)
4%
(B) 10%
(C) 14%
(D) 15%
(E) 18%
ticketÀÇ °¡ °ÝÀ» P , cost¸ ¦ C¶ó°í ÇÏ ¸ é, P× N = 1.2C, ±×· ¯³ ª ticketÀÌ 95%¸ ¸ ÆǸ Å µÇ¾ú±â ¶§¹ ®¿¡ ´ ÙÀ½°ú °°´ Ù. 0.95×(N×P) = 0.95×1.2C = 1.14C ÿ Á¤´ äÀº
(C)
37. Jeff drove to work from his home averaging 40 miles per hour, and was 12 minutes late. The next day he left home for work at the same time, took the same route, averaging 48 miles per hour, and was 7 minutes late. How far in miles is it from Jeff’ s home to his work? (A)
20.0
(B) 24.5
(C) 30.0
(D) 37.5
(E) 40.0
¼Óµµ´  40miles ¿¡ ¼ 48miles · Î º ¯È ÇÏ ¿© 20% Áõ°¡ ÇÏ ¿´ À¸ ¸ ç , ½Ã°£Àº 5º ÐÀÌ ´ ÜÃàµÇ¾ú½À´ Ï ´ Ù. Ãâ±Ù°Å¸ ®¸ ¦ D ¶ó° í ÇÏ ¸ é ´ ÙÀ½ÀÇ ½ÄÀÌ ¼º ¸ ³ ÇÕ´ Ï ´ Ù.
D = (¼Óµµ) × (ÁÖÇà½Ã°£), Ãâ±Ù°Å¸ ®´  º ¯ÈÇÏ Áö ¾Ê°í ¼Óµµ¿Í ½Ã°£¸ ¸ º ¯ÈÇÑ °Í ÀÌ ±â ¶§¹ ®¿¡ ¶ÇÇÑ ´ ÙÀ½ÀÇ ½ÄÀÌ ¼º ¸ ³ ÇÕ´ Ï ´ Ù. D = S × H = 1.2 S × xH À§ÀÇ ½ÄÀÌ ¼º ¸ ³ ÇÏ ±â À§Çؼ ´  48miles· Î ´ Þ¸ ± ¶§ ¼Ò¿äµÇ´  ½Ã°£Àº
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· Î½á ¹ ß»ýÇÏ ´  ½Ã°£ÀÇ Â÷ÀÌ
1 H ´  40miles· Î Ãâ±ÙÇßÀ» ¶§¿Í 48miles· Î Ãâ±ÙÇßÀ» ¶§ ¹ ß»ýÇÏ 6
´  ½Ã°£ÀÇ Â÷ÀÌ 5º ÐÀÌ µÇ´  °Í ÀÔ´ Ï ´ Ù. °á±¹ 40 mileÀÇ ¼Óµµ· Î 30º а£ ÃÑ20mileÀÇ °Å¸ ®¸ ¦ ´ Þ¸ ° °Í ÀÔ´ Ï ´ Ù. Çؼ³ 2 µµÂøÇÏ °í ½Í Àº ½Ã°£À» T¶ó °¡ Á¤ÇÏ °í 12º аú 7º Ð ´ ʾú´ Ù´  °Í Àº T¿¡ ´ õÇØÁÖ´  ½ÄÀ¸ · Î À¯µµÇÏ ¸ é: 40 miles(T + 12 minutes) = 48miles(T+7minutes) ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é T= 18 minutesÀ» ±¸ ÇÒ ¼ö ÀÖ³ ׿ä . ¾Æ¹ « °÷¿¡ T¸ ¦ ´ ëÀÔÇؼ Ç®¸ é °Å¸ ®¸ ¦ ±¸ ÇÒ ¼ö ÀÖÁÒ. ´ Ü ¿©±â¼ ´  ´ ÜÀ§´  hours ÀÌ ¹ Ç· Î minutesÀ» hours· Î ¹ Ù² ã¾ß°Ú³ ׿ä !!! ÿ Á¤´ äÀº
(A)ÀÔ´ Ï ´ Ù.
38. If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day? (A)
100
(B) 120
(C) 140
(D) 150
(E) 160
Æò±Õ 5 miles ´ õ »¡ ¸ ® ±×¸ ®°í ÁÖÇà ½Ã°£À» ÇÑ ½Ã°£ Áõ°¡ ÇÏ ¸ é 70miles¸ ¦ ´ õ °¡ °Ô µÈ´ Ù°í ÇÕ´Ï ´ Ù. ½ÇÁ¦ · Î ¿î ÇàÇÑ ½Ã°£À» h , ½ÇÁ¦ ¼Óµµ¸¦ s ¶ó ÇÏ ¸ é ´ ÙÀ½ ½ÄÀÌ ¼º ¸ ³ ÇÕ´ Ï ´ Ù: h × s = D¶ó °¡ Á¤ÇÏ ¸ é
]
( s + 5) × (1 × h ) = D + 70 (miles) h × s = D ÀÌ ¹ Ç· Î ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é
S + 5 h = 65À» ±¸ ÇÒ ¼ö ÀÖ´ Ù. ±× ´ ÙÀ½Àº 10miles ´ õ »¡ ¸ ® ±×¸®°í 2½Ã°£ ´ õ ÁÖÇàÇÑ´ Ù¸ é,
( s + 10) × (2 × h ) = D + X , ¿©±â¼ ±¸ ÇÒ °ª Àº XÀÌ °í , j h × s = D ÀÌ °í , k S + 5 h = 65 j°úkÀ» ÀÌ ¿ëÇØ À§ÀÇ ÿ Á¤´ äÀº
½ÄÀ» Á¤¸ ®ÇÏ ¸ é X °ª À» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù.
(D)ÀÔ´ Ï ´ Ù.
39. When a certain stretch of highway was rebuilt and straightened, the distance along the stretch was decreased by 20 percent and the speed limit was increased by 25 percent. By what percent was the driving time along this stretch reduced for a person who always drives at the speed limit? (A) 16%
(B) 36%
1 2
(C) 37 %
(D) 45%
1 4
(E) 56 %
°Å¸ ®(distance) = ¼Óµµ(speed) × ½Ã°£(time), ½Ã°£ = °Å¸ ® / ¼Óµµ = 0.8°Å¸ ®/ 5/4 ¼Óµµ ÿ
Á¤´ äÀº (B)
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GRE Math °- ÁÂ Set 8-1
Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water
40.
evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X ? (A)
30%
(B)
1 33 % 3
(C) 37
1 % 2
(D) 40%
(E) 50%
¿ø· ¡ ¿ë¾× Y ÀÇ ±¸ ¼º : liquid 30%, water 70% ±¸ ¼º µÊ ](1)
8 kilogramsÀÇ Y ¿ë¾×¿¡ ¼ ¹ °¸ ¸ 2 Kg Áõ¹ ßµÈ ÈÄ ¿ë¾×Y :
Liquid X ÀÇ Áú· ® : 8( Kg ) × 0.3 = 2.4( Kg ) (º ¯ÇÏ Áö ¾ÊÀ½) ¹ °ÀÇ Áú· ® ](2)
: 5.6 Kg (= 8kg × 70%) − 2 Kg = 3.6 Kg (2 Kg Áõ¹ ß)
÷ º Î ÇÒ 2 Kg solution Y ÀÇ ±¸ ¼º
Liquid X ÀÇ Áú· ® : 2( Kg ) × 0.3 = 0.6( Kg ) ¹ °ÀÇ Áú· ® ](3)
: 2( Kg ) × 0.7 = 1.4( Kg )
³ ² ¾ÆÀÖ´  6 kilograms (8kilograms¿¡¼ ¹ °ÀÌ 2 kilogramsÁõ¹ß )ÀÇ ¿ë¾× Y¿¡ »õ· Î ¿î 2
kilograms Y¸¦ È¥ÇÕÇÑ ÈÄ(8 kilograms) Liquid X ÀÇ Áú· ® : 2.4( Kg ) + 0.6( Kg ) = 3.0( Kg ) ¹ °ÀÇ Áú· ®
: 3.6( Kg ) + 1.4( Kg ) = 5.0( Kg )
Liquid XÀÇ percent =
ÿ Á¤´ äÀº
3.0 × 100 = 75 8.0 2
(C)ÀÔ´ Ï ´ Ù.
41. How many gallons of water must be mixed with 1 gallon of a 15-percent salt solution to obtain a 10-percent salt solution? (A) 0.50
(B) 0.67
(C) 1.00
(D) 1.50
(E) 2.00
ÇöÀç ¿ë¾× : 1 gallon, ±× Áß¿¡ ¼Ò±ÝÀº 0.15 gallon Èñ¸ Á ¿ë¾× : ¼Ò±Ý 10%À» ¸ ¸ µé· Á¸ é 0.15 gallonÀÌ Àüü ¿ë¾× 1.5gallonÀÇ 10%¸ ¦ Â÷ÁöÇÏ ¸ é µÇ¹ Ç · Î ÇÊ¿äÇÑ ¿ë¾×Àº 0.50ÀÌ µÈ´ Ù. ÿ Á¤´ äÀº
(A)
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42. The seating chart of an airplane shown 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window seat. The view from the window seats in 5 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and the window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view? (A)
1 6
(B)
1 3
(C)
2 3
(D)
5 6
(E)
17 18
ÃÑ Á¼® ¼ö : 180°³ ( ÇÑ ÁÙ¿¡ 6 Á¼®¾¿ 30 ÁÙ ) º ñÇà±â ³ ¯°³ ¿¡ ÀÇÇØ °æÄ¡ °¡ º ¸ ÀÌ Áö ¾Ê´  Á¼® ¼ö : 30 Á¼® °æÄ¡ °¡ º ¸ ÀÌ ´  Á¼®¿¡ ¾É°Ô µÉ È®· ü : 150 / 180 ÿ Á¤´ äÀº
(C)
43. One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week? (A)
18
(B) 16
(C) 12
(D) 8
(E) 4
ÃÑ 20´ ëÀÇ truckÀÌ ¿ù¿äÀÏ ¿¡ ÀÚµ¿Â÷ rentalȸ »çÀÇ ÁÖÂ÷Àå¿ ¡ ÀÖ°í º ô· Á ÁØ Â÷ÀÇ 50%°¡ Åä¿äÀÏ ¾Æħ Àü±î Áö ȸ ¼öµÇ¾î Åä¿äÀÏ ¾Æħ¿¡ ÃÖ¼Ò 12´ ëÀÇ truckÀÌ ÀÖÀ» ¶§ ÁÖÁß¿ ¡ ´ ë¿© µÇ¾ú´ ø Â÷ ÀÇ ¼ö¸ ¦ ¹ ¯°í ÀÖ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. Åä¿äÀÏ ¾Æħ Àü±î Áö ´ ë¿© µÇ¾ú´ ø Â÷ÀÇ 50%°¡ ȸ ¼öµÇ´  °Í ÀÌ ¹ Ç· Î º ô· ÁÁØ ÀÚµ¿Â÷ÀÇ ´ ë¼ö´  ¿ì ¼± ¦ ¼öÀÌ ¾î ¾ß ÇÕ´ Ï ´ Ù. ¸ ¸ ¾à 18´ ë°¡ ÁÖÁß¿¡ ´ ë¿ © µÇ¾ú´ Ù¸ é Åä¿äÀÏ ¾Æħ±î Áö 9´ ë°¡ ¹ ݳ ³ µÇ¾î Áú °Í ÀÌ °í ´ ë¿©µÇÁö ¾Ê °í ÁÖÂ÷Àå¿¡ ÀÖ´ ø Â÷ 2´ ë¿Í ÇÔ² ² 11´ ëÀÇ Â÷°¡ Åä¿äÀÏ ¾Æħ¿¡ ÀÖ¾î ¾ß ÇÕ´ Ï ´ Ù. ±×· ¯¹ Ç· Î 18Àº ´ äÀÌ ¾Æ´ Õ´ Ï ´ Ù. 16´ ë°¡ ´ ë¿© µÇ¾ú´ Ù¸ é 8° ³ °¡ ¹ ݳ ³ µÇ¾î Áö°í ÁÖÂ÷Àå¿¡ 4´ ëÀÇ Â÷°¡ ÀÖ¾úÀ» °Í ÀÌ ¹ Ç· Î Åä¿äÀÏ ¾Æħ¿¡ ÃÑ12´ ëÀÇ Â÷°¡ ÁÖÂ÷Àå¿¡ ÀÖ°Ô µË´ Ï ´ Ù. ÿ Á¤´ äÀº
(B)
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44. A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city? (A)
14
(B) 16
(C) 21
(D) 22
°í ¼Óµµ· Î ¿¡ ¼ per gallon ´ ç °¡ ´  °Å¸ ®¸ ¦ x ¶ó ÇÏ ¸ é:
462 336 = x x − 6
(E) 27
⇒ x = 22
µû¶ó¼ ½Ã³ »¿¡ ¼ ÀÇ per gallon´ ç °¡ ´  °Å¸ ®´  22 − 6 = 16 ÿ Á¤´ äÀº
(B)
45. On a 20-mile course Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and, without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course? (A)
75
(B) 105
(C) 117
(D) 150
(E) 162
20mileÀÇ °Å¸ ®¸ ¦ ó À½ 12º а£Àº 30mile· Î , ³ ª ¸ ÓÁö ° Ÿ ®´  8mileÀÇ ¼Óµµ· Î ´ Þ· ÈÀ» ¶§ 20mileÀ» ¿Ï ÁÖ ÇÏ ´ µ¥ ¼Ò¿äµÈ ½Ã°£À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 12º ÐÀº 1/5½Ã°£ÀÔ´ Ï ´ Ù. 30mileÀÇ ¼Óµµ· Î 12º а£ 6mileÀ» ´ Þ¸ ° °Í ÀÌ °í ³ ª ¸ ÓÁö °Å¸® 14mileÀº 8mileÀÇ ¼Óµµ· Î ´ Þ¸ ° °Í ÀÔ´ Ï ´ Ù. 14mileÀÇ °Å¸ ®¸ ¦ ¼Óµµ8mile· Î ³ ª ´ ©¾î ÁÖ¸é ¼Ò¿äµÈ ½Ã°£ÀÌ 1(3/4)° ¡ ³ ª ¿É´ Ï ´ Ù. 12º аú 1(3/4)½Ã°£ °ð 105º ÐÀ» ´ õÇÏ ¿© ÁÖ¸ é 117º ÐÀÌ ´ äÀÌ µË´ Ï ´ Ù. ÿ Á¤´ äÀº
(C)
46. An investor bought n shares of Company X stock at $75 per share. She sold 60 percent of the shares for $120 per share and the rest at a later date for $70 per share. If her gross profit on the sale of the n shares of stock was $7,500, how many shares did she buy? (A) 375
(B) 300
(C) 100
(D) 95
(E) 75
Company X ȸ »çÀÇ ÁÖ½ÄÀ» ÁÖ´ ç $75¿¡ nÁÖ ¸ żöÇÏ ¿© 60%´  $120¿¡ ³ ª ¸ ÓÁö´Â $70¿¡ ¸ ŵµÇÏ ¿´ À» ¶§ ¼öÀÍ ÀÌ $7,500ÀÌ ¿´ À» ¶§ ±¸ ÀÔÇÑ ÁÖ½ÄÀÇ ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ¿¬¸ ³ ½ÄÀ» ±¸ÇÏ ¿© ¹ ®Á¦ ¸ ¦ Ç® ¼ö ÀÖ½À´ Ï ´ Ù. $45 × (3/5)n + $5(2/5) =$7,500 ÿ Á¤´ äÀº
(B)
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47. In 1982 a certain company had losses of $10,000 per month. In the first three months of 1983, this company had gains of $4,000 per month. On the average, what would the company need to gain per month in the remainder of 1983 in order to break even over this two-year period? (A)
$9,000
(B) $10,800
(C) $12,000
(D) $13,500
(E) $18,000
1982³ â¿ ¡ ¸ Å ´ Þ $10,000ÀÇ ¼Õ½ÇÀÌ ¹ ß»ýÇß°í 1983³ â 1/4º б⠵¿¾È¿¡ ¸ Å´Þ $4,000¾¿ ¼öÀÍ ÀÌ ¹ ß »ý ÇßÀ» ¶§ ’ 82,’83³ ⠵ΠÇØ µ¿¾È¿¡ break evenÇÏ ±â À§ÇÏ ¿© ’ 83³ â ³ ª ¸ ÓÁö ±â°£ µ¿¾È¿¡ ¾ó¸¶¸ ¸ Å ÀÇ ¼öÀÍ ÀÌ ¹ ß»ýÇØ¾ß ÇÏ ´ ÂÁö¸ ¦ ¹ °¾î º ¸ °í ÀÖ´ Ù. ’82³ âµµ ÃѼսÇÀº
$ 120,000ÀÌ °í ’ 83³ âµµ 1/4º бâ ÃѼöÀÍ $12,000 ÀÌ ¹ Ç· Î break even ÇÏ ±â À§
Çؼ ´  ³ ª ¸ ÓÁö ±â° £ µ¿¾È¿¡ ¸ Å´ Þ $108,000/8(´ Þ) ¸ ¸ Å ÀÇ ¼öÀÍ À» ¿À· Á¾ß ÇÑ´ Ù. ÿ Á¤´ äÀº
(C)
48. An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.60 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold? (A)
130,000
(B) 300,000
(C) 380,000
(D) 400,000
(E) 420,000
{ $260,000 – ( $0.8×100,000) } / 0.6 = 30,000 , 3 ¸ ¸ ±ÇÀÇ Ã¥Àº 10,000±ÇÀÌ Æȸ ° ÈÄ Ãß° ¡ · Î Æȸ° Ã¥ ÀÓÀ» ÁÖÀÇ ÿ Á¤´ äÀº
(D)
1 2
49. For each hour worked in excess of 40 hours per week, a mechanic is paid 1 times her regular rate of $12 per hour. Her gross pay for a week in which she works 52 hours is equal to her pay at the regular rate for how many hours? (A)
58
(B) 64
(C) 66
(D) 70
(E) 78
40½Ã°£À» ÃÊ°úÇÏ ´  ±Ù¹ «½Ã°£¿¡ ´ ëÇؼ ´  ½Ã°£´ ç $12ÀÇ ±Þ· á¿¡ 1(1/2)¹ è¸ ¦ Áöº ÒÇÒ ¶§, 52½Ã°£ À» ±Ù¹ «ÇÏ ¿´ À» ¶§ ¹ Þ´  ±Þ· á´ Â ÃÊ°ú½Ã°£±Ù¹ «¸ ¦ ÇÏ Áö ¾Ê°í ¸ î ½Ã°£À» ÀÏ ÇÒ ¶§ ¹ Þ´Â ±Þ· á¿Í °°Àº Áö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÃÊ°ú±Ù¹ «¿¡ ´ ëÇÏ ¿©´  1(1/2)¹ èÀÇ ±Þ· Ḡ¦ ¹ Þ°í Àֱ⠶§¹ ®¿¡ Á¤»ó±Ù¹ «ÀÇ 2/3½Ã°£¸ ¸ À» ÀÏ ÇÏ °í µµ Á¤»ó±Ù¹ «½Ã°£¿¡ ¹ Þ´  ±Þ· Ḡ¦ ¹ ÞÀ» ¼ö ÀÖ½À´ Ï ´ Ù. ±×· ¯¹ Ç· Î ÃÊ°ú½Ã°£ ±Ù¹ « 1½Ã°£Àº Á¤»ó±Ù¹ « ½Ã°£ÀÇ 3/2¹ èÀÎ °Í ÀÔ´ Ï ´ Ù. ¹ ®Á¦ ¿¡ ¼ 12½Ã°£À» ÃÊ°ú±Ù¹ « ÇÏ ¿´ ±â ¶§¹ ®¿¡ ÀÌ ¸ ¦ Á¤»ó±Ù¹ «½Ã°£À¸ · Πȯ»êÇÏ ¸ é 18½Ã°£ÀÌ µË´Ï ´ Ù. ÀÌ ¹ ®Á¦ ÀÇ ÇÙ½ÉÀº ½Ã°£´ ç ±Þ· á $12¸ ¦ °è»ê½Ä¿¡ ¿¬°ü ½ÃÅ°Áö ¾Ê°í ¹ ®Á¦ ¸ ¦ Ç®¾î ½Ã°£À» ´ ÜÃà ÇÏ ´  °Í ÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(A)
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50. Fifty percent of the subscribers to newspaper X are corporate managers and of these, 30 percent are in the financial field. If 40 percent of the subscribers who are corporate managers in the financial field are money managers, how many of the newspaper’ s 25,000 subscribers are corporate money managers in the financial field? (A) 1,500
(B) 3,000
(C) 3,750
(D) 7,500
(E) 8,750
50% ±¸µ¶ÀÚ°¡ corporate managerÀÌ ¸ ç, À̵é Áß 30%° ¡ finance º о߿¡ ¼ ÀÏ ÇÑ´ Ù°í ÇÑ´ Ù. finance º о߿¡ ¼ ÀÏ ÇÏ ´  corporate managerÁß 40%°¡ money managerÀÏ °æ¿ì , 25,000¸ í ÀÇ ±¸ µ¶ÀÚ Áß finance º о߿¡ ¼ ÀÏ ÇÏ ´ Âcorporate money manager´  ¸ î ¸ í ÀÎ °¡ ¸ ¦ ¹ °¾î º ¸ °í ÀÖ´ Ù. Finance º о߿¡ ¼ ÀÏ ÇÏ ´  Corporate manager ÀÇ º ñÀ² : 50% × 30 % finance º о߿¡ ¼ ÀÏ ÇÏ ´ Âcorporate money manager ÀÇ º ñÀ² : 50% × 30 %× 40% µû¶ó¼ 25,000 × 50% × 30 %× 40% = 1,500 ÿ
Á¤´ äÀº (A)
51. Reggie had to type 90 letters. During the first day he typed second day he typed
1 of the letters, and during the 3
2 of the remaining letters. How many letters were still untyped at the 5
end of the second day? (A)
36
(B) 32
(C) 24
(D) 18
(E) 12
ù ¹ ø° ³ ¯ : (1/3) × 90 µÎ ¹ ø° ³ ¯ : 60 × (2/5) ¸ ¶Áö¸ · ³ ¯ : 90 – (30+24) = 36 ÿ
Á¤´ äÀº (A)
52. One karat signifies that
1 of an alloy is pure gold. If a certain ring is 14-karat gold, 24
approximately what percent of the alloy composing the ring is not gold? (A)
14%
(B) 24%
(C) 42%
(D) 55%
(E) 58%
one-karatÀº È¥ÇÕ¹ °ÀÇ 1/24°¡ ¼ø±ÝÀÓÀ» Àǹ Ì 14-karat goldÀº È¥ÇÕ¹ °ÀÇ 14/24° ¡ ¼ø±Ý. ÿ Á¤´ äÀº
(C)
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GRE Math °- ÁÂ Set 8-1
1 1 of the pizzas sold in one week were mushroom and of the 8 3 remaining pizzas sold were pepperoni. If n of the pizzas sold were pepperoni, how many
53. At a certain pizzeria,
were mushroom? (A)
3 n 8
(B)
3 n 7
(C)
7 n 16
(D)
7 n 8
(E) 3n
ÆǸ ÅµÈ ÇÇÀÚÀÇ ÃÑ· ®À» P¶ó ÇÏ ¸ é, Mushroom: 1/8P Pepperoni: 7/8P × 1/3 = 7/24P = n 1/8P = 7/24P × 3/7 = 3/7n ÿ Á¤´ äÀº
(B)
3 of the votes cast in a certain election. What fraction of the other votes 10 1 cast would she have needed in order to have received of the votes cast? 2 1 2 3 7 1 (A) (B) (C) (D) (E) 2 5 7 10 20
54. Beth received
¼±°ÅÀÇ °á°ú° ¡ 1/2°¡ µÇ±â À§Çؼ ´  2/10ÀÇ Ç¥° ¡ ´ õ ÇÊ¿äÇÕ´ Ï ´ Ù. (7/10) × X = 2/10 ÿ Á¤´ äÀº
(B)
55. From January 1, 1980, to January 1, 1984, the number of employees of Company X declined by 700 per year. If the number of employees on January 1, 1984, was 80 percent of the number on January 1, 1980, how many employees di d the company have on January 1, 1984? (A)
2,800
(B) 3,500
(C) 11,200
(D) 16,800
(E) 17,500
80³ âµµº Î ÅÍ 84³ â±î Áö ¸ ų â 700¸ í ¾¿ ±Ù· Î ÀÚ°¡ °¨ ¼ÒÇÏ ´  »óȲ ÇÏ ¿¡ ¼ 84³ âµµ ±Ù· Î ÀÚÀÇ ¼ö°¡ 80³ âµµÀÇ 80%ÀÏ ¶§ 84³ âµµ ±Ù· Î ÀÚÀÇ ¼ö¸ ¦ ±¸ÇÏ ¶ó´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. 80³ â¿¡ ¼ 84³ â±î Áö ¸ ų â 700¸ í ¾¿ ±Ù· Î ÀÚ°¡ °¨ ¼Ò Ç߱⠶§¹ ®¿¡ ÃÑ 2,800¸ í ÀÇ ±Ù· Î ÀÚ°¡ °¨ ¼Ò Çß´ Ù´  »ç½ÇÀ» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. ¶ÇÇÑ 84³ âµµÀÇ Ãѱٷ Î ÀÚ°¡ 80³ âµµ ±Ù· Î ÀÚÀÇ 80%¶ó°í Ç߱⠶§¹ ®¿¡ °¨ ¼ÒÇÑ ±Ù· Î ÀÚ 2,800¸í Àº 80³ âµµ¿¡ °í ¿ëµÇ¾î ÀÖ´ ø ±Ù· Î ÀÚÀÇ 20%ÀÓÀ» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù : 80³ â Àüü ±Ù· Î ÀÚ ¼ö
e 4³ â
ÈÄ e (80³ â ±Ù· Î ÀÚ ¼ö) × 0.8(=80%), Áï 4³ â µ¿¾È ±ÙÀÚÀÚ ¼ö
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ÀÇ 20% °¡ ÁÙ¾î ´ Ù´  Àǹ Ì ³ ׿ä. °á±¹ 80³ âµµ¿¡ °í ¿ëµÇ¾î ÀÖ´ ø ±Ù· Î ÀÚ ¼ö( x )´  ½Ä¨ ç° ú °°ÀÌ ±¸ ÇÒ ¼ö ÀÖÀ¸ ¸ ç, ¨ ç x × 0.2 = 2,800 ⇒ X = 14,000¸í 84³ âµµ¿¡ °í ¿ë µÇ¾î ÀÖ´  ±Ù· Î ÀÚÀÇ ¼ö´  ½Ä¨ è¿Í °°ÀÌ ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. ¨ è 14,000 × 0.8(80%) = 11,200 ÿ Á¤´ äÀº
(C)ÀÔ´ Ï ´ Ù.
56. Both marble tiles and terra-cotta tiles are available in squares with 12-centimeter sides, but marble tiles cost x cents more per tile than terra-cotta tiles. How much more would it cost, in cents, to tile a rectangular floor 240 centimeters by 120 centimeters with marble tiles than with terra-cotta tiles?
200 x
(A)
(B) 360 x
(C) 720 x
(D) 2,400 x
(E)
28,800−144 x
(240 cm × 120 cm) / (12×12) = 200 Á÷»ç°¢ÇüÀÇ ¸ ¶· ç¸ ¦ Àå½ÄÇÏ ´ µ¥ 200°³ ÀÇ Å¸ ÀÏ ÀÌ ÇÊ¿äÇÏ ¸ ç marble tile· Î Àå½ÄÀ» Çϱâ À§ÇÑ °³ ´ ç ° ¡ °ÝÀÌ terra-cotta tileÀÇ °¡ °Ýº ¸ ´ Ùx cents ¸ ¸ Å ³ ô±â ¶§¹ ®¿¡ Á¤´ äÀº (A)ÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(A)
57. If 6 machines ran at the same constant rate, they can complete a certain job in 8 hours. If only 5 of these machines run at this rate, how many more minutes will be required to complete the same job? (A) 38
(B) 72
(C) 80
(D) 90
(E) 96
À§ÀÇ ¹ ®Á¦ ´  ´ ÙÀ½ÀÇ °ø½Ä(word problems °ø½ÄÁ¤¸ ® Âü° í !)À» ÀÌ ¿ëÇÏ ¸ é ¾ÆÁÖ ½¬¾î Áý´ Ï ´ Ù. N1(6 machines) ×H1(8 hours) = N2(5 of these machines) × H2(?) : µ¿ÀÏ ÇÑ ÀÏ À» ÇÏ ¹ Ç· Î “=”ÀÓ ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é H2= 48/5ÀÌ´Ù. µû¶ó¼ 48/5¿¡ ¼ 8 hours À» »©ÁÖ¸ é 5 machines ÀÌ ¾ó¸ ¶¸ ¸ Å ÀÇ ½Ã°£ÀÌ ´ õ °É¸ ®´ ÂÁö °è»êÇÒ ¼ö ÀÖ´ Ù. 48/5 – 8 = 8/5 hoursÁÒ. Hours¸ ¦ minutesÀ¸ · Î ¹ Ù² Ù¸ é (8/5) × 60 = 96 minutes, Çؼ³ 2 µ¿ÀÏ ÇÑ ÀÛ¾÷ ¼Óµµ· Î (at the same constant rate) ÀÏ ÇÏ ´  6´ ëÀÇ ±â° è°¡ ƯÁ¤ÇÑ ÀÛ¾÷À» ¿Ï ¼ö ÇÏ ´ µ¥ 8½Ã°£ÀÇ ½Ã°£ÀÌ ¼Ò¿äµÉ ¶§, 5°³ ÀÇ ±â°è¸ ¸ ÀÌ ÀÛ¾÷À» ¼öÇàÇÒ ¶§ Ãß°¡ ÀûÀ¸ · Î ¼Ò¿äµÇ´  ½Ã°£Àº (º д ÜÀ§· Î ) ¾ó¸ ¶ÀÎ Áö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 6´ ëÀÇ ±â°è°¡ ÀÛ¾÷À» ¿Ï ¼öÇÏ ´ µ¥ ° ɸ ®´  ½Ã°£ÀÌ 8½Ã°£ÀÌ ±â ¶§¹ ®¿¡ 1½Ã°£ µ¿¾È¿¡ ¿Ï ¼öÇÏ ´  ÀÛ¾÷ÀÇ ¾çÀº 1/8ÀÌ ¸ ç, ÇÑ ´ ëÀÇ ±â° è°¡ ¿Ï ¼öÇÏ ´  ÀÏ ÀÇ ¾çÀº 1/48 ÀÔ´ Ï ´ Ù. 6´ ëÀÇ ±â°è°¡ ¾Æ´ Ñ 5´ ëÀÇ ±â°è°¡ ÀÏ ÇÒ °æ¿ì ¿¡ µµ ±â°è° ¡ 1½Ã°£¿¡ ¿Ï ¼öÇÏ ´  ÀÛ¾÷·®ÀÎ 1/48Àº º ¯ÇÏ Áö ¾Ê½À´ Ï ´ Ù. ÀÌÁ¦ 5´ ëÀÇ ±â° è° ¡ ÀÏ ÇÏ ±â ¶§¹ ®¿¡ 1½Ã°£µ¿¾È¿¡ ¿Ï ¼öÇÏ ´  ÀÛ¾÷· ®Àº 5/48ÀÌ
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¸ ç ÀÛ¾÷À» ¿Ï ¼öÇÏ ´ µ¥ ¼Ò¿äµÇ´  ½Ã°£Àº ÃÑ 48/5½Ã°£ÀÔ´ Ï ´ Ù. ¹ ®Á¦ ¿¡ ¼ ´  8½Ã°£º ¸ ´ Ù ¸ î º ÐÀÌ ´ õ ¼Ò¿ä µÇ´ ÂÁö¸ ¦ ¹ °¾î º ¸ °í Àֱ⠶ §¹ ®¿¡ ´ ÙÀ½ÀÇ °è»êÀ» ÇØÁÖ¾î ¾ß ÇÕ´ Ï ´ Ù.
(8 × 60) − (
48 × 60) = 96 5
ÿ Á¤´ äÀº
(E)
58. An inlet pipe can fill an empty pool with water in 3 hours, and the pool’ s outlet pipe can empty a full pool in 4 hours. The water flows at constant rates through both pipes regardless of the water level in the pool. If both pipes were inadvertently left open, what fraction of the pool would be filled exactly 2 hours after water began to flow into the empty pool? (A)
1 12
(B)
1 6
(C)
1 4
(D)
1 3
(E)
1 2
¹ °À» ä¿ì ´  ÆÄÀÌ ÇÁ· Î (an inlet pipe) ¹ °À» ä¿ì ´ µ¥ 3½Ã°£ ¼Ò¿äµË´ Ï ´ Ù. Ý
1½Ã°£µ¿¾È an empty poolÀ» 1/3ÀÌ Ã¤¿ö ³ ª °©´ Ï ´ Ù.
¹ °À» ¹ èÃâÇÏ ´  ÆÄÀÌ ÇÁ· Î (an outlet pipe) ¹ °À» º ñ¿ì ´ µ¥ 4½Ã°£ ¼Ò¿ä µË´ Ï ´ Ù 1½Ã°£µ¿¾È a full poolÀ» 1/4ÀÌ º ñ¿ö ³ ª °©´ Ï ´ Ù. ¸ ¸ ¾à ¹ °ÀÌ Ã¤¿öÁö´  µ¿½Ã¿¡ ¹ °ÀÌ º ñ¿öÁö´  °æ¿ì ÇÑ ½Ã°£ µ¿¾È¿¡ ä¿öÁö´  ¹ °ÀÇ ¾çÀº ´ ÙÀ½½Ä ¿¡ µû¶ó °è»êÇÕ´ Ï ´ Ù. Ý
1 − 3
1 = 1 4 12
ÇÑ ½Ã°£ÀÌ Áö³ ª ¸ é 1/3ÀÇ ¹ °ÀÌ Ã¤¿öÁö°í , 1/4 ¹ °ÀÌ º üÁ® ³ ª °¡ ´ Ï ±î ³ ² ´  ¹ °ÀÇ ¾çÀº 1/12ÁÒ. ¹ ®Á¦ ¿¡ ¼ ´  µÎ ½Ã°£µ¿¾È¿¡ ä¿öÁö´  ¹ °ÀÇ ¾çÀÇ ¾çÀ» ¹ °¾î º ¸ °í ÀÖÀ¸ ¹ Ç· Î ÇÑ ½Ã°£µ¿¾È¿¡ ä ¿öÁö´  ¹ °ÀÇ ¾ç¿¡ 2½Ã°£À» ° öÇØ ÁÖ¾î ¾ß ÇÕ´ Ï ´ Ù .⇒ (1/12)×2 = 1/6 ÿ Á¤´ äÀº
(B)ÀÔ´ Ï ´ Ù
59. Working alone, R can complete a certain kind of job in 9 hours. R and S , working together at their respective rates, can complete one of these jobs in 6 hours. In how many hours can S , working alone, complete one of these jobs? (A)
18
(B) 12
(C)
9
(D) 6
(E) 3
R : 9½Ã°£ ° É· Á ÀÛ¾÷ ¿Ï ¼ö 1½Ã°£¿¡ 1/9ÀÛ¾÷ ¿Ï ¼ö R°ú S°¡ µ¿½Ã¿¡ °°ÀÌ ÀÏ ÇÒ °æ¿ì 6½Ã°£ ¼Ò¿ä RÀº 6½Ã°£ µ¿¾È ÀÛ¾÷· ®ÀÇ 2/3¸ ¦ ¿Ï ¼ö ÇÔÀ¸ · Î S° ¡ ³ ª ¸ ÓÁö 1/3À» 6½Ã°£ µ¿¾È ¿Ï ¼öÇÑ´ Ù. °á±¹ S´  ½Ã°£´ ç 1/18¸ ¸ Å ¾¿ ÀÏ À» ÇÑ´ Ù. ÿ Á¤´ äÀº
(A)
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60. Machines A, B, and C working together, but independently, at their respective constant
1 hours. If A alone can do the job in 5 hours, and B 2 alone can do the job in 3 hours, in how many hours can C alone do the job? 1 1 1 (A) 1 (B) 2 (C) 3 (D) 5 (E) 7 3 7 2 rates can do a certain job in 1
(A+B+C)
1(1/2) hours
½Ã°£´ ç 2/3¸ ¸ Å ¾¿ ÀÛ¾÷· ® ¿Ï ¼ö
±â° è A : ½Ã°£´ ç 1/5¸ ¸ Å ¾¿ ÀÛ¾÷· ® ¿Ï ¼ö 1(1/2)½Ã°£µ¿¾È 3/10 ¿Ï ¼ö ±â° è B : ½Ã°£´ ç 1/3¸ ¸ Å ¾¿ ÀÛ¾÷· ® ¿Ï ¼ö 1(1/2)½Ã°£µ¿¾È 1/2 ¿Ï ¼ö ±â°è C : 3/2½Ã°£µ¿¾È 1/5 ¿Ï ¼ö ÇÏ ¿©¾ß ÇÔ. 1(1/2)½Ã°£µ¿¾È 3/10 ¿Ï ¼ö ÿ Á¤´ äÀº
(E)
61. Bell X rings once every 12 minutes, bell Y once every 14 minutes, and bell Z once every 15 minutes. If, during a given day, the three bells ring at exactly the same instant, how many minutes will elapse before the three bells next ring simultaneously? (A)
60
(B) 210
(C) 420
(D) 840
(E) 2,520
Bell X´  ¸ Å 12ºÐ¸ ¶´ Ù, Bell Y´  ¸ Å 14ºÐ¸ ¶´Ù, Bell Z´  15ºÐ¸ ¶´ Ù ¿ï ¸ ± ¶§ 3°³ ÀÇ º §ÀÌ µ¿½Ã ¿¡ ¿ï ¸ ®°í ´ ٽà µ¿½Ã¿¡ ¿ï ¸ ®±â À§Çؼ ´  ¸ î º ÐÀÇ ½Ã°£ÀÌ Èê· ¯¾ß ÇÏ ´ ÂÁö¸ ¦ ¹ °¾î º ¸ °í ÀÖ´ Ù. ÃÖ¼Ò°ø¾à¼ö¸ ¦ ±¸ ÇÏ ´  °Í °ú °°ÀÌ Ç®¸ é µÈ´ Ù. ÿ Á¤´ äÀº
62.
(C)
How many bits of computer memory will be required to store the integer
x , were
x = − 810 , 000 , if each digit requires 4 bits of memory and the sign of x requires 1 bit? (A)
25
(B) 24
(C) 17
(D) 13
(E) 12
ÀÚ¸ ´ ¼ö¸ ¦ Ç¥½ÃÇÏ ´  µ¥´Â 4º ñÆ®, ¾ç¼öÀÎ Áö À½¼öÀÎ Áö¸ ¦ Ç¥½ÃÇÏ ´  µ¥´  1º ñÆ®°¡ ÇÊ¿äÇÏ ´ Ù°í ¸ » ÇÏ °í ÀÖ½À´ Ï ´ Ù. X = - 810,000 = - 900 ÿ Á¤´ äÀº
(D)
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GRE Math °- ÁÂ Set 8-1
63. Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science? (A)
81
(B) 159
(C) 166
(D) 285
(E) 324
supply room¿¡ 5Á¾· ùÀÇ Ã¥ÀÌ ÀÖ°í , supply roomÀ¸ · Î º Î ÅÍ ÀÓÀÇ· ΠåÀ» ¿Å±æ ¶§ ¿Å°ÜÁø Ã¥ Áß 80±ÇÀÇ Ã¥ÀÌ °°Àº Á¾· ùÀÇ Ã¥ÀÌ ±â À§Çؼ ´  ¸ î ±ÇÀÇ Ã¥ÀÌ ¿Å°ÜÁö¸ é µÇ´ ÂÁö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À ´ Ï ´ Ù. ÀÏ ´ Ü 80±Ç ¹Ì ¸ ¸ ÀÎ º оßÀÇ Ã¥À» ¸ ðµÎ ¿Å±â¸ é , Botany 50±Ç ,zoology 65±Ç, geology 50±Ç ÃÑ 165±Ç ÀÔ´ Ï ´ Ù. ±× ´ÙÀ½¿¡ 80±ÇÀÌ ³ Ñ´  º оßÀÇ Ã¥µé Áß¿¡ ¼ physics 79±Ç,chemistry 79±ÇÀÌ ¿Å°Ü¿À¸ é supply room¿¡ ´Â physics¿Í chemistry¿¡ °ü· ÃµÈ Ã¥¸ ¸ ÀÌ ³ ² °ÜÁö°Ô µË´ Ï ´ Ù. ¿©±â¼ ÇÑ ±ÇÀÇ Ã¥À» ¿Å±â¸ é physics ¶Ç´  chemistry¿¡ »ó°ü ¾øÀÌ ¿Å°ÜÁø Ã¥ Áß ÇÑ Á¾· ùÀÇ Ã¥ÀÌ Á¤È®È÷ 80±ÇÀÌ µÇ ¾î Áý´ Ï ´ Ù. ¿¹ ¸ ¦ µé¸ é ¿Å°ÜÁø Ã¥ÀÌ physicsÀÏ °æ¿ì physics° ¡ 80±ÇÀÌ µÇ¸ ç, ¿Å°ÜÁø Ã¥ÀÌ chemistryÀÏ °æ¿ì chemistry°¡ 80±ÇÀÌ µË´ Ï ´ Ù. ¸ ðµÎ Á¤¸ ®ÇÏ ¸ é 165±Ç + 79±Ç + 80±Ç = 324±Ç ÿ Á¤´ äÀº
(E)
64. In a certain game, a player can accumulate points only by scoring either an X , which counts 3 points, or a Y , which counts 2 points. If a player scored 24 points in the game and t points were made by scoring X ’ s how many different values could t have? (A)
Four
(B)
Five
(C)
Six
(D)
Seven
(E)
Eight
3 points¿Í 2 points¸ ¦ ÇÕÇÏ ¿© 24° ¡ µÇ¾î ¾ß ÇÏ ¹ Ç· Î 3 X
+ 2
Y =
24
¿©±â¼ X· Î ÃëµæÇÑ Á¡ ¼ö´  ¾ðÁ¦ ³ ª ¦ ¼ö°¡ (0, 6, 12, 18, 24) µÇ¾î ¾ß ÇÑ´ Ù. ¿Ö³ ÄÇÏ ¸ é ¦ ¼ö¿Í ¦ ¼öÀÇ ÇÕÀÌ Ç×»ó ¦ ¼ö 24°¡ µÇ¾î ¾ß ÇÏ ¹ Ç· Î 2 Y ´  Ç×»ó ¦ ¼öÀÌ ¹ Ç· Î 3 X °¡ ¦ ¼ö°¡ µÇ´  °æ ¿ì °¡ »ý°¢ÇÏ ¸ é µË´ Ï ´ Ù. Áï ÿ
X = 0, 2, 4, 6, 8
Á¤´ äÀº (B)
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GRE Math °- ÁÂ Set 8-1
65. An apartment building has 9 floors with 2 n apartments per floor. If
1 of the apartments 3
are to have walls removed to form, in each case, one bigger apartment from two smaller ones, how many apartments will there be after the remodeling? (A)
3n
(B)
5n
(C) 6n
(D) 12n
(E) 15n
remodel ÀÌ Àü¿ ¡ 18n°³ ÀÇ ¹ æÀÌ ÀÖ´ µ¥ ¾ÆÆÄÆ® ¹ æÀÇ 1/3ÀÇ º ®ÀÌ Çæ· Á ÇÏ ³ ª ÀÇ ¾ÆÆÄÆ®°¡ µÇ¹ Ç· Î 18nÀÇ 1/3ÀÎ 6n° ³ ÀÇ ¾ÆÆÄÆ® ¹ æ¼ö° ¡ 3n° ³ °¡ µÇ¾î Áø´ Ù´  Àǹ Ì ÀÔ´ Ï ´ Ù. Áï 18n − 3n = 15n ÿ Á¤´ äÀº
(E)
66. One-fourth of a solution that was 10 percent sugar by weight was replaced by a second solution, resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight? (A)
34%
(B)
24%
(C)
22%
(D)
18%
(E)
8.5%
10% ¼³ ÅÁ¿ë¾×ÀÇ 1/4ÀÌ ´Ù¸¥ ¿ë¾×À¸ · Î ´ ëü µÇ¾î Áø ° á°ú 16% ¼³ ÅÁ¿ë¾×ÀÌ µÇ¾úÀ» ¶§,´ Ù¸ ¥ ¿ë ¾×ÀÇ ¼³ ÅÁ ³ 󵵸 ¦ ±¸ÇÏ ¶ó´  ¹ ®Á¦ . ÀÌ · ¯ÇÑ ¹ ®Á¦ ´  ¹ «° Ô¸ ¦ ¼³ Á¤ÇÏ ¿© ÁÖ°í Ç®¸ é ½±°Ô Ç® ¼ö ÀÖ´ Ù. ¸ ¸ ¾à 10%³ óµµÀÇ ¼³ ÅÁ ¿ë¾×ÀÌ 100gÀÌ ¾ú´ Ù¸ é Æ÷ÇԵǾî Áø ¼³ ÅÁÀÇ ¹ «°Ô´  10gÀÌ ¾úÀ» °ÍÀÌ ¸ ç 1/4¸ ¦ Á¦ °Å ÇÏ ¸ é ¼³ ÅÁÀº 7.5gÀÌ ³ ² °Ô µÈ´ Ù. ÀÌ · ¯ÇÑ »óȲ ¼Ó¿¡ ¼ ´ Ù¸ ¥ ¿ë¾× 25g°ú È¥ÇÕ µÇ¾úÀ» ¶§ ¼³ ÅÁÀÇ ³ óµµ°¡ 16%°¡ µÇ ¾ú´ Ù¸ é ÀÌ Á¦ 100g¼Ó¿¡ 16gÀÇ ¼³ ÅÁÀÌ ÀÖ´  °Í ÀÌ ´ Ù. ÀÌ ´  »õ· Î À¯ÀÔµÈ ¼³ ÅÁÀÌ 8.5gÀÌ ¾úÀ½À» °¡ ¸ £ÃÄ ÁÖ°í ÀÖ´Ù. »õ·Î ÀÌ À¯ÀÔµÈ ¼³ ÅÁ¿ë¾×ÀÇ ¾çÀÌ 25gÀÌ ¾úÀ¸ ¹ Ç· Î 4¸ ¦ °öÇÏ ¿© ÁÖ¾î 100g ³ »¿¡ Æ÷ÇԵǾî ÀÖÀ» ¼³ ÅÁÀÇ ¾çÀ» ±¸ÇÏ ¸ é ³ 󵵸 ¦ ¾Ë ¼ö ÀÖ´ Ù. ÿ
Á¤´ äÀº (A)
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GRE Math °-ÁÂ Set 8-2
Category 8-2 Wor d Problems 1. George is one of 500 people standing in line. If there are 345 people in front of George, how
answer
many people are behind him? (A)
153
(B)
154
(C)
155
(D)
254
(E)
255
2. Each of the 750 students at a certain school is taking history or mathematics or both. If 489
answer
students are taking history and 606 students are taking mathematics, how many students are taking both? (A)
117
(B)
144
(C)
261
(D)
345
(E)
489 EVENT 1
EVENT 2
6 points
Team A
Team C
Second Place: 3 points
Team C
Team B
Third Place: 1 point
Team B
Team A
First Place:
EVENT 3
3. The table above shown the results of the first two events in a competition that involved three teams and three events. If there are no disqualifications, what is the greatest possible difference in points between the total scores of any two teams after the third event? (A)
15
(B)
10
(C)
8
(D)
7
(E)
5
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GRE Math °-ÁÂ Set 8-2
4. The map above shows the eight locations where an agent must collect the amounts indicated.
answer
If the agent wants to start and stop at the same point and not retrace any part of the trip, what is the greatest amount that the agent can collect on one trip? (A)
$300
(B)
$650
(C)
$700
(D)
$750
(E)
$900
5. If 0.497 mark has the value of one dollar, what is the value to the nearest dollar of 350 marks? (A)
$174
(B)
$176
(C)
$524
(D)
$696
(E)
$704
C
6. If the number n of calculators sold per week varies with the price p in dollars according to the equation n = 300 − 20 p , what would be the total weekly revenue from the sale of $10 calculators? (A)
$100
(B)
$300
(C)
$1,000
(D)
$2,800
(E)
$3,000
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GRE Math °-ÁÂ Set 8-2
7. Starting from Town S , Fred rode his bicycle 8 miles due east, 3 miles due south, 2 miles due west, and 11 miles due north, finally stopping at Town T . If the entire region is flat, what is
answer
the straight-line distance, in miles, between Towns S and T ? (A)
10
(B)
8 2 157
(C) (D)
14
(E)
24
8. A dress shop is having a sale in which for every dress purchased at the full price a second dress answer
that has the same price or a lower price may be purchased for $1. If during the sale a customer buys six dresses priced at $40, $42, $48, $50, $52, and $60, what is the least amount the customer can expect to pay for the dresses? (A)
$134
(B)
$143
(C)
$146
(D)
$152
(E)
$155
9. Kim put d dollars into a new savings account in 1966. The account doubled in value during the next 8 years, and doubled again in the 10 years that followed. If the increase in the value of the account over those last 10 years was $1,230, then d = (A)
246
(B)
308
(C)
615
(D)
984
(E)
1,230
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answer
GRE Math °-ÁÂ Set 8-2
*8
9
6
*7
4
5
*2
3
−9
* −8
10. In a certain game 4 disks are tossed onto numbered spaces. The figure above shows the
answer
location of the disks after such a toss. The score is determined by adding 2 times the sum of the numbers in left-hand spaces, containing disks to 3 times the sum of the numbers in righthand spaces containing disks. What is the score for this toss? (A) 9
(B) 17
(C) 23
(D) 27
(E) 28
11. If a, b , and m are integers, then a and b are said to be m -related if m is a factor of
a − b . If 15 and –3 are m -related, which of the following could NOT be a value of m ? (A)
2
(B)
3
(C)
4
(D)
6
(E)
9
x
27
z
29
31
33
30
y
28
12 . In the figure above, the sum of the numbers in any row is equal to the sum of the numbers in any column. What is the sum of x, y, and z ? (A)
101
(B)
97
(C)
93
(D)
89
(E)
85
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answer
GRE Math °-ÁÂ Set 8-2
13. On the first day of her vacation, Louisa traveled 216 miles. On the second day, traveling at
answer
the same average speed, she traveled 378 miles. If the 216-mile trip took 3 hours less than the 378-mile trip, what was the average speed, in miles per hour? (A)
31
(B)
38
(C)
50
(D)
54
(E)
56
14. An express train traveled between two stations at a constant rate of 50 miles per hour. If it traveled
answer
1 the distance between the two stations in 15 minutes, which of the following is 3
closest to the number of miles between the two stations? (A)
13
(B)
38
(C)
45
(D)
67
(E)
88
15. How many minutes does it take a car traveling at 80 kilometers per hour to travel 100 kilometers? (A)
65
(B)
70
(C)
75
(D)
80
(E)
85
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GRE Math °-ÁÂ Set 8-2
16. Juan and Carla each drove their motorbike up a logging road. Juan reached the top 3 hours
answer
after starting but Carla took 1 additional hour. If the distance along the logging road to the top was 15 miles, how many more miles per hour did Juan a average than? (A)
1
(B)
5 4
(C)
2
(D)
15 4
(E)
5
17. If a hiker walks at a constant speed of 2
1 miles per hour, how many miles can the hiker 2
answer
walk in 4 hours and 12 minutes? (A)
10.0
(B)
10.3
(C)
10.4
(D)
10.5
(E)
10.8
18. The number of bacteria in a certain culture doubles once every minute. If there were p bacteria in the culture at 8:55 a.m., how many bacteria were there at 9:00 a.m. the same morning? (A) (B) (C) (D) (E)
10 p 32 p 5 p 2 2 p 5 32 p 5
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GRE Math °-ÁÂ Set 8-2
19. How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent
answer
alcohol in order to produce a solution t hat is 25 percent alcohol? (A)
7 2
(B) 5 (C)
20 3
(D) 8 (E)
39 4
20. A lunar month, the time between two successive new moon, is approximately 29 days, 12 hours,
answer
and 44 minutes long. What is the approximate length of two lunar months? (A)
29 days 1 hour 28 min.
(B)
49 days 0 hour 18 min,.
(C)
58 days 1 hour 18 min.
(D)
59 days 0 hour 28 min.
(E)
59 days 1 hour 28 min.
21. One glass bulb can be manufactured in 10 seconds. At that rate, approximately how many minutes will it take to manufacture 100 glass bulbs? (A)
0.6
(B)
6.0
(C)
15.0
(D)
16.7
(E)
36.0
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GRE Math °-ÁÂ Set 8-2
22. If every 31 weeks an electric clock uses an amount of energy equivalent to that released in
answer
burning 1 liter of gasoline, then in 1 year the clock would use an amount of energy equivalent to that released in burning approximately how many liters of gasoline? (A) 0.6
(B) 1.4
(C) 1.5
(D) 1.7
(E) 2.0
23. If a certain data entry operator types characters at the rate of 10,000 per hour, how many answer
characters will the operator type in 12 minutes? (A)
50,000
(B)
2,500
(C)
2,000
(D)
1,200
(E)
120
Annual Salaries of Acme Tool Corporation Officers Salary
Number of Employees
$80,000
1
70,000
2
60,000
1
50,000
3
40,000
1
30,000
1
20,000
1
24. According to the table above, what is the average (arithmetic mean) annual salary of the 10 officers of the Acme Tool Corporation? (A)
$34,820
(B)
$35,000
(C)
$47,500
(D)
$52,000
(E)
$53,600
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GRE Math °-ÁÂ Set 8-2
25. In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the
answer
number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985? (A)
$2.4 million
(B)
$2.9 million
(C)
$3.0 million
(D)
$3.1 million
(E)
$3.6 million
26. A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an
answer
average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day? (A)
2 mph
(B)
3 mph
(C)
4 mph
(D)
5 mph
(E)
6 mph
27. An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,690, what was the total number of pairs of contact lenses that she sold? (A)
11
(B)
13
(C)
15
(D)
17
(E)
19
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GRE Math °-ÁÂ Set 8-2
28. On a certain trip, a cyclist averaged 20 miles per hour for the first 10 miles and 16 miles per
answer
hour for the remaining 20 miles. If the cyclist returned immediately via the same route and took a total of 4 hours for the round trip, what was the average speed, in miles per hour, for the return trip? (A)
24
(B)
18
(C)
17
(D)
15
(E)
13
1 7 1 3
29. The cost of chartering a plane was shared equally among 30 passengers. If there had been 35
answer
passengers sharing that cost, the cost per passenger would have been $30 less. What was the cost of chartering the plane? (A)
$5,400
(B)
$6,125
(C)
$6,300
(D)
$6,800
(E)
$7,350
30. In traveling a certain distance, car R averaged
x miles per gallon of gasoline. Car S
traveled 300 miles and averaged 25 miles per gallon of gasoline. If car R used the same amount of gasoline as car (A) (B) (C) (D) (E)
S , how many miles, in terms of x , did car R travel?
12 x x x + 12 x 12 12 x
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GRE Math °-ÁÂ Set 8-2
31. Under a certain company’ s medical insurance plan, the amount an employee must pay for
answer
medical expenses consists of payment of the first $450 of expenses plus 20 percent of additional expenses, up to a maximum total payment of $1,350 per year. All remaining expenses are paid by the plan. Last year, if an employee paid the maximum amount for medical expenses, what is the least amount that the plan could have paid? (A)
$720
(B)
$1,080
(C)
$3,600
(D)
$4,500
(E)
$4,950
32. A delivery truck starts on its route with a load of goods weighing T tons. At each of its first 4 stops,
answer
1 of the weight of the goods still on the truck is unloaded. After the 4th stop, 2
what is the weight, in tons, of the goods still on the truck? (A)
15 T 16
(B)
1 T 4
(C)
1 T 6
(D)
1 T 8
(E)
1 T 16
33. Analysts of the automobile industry say that the total number of domestic suppliers of automobile parts was reduced by reduced by
1 from 1980 to 1985 and that the number was again 3
1 from 1985 to 1988. According to these analysts, if there were 2,520 domestic 3
suppliers in 1985, how many fewer were there in 1988 than th ere were in 1980? (A)
1,260
(B)
1,400
(C)
1,680
(D)
2,100
(E)
2,940
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GRE Math °-ÁÂ Set 8-2
34. A subway train made eleven stops on its route. If an average (arithmetic mean) of 30
answer
passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop? (A)
60
(B)
50
(C)
30
(D)
20
(E)
10
35. Fox jeans regularly sell for $15 a pair and Pony jeans regularly, sell for $18 a pair. During a
answer
sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans? (A)
9%
(B)
10%
(C)
11%
(D)
12%
(E)
15%
36. A mixture of nuts is to contain 3 parts cashews to 6 parts almonds to 7 parts walnuts by weight. How many pounds of almonds will be needed to make 5 pounds of the mixture? (A) (B) (C) (D) (E)
3 8 8 15 1 1 5 2 1 3 7 1 8
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GRE Math °-ÁÂ Set 8-2
37. The time it took car A to travel 400 miles was 2 hours less than the time it took car B to
answer
travel the same distance. If car A ’ s average speed was 10 miles per hour greater than that of car B , what was car B ’ s average speed, in miles per hour? (A)
20
(B)
30
(C)
40
(D)
50
(E)
80
38. Ms. Jiminez plans an automobile trip of 7,000 to 9,000 miles. The cost of gasoline will be 85
answer
to 95 cents per gallon, and her automobile will average 20 to 30 miles per gallon. What is the maximum possible cost of the gasoline for the trip? (A)
$485.00
(B) $427.50
(C) $382.50
(D) $297.50
(E) $256.00
39. A group of 12 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If
n of the people decide not to participate at the last minute, by how
many dollars will each remaining person’ s share of the total cost increase?
E 12 − n 12 − n (B) E E (C) 12(12 − n) nE (D) 12(12 − n) (A)
(E)
(12 − n) E 12n
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GRE Math °-ÁÂ Set 8-2
40. The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is
x feet below the top of the tank, the concentration is 3 +
per million, where 0 <
4 parts 5 − x
answer
x < 4. To the nearest 0.1 foot, at what depth is the concentration
equal to 6 parts per million? (A)
2.4 ft
(B)
2.5 ft
(C)
2.8 ft
(D)
3.0 ft
(E)
3.2 ft
41. A breakfast that consists of 1 ounce of corn puffs and 8 ounces of fruit X provides 257
answer
calories. When 8 ounces of fruit Y is substituted for the 8 ounces of fruit X , the total number of calories is reduced to 185. If fruit X provides 1.8 times as many calories as fruit
Y , how many calories does 8 ounces of fruit Y alone provide? (A)
11.25
(B)
72
(C)
90
(D)
95
(E)
129.6
42. A 2-year certificate of deposit is purchased for
k dollars. If the certificate earns interest at
an annual rate of 6 percent compounded quarterly, which of the following represents the value, in dollars, of the certificate at the end of the 2 year? (A) (B) (C) (D) (E)
(1.06) 2 k (1.06) 8 k (1.015) 2 k (1.015) 8 k (1.04) 4 k
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GRE Math °-ÁÂ Set 8-2
43. On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60.
answer
If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent to motel actually charged for that night? (A)
$600
(B)
$800
(C)
$1,000
(D)
$1,600
(E)
$2,400
44. On level farmland, two runners leave at the same time from the intersection of two country
answer
roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 4 miles per hour faster than the first runner’ s rate. How far apart, to the nearest mile, will they be after (A)
6
(B)
7
(C)
8
(D)
12
(E)
14
1 hour? 2
45. The rear wheels of a car crossed a certain line 0.5 second after the front wheels crossed the same line. If the centers of the front and rear wheels are 20 feet apart and the car traveled in a straight line at a constant speed, which of the following gives the speed of the car in miles per hour? (5,280 feet = 1 mile) (A)
(B) (C)
20 60 2 5,280 0.5 20 60 5,280 0.5 20 0.5 2 5 , 280 60
(D)
(20)(5,280) (60 2 )(0.5)
(E)
(20)(5,280) (60)(0.5)
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GRE Math °-ÁÂ Set 8-2
46. A cashier mentally reversed the digits of one customer’s correct amount of change and thus
answer
gave the customer an incorrect amount of change. If the cash register contained 45 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents? (A)
14
(B)
45
(C)
54
(D)
65
(E)
83
47. A shipment of 1,500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived,
answer
2 of the heads were sold, each at 25 3
percent above the cost per head. The following day the rest were sold at a price per head equal to 10 percent less than the price each head sold for on the day before. What was the gross profit on this shipment? (A) $100 (B) $115 (C) $125 (D) $130 (E) $135
48. If Sam were twice as old as he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam? (A)
20
(B)
30
(C)
40
(D)
50
(E)
60
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GRE Math °-ÁÂ Set 8-2
49. A store currently charges the same price for each towel that it sells. If the current price of
answer
each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel? (A)
$1
(B)
$2
(C) $3
(D) $4
(E) $12
50. A ruby and a diamond have insured values of $1,800 and $1,200, respectively, and the annual
answer
premium rate for each gem is $1.50 per $100 of insured value. If the rate and insured values of the two gems remain constant over the years, after how many years will the total of the insurance premiums on both gems for those years first exceed the insured value of the diamond? (A)
8
(B) 12
(C) 20
(D) 27
(E) 40
51. A furnace service contract costs $48 per year and covers payment of 80 percent of all repair costs. The total amount paid by the owner, including the cost of the contract, will equal the payment covered by the contract when the total repair costs for the year are (A)
$48
(B) $60
(C) $72
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(E) $92
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answer
GRE Math °-ÁÂ Set 8-2
¼öÇÐÇؼ³
Word Problems
1. George is one of 500 people standing in line. If there are 345 people in front of George, how many people are behind him? (A)
153
(B)
154
(C)
155
(D)
254
(E)
255
500¸í ÀÇ »ç¶÷ÀÇ ÁÙÀ» ¼°í ÀÖ´ µ¥ George ¾Õ¿¡ 345¸ í ÀÌ ¼ ÀÖÀ¸ ´ Ï ±î ±×ÀÇ µÚ· Î ´  154¸ í ÀÌ ¼ ÀÖ°Ú³ ׿ä. . ´ äÀº
(B)ÀÔ´ Ï ´ Ù.
2. Each of the 750 students at a certain school is taking history or mathematics or both. If 489 students are taking history and 606 students are taking mathematics, how many students are taking both? (A)
117
(B)
144
(C)
261
(D)
345
(E)
489
750¸ í ÀÇ ÇлýÀÌ ¿ª »ç ¶Ç´  ¼öÇÐ °ú¸ ñ Áß ÇÑ °ú¸ ñÀ» ¶Ç´Â µÎ °ú¸ ñ ¸ ðµÎ ¸ ¦ ¼ö° ÇÏ °í ÀÖ½À´ Ï ´ Ù. 489¸ í ÀÌ ¿ª »ç¸ ¦ 606¸ í ÀÌ ¼öÇÐÀ» ¼ö° ÇÏ °í ÀÖ½À´ Ï ´ Ù. µÎ °ú¸ ñÀ» ¸ ðµÎ ¼ö° ÇÏ °í ÀÖ´  Çлý ÀÇ ¼ö( n( A ∩ B ) À» ¾Ë· Á¸ é ¿ ª »ç¸ ¦ ¼ö° ÇÏ ´  ÇлýÀÇ ¼ö(489¸ í )¿Í ¼öÇÐÀ» ¼ö° ÇÏ °í ÀÖ´  Çлý (606¸ í )À» ´ õÇÑ °ª ¿¡ ¼ ÃÑ Çлý¼ö 750¸ í À» »©¸ é ¾Ë ¼ö ÀÖ°Ú³ ׿ä. ÀÏ ¹ ÝÀûÀ¸ · Î n( A ∪ B ) = n( A) + n( B ) − n( A ∩ B ) . ´ äÀº
(D)ÀÔ´ Ï ´ Ù.
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GRE Math °-ÁÂ Set 8-2
First Place
Event 1
Event 2
Team A
Team C
Team C
Team B
Team B
Team A
Event 3
6 points Second Place 3 points Third Place 1 point 3. The table above shown the results of the first two events in a competition that involved three teams and three events. If there are no disqualifications, what is the greatest possible difference in points between the total scores of any two teams after the third event ? (A)
15
(B)
10
(C)
8
(D)
7
(E)
5
¼¼ ÆÀÀÌ ¼¼ °¡ ÁöÀÇ event¿¡ ¼ °æÀï À» ÇÏ ¿© ¾òÀº ÃÑÁ¡ ÀÌ Â÷°¡ °¡ Àå Ä¿Áú ¼ö ÀÖ´Â °æ¿ì ¿¡ ±× Á¡ ¼öÀÇ Â÷ÀÌ ¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÀÌ ¹ Ì event1,2ÀÇ Á¡ ¼ö¸ ¦ ¾Ë°í Àֱ⠶§¹ ®¿¡ event3ÈÄ¿¡ °¡ Àå ³ ôÀº Á¡ ¼ö¸ ¦ ¿Ã¸± ¼ö ÀÖ´  °æ¿ì ¿Í °¡ Àå ³ · Àº Á¡ ¼ö¸ ¦ ¾òÀ» ¼ö ÀÖ´  °æ¿ì ¸ ¦ »ý°¢ÇÏ ¿© ±× °á° ú¸ ¦ ´ äÇÏ ¸ é µÇ°Ú½À´ Ï ´ Ù. Event1,2°¡ ³ ¡ ³ °á° ú team CÀÇ Á¡ ¼ö°¡ 9Á¡ À¸ · Î ÃÑÁ¡ ¿¡ ¼ 1À§¸ ¦ ±â· Ï ÇÏ °í ÀÖ°í team B°¡ 4Á¡ À¸ · Î ² ÃÂî ³ ׿ä . ±×· ¯¸ é team C°¡ event 3¿¡ ¼ 1À§¸ ¦ ÇÏ°í team B°¡ event3¿¡ ¼ 3À§¸ ¦ Çϸé ÃÑ Á¡ ÀÇ Â÷ÀÌ °¡ °¡ Àå Ä¿Áú ¼ö ÀÖ°Ú³ ׿ä. Team C°¡ event 3¿¡ ¼ 1À§¸ ¦ Â÷ÁöÇÏ ¸ é ÃÑÁ¡ Àº 15Á¡ , Team B°¡ event 3¿¡ ¼ 3À§¸¦ Â÷ÁöÇÏ ¸ é ÃÑ Á¡ Àº 5Á¡ À¸ · Î ÃÖ°í ÀÇ Á¡ ¼ö Â÷ÀÌ ´  10Á¡ ÀÌ µÇ°Ú³ ×¿ä… . Á¤´ äÀº
(B)ÀÔ´ Ï ´ Ù.
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GRE Math °-ÁÂ Set 8-2
4. The map above shows the eight locations where an agent must collect the amounts indicated. If the agent wants to start and stop at the same point and not retrace any part of the trip, what is the greatest amount that the agent can collect on one trip? (A)
$300
(B)
$650
(C)
$700
(D)
$750
(E)
$900
»ó±âÀÇ Áöµµ¿¡ ¼ 8°³ ÀÇ À§Ä¡ °¡ Ç¥½Ã µÇ¾î ÀÖÀ¸ ¸ ç °¢ À§Ä¡ ¿¡ ¼ Ç¥±â µÇ¾î Áø ¸ ¸ Å ÀÇ µ· À» ¼ö ±ÝÇÒ °æ¿ì , ½ÃÀÛÁ¡ °ú ³ ¡ Á¡ ÀÌ °°À¸ ¸ ç ÇÑ ¹ ø Áö³ ª °£ ±æÀ» µÇµ¹ ¾Æ °¡ Áö ¾Ê´ ´ Ù´  Á¶°ÇÇÏ ¿¡ ¼ ÃÖ°í · Î ¸ ¹ Àº ±Ý¾×À» ¼ö±ÝÇÒ ¼ö °æ¿ì ÀÇ ±Ý¾×À» ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. Áß¾ÓÀ» Åë°úÇÏ °í ÀÖ´  ¼±À» Áß½ÉÀ¸ · Î »ý°¢À» Çؾ߰ڽÀ´ Ï ´ Ù. ¿Ü°ûÀ¸ · Î ¸ ¸ µ¹ °Í ÀÎ Áö ¾Æ´Ï ¸ é Áß¾ÓÀ» Åë°úÇÏ µ¥ ¿À¸ ¥ÂÊÀ¸ · Î µ¹ ¾Æ¾ß ÇÒÁö ¾Æ´ Ï ¸ é ¿ÞÂÊÀ¸ · Î µ¹ ¾Æ¾ß ÇÒÁö… ¿Ü°ûÀ¸ · Î ¸ ¸ µ¹ °æ¿ì ¼ö±ÝÇÒ ¼ö ÀÖ´  ±Ý¾× : $500 Áß¾ÓÀ» Áß½ÉÀ¸ · Î ¿ÞÂʸ ¸ À» µ¹ °æ¿ì
: $700
Áß¾ÓÀ» Áß½ÉÀ¸ · Î ¿À¸ ¥Âʸ ¸ À» µ¹ °æ¿ì
: $650
. Á¤´ äÀº
(C)ÀÔ´ Ï ´ Ù.
5. If 0.497 mark has the value of one dollar, what is the value to the nearest dollar of 350 marks? (A)
$174
(B)
$176
(C)
$524
(D)
$696
(E)
$704
$1= 0.497 markÀÏ ¶§ 350 marks´  ¸ î DollarÀÎ °¡ ? $ 1 : X = 0.497 mark : 350 marks . Á¤´ äÀº
(E)
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GRE Math °-ÁÂ Set 8-2
6. If the number n of calculators sold per week varies with the price p in dollars according to the equation n = 300 − 20 p , what would be the total weekly revenue from the sale of $10 calculators? (A)
$100
(B)
$300
(C)
$1,000
(D)
$2,800
(E)
$3,000
ÆǸ Å °³ ¼ö : n = 300 – 20p¿¡ ¼ p¿¡ $10À» ´ ëÀÔÇÏ ¸ é ¹ ®Á¦ °¡ ÇØ°áµË´ Ï ´ Ù. . Á¤´ äÀº
(C)
7. Starting from Town S , Fred rode his bicycle 8 miles due east, 3 miles due south, 2 miles due west, and 11 miles due north, finally stopping at Town T . If the entire region is flat, what is the straight-line distance, in miles, between Towns S and T ? (A)
10
(B)
8 2 157
(C) (D)
14
(E)
24 T 11 miles
8 miles
S 3 miles 2 miles S¿¡ ¼ TÀÇ Á÷¼± °Å¸ ®´  8 2 (11 − 3) + 62 (8 − 2) = 10 2 . Á¤´ äÀº
(A)
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GRE Math °-ÁÂ Set 8-2
8. A dress shop is having a sale in which for every dress purchased at the full price a second dress that has the same price or a lower price may be purchased for $1 . If during the sale a customer buys six dresses priced at $40, $42, $48, $50, $52, and $60, what is the least amount the customer can expect to pay for the dresses? (A)
$134
(B)
$143
(C)
$146
(D)
$152
(E)
$155
µå· ¹ ½º ÇÏ ³ ª ¸ ¦ ¿ø· ¡ ÀÇ °¡ °Ý´ ë· Î ±¸ ÀÔÇÏ ¸ é µÎ ¹ ø°· Î ±¸ ÀÔÇÏ ´  µå· ¹ ½º °¡ ù ¹ ø° ±¸ ÀÔÇÏ ´  µå · ¹ ½º ¿Í °¡ °ÝÀÌ °°°Å³ ª ¶Ç´Â ³ · À» °æ¿ì ±× µå· ¹ ½º ¸ ¦ $1¿¡ ±¸ÀÔÇÒ ¼ö ÀÖ´  °æ¿ì ¿¡ 6° ¡ Áö µå·¹ ½º ¸ ¦ °¡ Àå ½Î°Ô ±¸ ÀÔÇÒ ¶§ Áöº ÒÇØ¾ß ÇÏ ´  ±Ý¾×À» ¹ °¾î º ¸°í ÀÖ½À´ Ï ´ Ù. Á¦ ÀÏ º ñ½Ñ ¿ÊÀÎ $60 À» ±¸ ÀÔÇÏ ¸ é ±× ´ ÙÀ½À¸ · Î º ñ½Ñ $52À» $1ÀÇ °¡ °ÝÀ¸ · Î »ì ¼ö ÀÖ´  °æ¿ì ³ ׿ä . ($ 60 + $1 ($52)) + ( $ 50 + $1( $48)) + ($42 + $1($40)) = $155 . Á¤´ äÀº
(E)
9. Kim put d dollars into a new savings account in 1966. The account doubled in value during the next 8 years, and doubled again in the 10 years that followed. If the increase in the value of the account over those last 10 years was $1,230, then d = (A)
246
(B)
308
(C)
615
(D)
984
(E)
1,230
8³ â° £ 2¹ è°¡ Áõ°¡ ÇÏ ¸ é 2d°¡ µÇ°í , ´ ÙÀ½ ½Ê³ â °£ 2d°¡ 4d°¡ µÉ ¶§ ½Ê³ â °£ Áõ°¡ ÇÑ ±Ý¾× Áï 2d°¡
$1,230¶ó´Â ¸ »ÀÌ ³ ׿ä.
2d = $1,230 ⇒ d = $615 . ´ äÀº
(C)
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GRE Math °-ÁÂ Set 8-2
*8
9
6
*7
4
5
*2
3
−9
* −8
10. In a certain game 4 disks are tossed onto numbered spaces. The figure above shows the location of the disks after such a toss. The score is determined by adding 2 times the sum of the numbers in left-hand spaces, containing disks to 3 times the sum of the numbers in righthand spaces containing disks. What is the score for this toss? (A) 9
(B) 17
(C) 23
(D) 27
(E) 28
4° ³ ÀÇ µð½º Å©°¡ ´ øÁ®Áö°í µð½º Å© ¶³ ¾î Áø ¼ýÀÚ¸ ¦ º ¸ ¿© ÁÖ´  ÆÇÀÌ ±×· ÁÁ® ÀÖ½À´ Ï ´ Ù. µð½º Å©°¡ ¶³ ¾î Á® ÀÖ´Â ¿ÞÆíÀÇ ¼ýÀÚ¿¡ ´ ëÇÏ ¿©´  ÇÕÀ» ÇÏ ¿© µÎ ¹ è¸ ¦ , µð½º Å©°¡ ¶³ ¾î Á® ÀÖ´  ¿À¸ ¥ÆíÀÇ ¼ýÀÚ¿¡ ´ ëÇÏ ¿©´  ÇÕÀ» ÇÏ ¿© 3¹ è¸ ¦ ÇØÁØ ÈÄ ½º ÄÚ¾î ¸ ¦ °áÁ¤ÇÑ´ Ù°í ÇÕ´ Ï ´ Ù. 2(8 + 2) + 3(7- 8) = 17 . Á¤´ äÀº
(B)
11. If a, b , and m are integers, then a and b are said to be m -related if m is a factor of
a − b . If 15 and –3 are m -related, which of the following could NOT be a value of m ? (A)
2
(B)
3
(C)
4
(D)
6
(E)
9
¸ ¸ ¾à (a-b)ÀÇ ÀÎ ¼ö( factor )° ¡ mÀÌ ¸ é a , b°¡ m-related¶ó° í ÇÕ´ Ï ´ Ù. ( 15 - (-3) ) =18À̸ç 18ÀÇ factors· Î ´  1,2,3,6,9,18ÀÌ ÀÖÀ¸ ¸ ç ÀÌ ¸ ðµç ¼ýÀÚ´  m-related µÇ¾ú´ Ù°í ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. . Á¤´ äÀº
(C)
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GRE Math °-ÁÂ Set 8-2
x
27
z
29
31
33
30
y
28
12. In the figure above, the sum of the numbers in any row is equal to the sum of the numbers in any column. What is the sum of x, y, and z ? (A)
101
(B)
97
(C)
93
(D)
89
(E)
85
°¢ Çà°ú ¿ ¿¡ ¼ÓÇÑ ¼ýÀÚµéÀÇ ÇÕÀÌ ÀÏ Ä¡ ÇÑ´ Ù´  Á¶°ÇÀÌ ÀÖ½À´ Ï ´ Ù. 29+31+33 = x+29+30 = 27+31+y = z+33+28 . Á¤´ äÀº
(A)
13. On the first day of her vacation, Louisa traveled 216 miles. On the second day, traveling at the same average speed, she traveled 378 miles. If the 216-mile trip took 3 hours less than the 378-mile trip, what was the average speed, in miles per hour? (A)
31
(B)
38
(C)
50
(D)
54
(E)
56
¿©ÇàÀÇ Ã¹ ³ ¯¿¡´  216miles¸ ¦ ÀÌ µ¿Çß°í
µÎ ¹ ø° ³ ¯¿¡ ´  ù ³ ¯°ú °°Àº ¼Óµµ¸ ¦
À¯ÁöÇÏ ¸ ç
378miles¸ ¦ ÀÌ µ¿Çß°í ù ³ ¯ º ¸ ´ Ù 3½Ã°£À» ´ õ ¿©Çà ÇßÀ» ¶§ ½Ã°£´ ç ¼Óµµ¸ ¦ ±¸ÇÏ ¶ó´  ¹ ®Á¦ ÀÔ ´ Ï ´ Ù. ù ° ³ ¯° ú µÑ° ³ ¯ÀÇ ÀÌ µ¿° Ÿ ®ÀÇ Â÷ÀÌ378 − 216= 162¸ ¦ 3½Ã°£À¸ · Î ³ ª ´ ©¾î ÁÖ¸ é 54¸ ¦ ±¸ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. . Á¤´ äÀº
(D)
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GRE Math °-ÁÂ Set 8-2
14. An express train traveled between two stations at a constant rate of 50 miles per hour. If it
1 the distance between the two stations in 15 minutes, which of the following is 3
traveled
closest to the number of miles between the two stations? (A)
13
(B)
38
(C)
45
(D)
67
(E)
88
¿©±â¼ µÎ Á¤°ÅÀå »çÀÌ ÀÇ °Å¸ ®¸ ¦ D ¶ó °¡ Á¤ÇÏ °í ½Ã°£ÀÇ ´ ÜÀ§¸ ¦ minutes¿¡ ¼ hours· Î º ¯È¯ÇÏ ¸ é 15 minutesÀº 15/60 hours· Î ¹ Ù² ã¾ß ÇÕ´ Ï ´ Ù. 1/3ÀÇ °Å¸ ®¸ ¦ °¡ ´ µ¥ 15/60 hours °É¸ ± ¶§: D = 50 × 15 , ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é D ≈ 38 3 60
Distance(°Å¸®) = Rate(¼Óµµ) × Time(½Ã° £) . Á¤´ äÀº
(B)
15. How many minutes does it take a car traveling at 80 kilometers per hour to travel 100 kilometers? (A)
65
(B)
70
(C)
75
(D)
80
(E)
85
ÁÖÀÇÇÒ Á¡ Àº hoursÀÇ ´ÜÀ§¸ ¦ minutes· Î ¹ Ù² ã¾ß ÇÑ´ Ù´  °Í ÀÔ´ Ï ´ Ù. 60À» °öÇØÁÖ¸ é µÇÁÒ! (100 kilometers ÷80) × 60 = 75 . Á¤´ äÀº
(C)
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16. Juan and Carla each drove their motorbike up a logging road. Juan reached the top 3 hours after starting but Carla took 1 additional hour. If the distance along the logging road to the top was 15 miles, how many more miles per hour did Juan average than Carla? (A)
1
(B)
5 4
(C) 2
(D)
15 4
(E) 5
15/3 –15/4 = 5/4 . Á¤´ äÀº
(B)
17. If a hiker walks at a constant speed of 2
1 miles per hour, how many miles can the hiker 2
walk in 4 hours and 12 minutes? (A)
10.0
(B)
10.3
(C)
10.4
(D)
10.5
(E)
10.8
¹ ®Á¦ ¿¡ ¼ walk in 4 hours and 12 minutes ´  4
1 hours ÀÔ´ Ï ´ Ù. ´ ÙÀ½ °ø½Ä¿¡ ´ ëÀÔÇÏ ¸ é 5
Distance( °Å¸ ®) = Rate( ¼Óµµ) × Τιµε( ℘°≤)= 21 × 5 = 105 = 10.5 5
. Á¤´ äÀº
2
10
(D)
18. The number of bacteria in a certain culture doubles once every minute. If there were p bacteria in the culture at 8:55 a.m., how many bacteria were there at 9:00 a.m. the same morning? (A)
10 p
(B) 32 p
(C) 5 p 2
(D)
2 p 5
(E) 32 p 5
¹ ÚÅ׸ ®¾ÆÀÇ ¼ö°¡ ¸ Å º и ¶´ Ù µÎ ¹ è° ¡ µÉ °æ¿ì ¿ÀÀü 8:55¿¡ ¼ö°¡ P¿´ ´ø ¹ ÚÅ׸®¾Æ´  ¿ÀÀü9:00 ½Ã¿¡ ¹ ÚÅ׸®¾Æ¼ö¸ ¦ ¹ °¾î º ¸ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. 1º ÐÀÌ Áö³ ª ¸ é 2P, 2º ÐÀÌ Áö³ ª ¸ é 4P, 3º ÐÀÌ Áö³ ª ¸ é 8P, 5º ÐÀÌ Áö³ ª ¸ é 32P° ¡ µÇ°ÚÁÒ.. . ´ äÀº
(B)ÀÔ´ Ï ´ Ù.
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GRE Math °-ÁÂ Set 8-2
19. How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution t hat is 25 percent alcohol? (A)
7 2
(B)
5
(C)
20 3
(D)
8
(E)
39 4 If N1 units of an item having a unit value of U1 are mixed with N2 units of an item having a unit value of U2, then The Value of the M ixtur e ( È¥ÇÕÈÄÀÇ ° ª) =
N1× U1 + N2 × U2
±âÁ¸ ÀÇ 20% ¾ËÄÚ¿Ã100-liter ¿ë¾×¿¡ x ¾çÀÇ pure alcoholÀ» º Î ¾î ¼ 25% ¾ËÄڿ÷ Î ¸ ¸ µé ¶§ x ¾çÀ» ±¸ ÇÏ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. À§ÀÇ °ø½Ä¿¡ Àû¿ëÇØ º ¸ ¸ é:
(100 + x )0.25 = 100 × 0.2 + x ⇒ x = . Á¤´ äÀº
20 3
(C)
20. A lunar month, the time between two successive new moon, is approximately 29 days, 12 hours, and 44 minutes long. What is the approximate length of two lunar months? (A)
29 days 1 hour 28 min.
(B)
49 days 0 hour 18 min,.
(C)
58 days 1 hour 18 min.
(D)
59 days 0 hour 28 min.
(E)
59 days 1 hour 28 min.
. Á¤´ äÀº
Âü° í :
(E)
Çؼ³ ÀÌ ÇÊ¿äÇϽŠº ÐÀº ¾ðÁ¦ µç Áö [email protected]· Î ¸ ÞÀÏ À» Áֽø é Çؼ³ À» ÷ º Î ÇØµå ¸ ³ ´ Ï ´ Ù.
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GRE Math °-ÁÂ Set 8-2
21. One glass bulb can be manufactured in 10 seconds. At that rate, approximately how many minutes will it take to manufacture 100 glass bulbs? (A)
0.6
(B)
6.0
(C)
15.0
(D)
16.7
(E)
36.0
100 ×(10/60) ≈ 16.7 . Á¤´ äÀº
(D)
22. If every 31 weeks an electric clock uses an amount of energy equivalent to that released in burning 1 liter of gasoline, then in 1 year the clock would use an amount of energy equivalent to that released in burning approximately how many liters of gasoline? (A)
0.6
(B)
1.4
(C)
1.5
(D)
1.7
(E)
2.0
52 weeks ÷ 31 weeks ≈ 1.7 . Á¤´ äÀº
(D)
23. If a certain data entry operator types characters at the rate of 10,000 per hour, how many characters will the operator type in 12 minutes? (A)
50,000
(B)
2,500
(C)
2,000
(D)
1,200
(E)
120
12º ÐÀº 12/ 60ÀÌ ¹ Ç· Î 1/5 hourÀÔ´ Ï ´ Ù. 10,000 × (1/5) = 2,000 . Á¤´ äÀº
(C)
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GRE Math °-ÁÂ Set 8-2
Annual Salaries of Acme Tool Corporation Officers Salary
Number of Employees
$80,000
1
70,000
2
60,000
1
50,000
3
40,000
1
30,000
1
20,000
1
24. According to the table above, what is the average (arithmetic mean) annual salary of the 10 officers of the Acme Tool Corporation? (A)
$34,820
(B)
$35,000
(C)
$47,500
(D)
$52,000
(E)
$53,600
º ¯ · ® x ° ÷Ç¥· Î ÁÖ¾î Á³ À» ¶§ÀÇ º ¯· ®ÀÇ Æò±Õ m Àº i ¡ µµ¼öº ÐÆ
x1 f 1 + x2 f 2 + ⋅ ⋅ ⋅ + xn f n 1 n = m= xi f i f 1 + f 2 + ⋅ ⋅ ⋅ + f n N i =1
∑
À§ÀÇ °ø½Ä¿¡ ´ ëÀÔÇؼ Ç®¸ é: 80, 000 + 140,000 + 60,000 + 150,000 + 40,000 + 30,000 + 20, 000 = 52,000 10
. Á¤´ äÀº
(D)
25. In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985? (A)
$2.4 million
(B) $2.9 million
(D)
$3.1 million
(E) $3.6 million
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GRE Math °-ÁÂ Set 8-2
’ 85³ âµµ ½Å¹ ßÀÇ °¡ °Ý: P , ’ 85³ âµµ ÆǸ ÅµÈ ½Å¹ ßÀÇ ¼ö : Q 1.2 P × 0.8Q = 3,000,000 ⇒ PQ ≈ 3,100,000 ÿ Á¤´ äÀº
(D)
26. A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day? (A)
2 mph
(B)
3 mph
(C)
4 mph
(D)
5 mph
(E)
6 mph
ÀÌƲ¿¡ °ÉÃÄ 18½Ã°£ µ¿¾È 64 milesÀ» ° ɾú° í , µÑ° ³ ¯¿¡ ´  ù ¹ ø° ³ ¯º ¸ ´ Ù 2½Ã°£À» ´ õ °É¾ú´Ù °í Çß½À´ Ï ´ Ù.°á±¹ ù ° ³ ¯¿¡ ´  8½Ã°£ µÑ° ³ ¯¿¡ ´  10½Ã°£À» ° ɾú½À´ Ï ´ Ù. ù ¹ ø° ³ ¯ÀÇ Æò±Õ¼Óµµ¸ ¦ s¶ó°í ÇÏ ¸ ç 8s+ 10(s+1) =64 ⇒ s = 3 ÿ Á¤´ äÀº
(B)
27. An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,690, what was the total number of pairs of contact lenses that she sold? (A)
11
(B)
13
(C)
15
(D)
17
(E)
19
Hard contact lensesÀÇ ÆǸ Å ¼ö¸ ¦ Q¶ó °¡ Á¤ÇÏ ¸ é ´ ÙÀ½ÀÇ ½ÄÀ» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù: $ 150(5+Q) + $85Q = $1,690 ⇒ Q = 4. µû¶ó¼ soft contact lensesÀÇ ¼ö´  9°³ °¡ µÇ°í µÑÀÇ ÇÕ Àº 13ÀÌ µÇÁÒ. ÿ Á¤´ äÀº
(B)
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GRE Math °-ÁÂ Set 8-2
28. On a certain trip, a cyclist averaged 20 miles per hour for the first 10 miles and 16 miles per hour for the remaining 20 miles. If the cyclist returned immediately via the same route and took a total of 4 hours for the round trip, what was the average speed, in miles per hour, for the return trip? (A)
24
(B)
18
(C)
17
(D)
15
(E)
13
1 7 1 3
10miles ÷ 20miles per hour = 1/2 hour, 20miles ÷ 16miles per hour = 1(1/4) hour µ¹ ¾Æ¿À´ µ¥ ¼Òº ñµÈ ½Ã°£ : 4 hours(Àüü °É¸ ° ½Ã°£) – (1/2 +1(1/4)) = 9/4 30miles ÷ (9/4) = 13 ÿ Á¤´ äÀº
1 3
(E)
29. The cost of chartering a plane was shared equally among 30 passengers. If there had been 35 passengers sharing that cost, the cost per passenger would have been $30 less. What was the cost of chartering the plane? (A)
$5,400
(B)
$6,125
(C)
$6,300
(D)
$6,800
(E)
$7,350
30¸ í ÀÏ ¶§ 1¸ í ´ ç º д ãÇØ¾ß ÇÏ ´  ±Ý¾× C¶ó ÇÏ ¸ é: 30 × C = 35 × (C - 30) ¶Ç´  5 × (C - 30) = $ 900 , 5¸ í ÀÌ ´ Ã¾î ³ ² ¿¡ µû¶ó 1¸ í ´ç º д ãÇÏ ¿©¾ß ÇÏ´Â ±Ý¾× $30¾¿ ÁÙ¾î µé±â ¶§¹ ®ÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(C)
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GRE Math °-ÁÂ Set 8-2
30. In traveling a certain distance, car R averaged
x miles per gallon of gasoline. Car S
traveled 300 miles and averaged 25 miles per gallon of gasoline. If car R used the same amount of gasoline as car (A) 12 x (B) (C) (D) (E)
S , how many miles, in terms of x , did car R travel?
x x + 12 x 12 12 x
Car S°¡ ¼Òº ñÇÑ gasolineÀÇ ¾ç : 300miles
÷
25miles per gallon of gasoline = 12gallons
Car RÀÌ 12 gallons À» ¼Òº ñÇÏ ¸ ç ÀÌ µ¿ÇÏ ´  °Å¸ ®´ Â:
x miles per gallon of gasoline × 12 gallons of gasoline ÿ Á¤´ äÀº
(A)
31. Under a certain company’ s medical insurance plan, the amount an employee must pay for medical expenses consists of payment of the first $450 of expenses plus 20 percent of additional expenses, up to a maximum total payment of $1,350 per year. All remaining expenses are paid by the plan. Last year, if an employee paid the maximum amount for medical expenses, what is the least amount that the plan could have paid? (A)
$720
(B)
$1,080
(C)
$3,600
(D)
$4,500
(E)
$4,950
$450´  ó À½¿¡ °³ ÀÎ ÀÌ º Î ´ ãÇÏ ¸ ç ±× ÀÌ »ó ¹ ß»ýÇÏ ´  º ñ¿ë¿¡ ´ ëÇؼ ´  20%¸¸À» Áö±ÞÇÏ ¸ ç °³ ÀÎ ÀÌ ÃÖ°í · Î Áöº ÒÇÏ ´  ÀÇ· Ạñ¿ë ÀÇ ÇÕ°è´ Â $1,350ÀÌ ¶ó´  Á¶° ÇÀÔ´ Ï ´ Ù. $450 + ( x − $450) ×0.2 = $1,350 ⇒ x = $4,950, ¿©±â¿ ¡ ó À½¿¡ Áöº ÒÇÏ ´  $450À» »« ÈÄ 80%À» °öÇØÁÖ¸ é $4,500×0.8 = $3,600, the planÀÌ Áöº ÒÇÏ ´  ¾×¼ö¸ ¦ ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. ÿ Á¤´ äÀº
(C)
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GRE Math °-ÁÂ Set 8-2
32. A delivery truck starts on its route with a load of goods weighing T tons. At each of its first 4 stops,
1 of the weight of the goods still on the truck is unloaded. After the 4th stop, 2
what is the weight, in tons, of the goods still on the truck? (A)
15 T 16
(B)
1 T 4
(C)
1 T 6
(D)
1 T 8
(E)
1 T 16
4¹ ø Á¤ÁöÇÏ ¸ é¼ ¸ Ź ø Á¤ÁöÇÒ ¶§ ¸ ¶´ Ù ½Ç· Á ÀÖ´  ÁüÀÇ 1/2¾¿À» ³ »· È´ Ù´  Á¶°ÇÀÌ ÁÖ¾î Á® ÀÖ½À ´ Ï ´ Ù. T – (1/2T) =(1/2)T, (1/2)T−(1/4)T=(1/4)T, (1/4)T−(1/8)T=(1/8)T, (1/8)T−(1/16)T=(1/16)T T- (1/2T+1/4+1/8T+1/16T) = ÿ Á¤´ äÀº
1 T 16
(E)
33. Analysts of the automobile industry say that the total number of domestic suppliers of automobile parts was reduced by reduced by
1 from 1980 to 1985 and that the number was again 3
1 from 1985 to 1988. According to these analysts, if there were 2,520 domestic 3
suppliers in 1985, how many fewer were there in 1988 than there were in 1980? (A)
1,260
(B)
1,400
(C)
1,680
(D)
2,100
(E)
2,940
The total number of domestic suppliers in 1985(2,520) =
2 1 (1 − ) (the total number of domestic 3 3
suppliers in 1980) ⇒ 1980³ âÀÇ domestic suppliersÀÇ ÃÑ ¼ö´  = 3,780ÀÌ µË´ Ï ´ Ù. The total number of domestic suppliers in 1988 =
2 1 (1 − ) (the total number of domestic suppliers in 3 3
⇒ 1988³ â domestic suppliersÀÇ ÃѼö´  1,680ÀÌ µË´ Ï ´ Ù. µû¶ó¼ µÎ ¼öÀÇ Â÷ÀÌ 3,780 − 1,680 = 2,100ÀÌ ¿ì ¸ ®°¡ ã´  ´ äÀÌ ³ ׿ä! 1985)
ÿ Á¤´ äÀº
(D)
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GRE Math °-ÁÂ Set 8-2
34. A subway train made eleven stops on its route. If an average (arithmetic mean) of 30 passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop? (A)
60
(B)
50
(C)
30
(D)
20
(E)
10
ÁöÇÏ Ã¶ÀÌ 11Â÷· Ê Á¤Â÷ÇÏ ¸ é¼ Ã³ À½ 9¹ øÀÇ Á¤Â÷¿¡ ¼ ž½ÂÇÑ ½Â°´ ÀÇ Æò±ÕÀÌ 30¸ í ÀÌ ¸ ç, ÀÌ ¾ÆÈ© Á¤° ÅÀå Áß µÎ ¹ ø° Á¤Â÷¿¡ ¼ º Î ÅÍ ¹ Ù· Î ¾Õ Á¤Â÷¿¡ ¼ ½ÂÂ÷ÇÑ ½Â°´ º ¸ ´ Ù 5¸ í ¾¿ ½ÂÂ÷ÀÎ ¿øÀÌ ÁÙ¾î µé ¶§, B(ù ¹ ø° Á¤Â÷¿¡ ¼ ž½ÂÇÑ ½Â°´ ÀÇ ¼ö) − 5, B − 10, …., B − 40), ù ¹ ø° Á¤Â÷¿¡ ¼ ž½ÂÇÑ ½Â°´ ÀÇ ¼ö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 9B − (5 + 10 + 15 + ⋅⋅⋅ + 40) = 270 ⇒ B = 50 ÿ Á¤´ äÀº
(B)
Tips : ¹ ®Á¦ ¿¡ ¼- 5ºÎÅÍ 40±î ÁöÀÇ ÇÕÀ» µî Â÷¼ö¿- ° ø½ÄÀ¸ · Î ±¸ Çϸ é Á» ´ õ º ü¸ £° ÚÁÒ! ù °
Ç× a, °øÂ÷ dÀÎ µî Â÷¼ö¿- ÀÇÀÏ ¹ ÝÇ×À» a n ÀÌ ¶ó Çϸé
a n = a + (n-1)d, a n+1 − a n = d (°øÂ÷) ³ ¡ Ç×ÀÌ ÁÖ¾î Áú ¶§ÀÇ ÇÕÀº : S n = n ( a + l ) 2
°øÂ÷°¡ ÁÖ¾î Áú ¶§ÀÇ ÇÕÀº :
S n =
n(2a + (n − 1)d ) 2
35. Fox jeans regularly sell for $15 a pair and Pony jeans regularly, sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans? (A)
9%
(B)
10%
(C)
11%
(D)
12%
(E)
15%
Fox jeans, Pony jeans¿¡ ´ ëÇÑ ÀÎ ÇÏ À² À» °¢°¢ f , p¶ó ÇÏ ¸ é, j f
+ p = 0.22
ÿ Á¤´ äÀº
k$15
× 3 × f + $18 × 2 × p = $ 9, ÀÌ µÎ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é f¿ Í p °ª À» ±¸ ÇÒ ¼ö ÀÖÁÒ.
(B)
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GRE Math °-ÁÂ Set 8-2
36. A mixture of nuts is to contain 3 parts cashews to 6 parts almonds to 7 parts walnuts by weight. How many pounds of almonds will be needed to make 5 pounds of the mixture? (A)
3 8
8 15
(B)
(C) 1
1 5
2 3
(D) 1
cashews : almonds : walnuts = 3 : 6 : 7 ⇒ 5 pounds ×( 6/16) = 1 ÿ Á¤´ äÀº
(E) 1
7 8
7 8
(E)
37. The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A ’ s average speed was 10 miles per hour greater than that of car B , what was car B ’ s average speed, in miles per hour? (A)
20
(B)
30
(C)
40
(D)
50
(E)
80
car A°¡ 400 miles¸ ¦ °¡ ´ µ¥ ¼Ò¿äµÈ ½Ã°£À» H¶ó ÇÏ °í BÀÇ ½Ã°£À» H+2ÀÌ ¸ ç , AÀÇ ¼Óµµ¿Í BÀÇ ¼ÓµµÀÇ Â÷ÀÌ °¡ 10 milesÀ̶ó ÇßÀ¸ ´ Ï ´ ÙÀ½°ú °°ÀÌ ½ÄÀ» ¸ ¸ µé ¼ö ÀÖ½À´ Ï ´ Ù: (400 / H) – 10 miles = 400/ H+2 ⇒ H = 8, µû¶ó¼ BÀÇ °É¸ ° ½Ã°£Àº 10ÀÌ °í Æò±Õ¼Óµµ´  400 ÷ 10 = 40 ÿ Á¤´ äÀº
(C)
38. Ms. Jiminez plans an automobile trip of 7,000 to 9,000 miles. The cost of gasoline will be 85 to 95 cents per gallon, and her automobile will average 20 to 30 miles per gallon. What is the maximum possible cost of the gasoline for the trip? (A)
$485.00
(B)
$427.50
(C)
$382.50
(D)
$297.50
(E)
$256.00
°¡ Àå ¸ Õ °Å¸ ®,°¡ Àå º ñ½Ñ gasolineº ñ¿ë ,°¡ Àå ³ ·Àº average miles per gallonÀÇ Á¶°ÇÀ¸ · Î ¿©ÇàÇÏ ¸ é Á¤´ äÀ» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. . (9,000miles ÷ 20miles) × $0.95 = $427.5 ÿ Á¤´ äÀº
(B)
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GRE Math °-ÁÂ Set 8-2
39. A group of 12 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If
n of the people decide not to participate at the last minute, by how
many dollars will each remaining person’ s share of the total cost increase? (A) (B) (C) (D) (E)
E 12 − n 12 − n E E 12(12 − n) nE 12(12 − n) (12 − n) E 12n
´ çÃÊ¿¡ °³ ÀÎ º ° º Î ´ ã±ÝÀº $E/12ÀÌ ¾úÀ¸ ³ ª , ÀÌ Á¦ n¸ í ÀÌ Âü°¡ ÇÏ Áö ¾ÊÀ¸ ¹ Ç· Î ³ ² Àº »ç¶÷µé(12 − n ) ÀÌ º Î ´ ãÇØ¾ß ÇÏ ´  Ãѱݾ×Àº : ÿ Á¤´ äÀº
E − E 12 − n 12
(D)
40. The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is
x feet below the top of the tank, the concentration is 3 +
per million, where 0 <
4 parts 5 − x
x < 4. To the nearest 0.1 foot, at what depth is the concentration
equal to 6 parts per million? (A)
2.4 ft
(B)
2.5 ft
(C)
2.8 ft
(D)
3.0 ft
(E)
3.2 ft
È Çй °ÀÇ ³ óµµ°¡ tankÀÇ Á¦ ÀÏ À§ÂÊ¿¡ ¼ x feet ±í ¾î Áö¸ é ³ óµµ´  (°ø½Ä)ÀÏ ¶§ ³ óµµ°¡ 6 parts per millionÀÏ ¶§ÀÇ ±í ÀÌ ¸ ¦ ±¸ÇÏ ´  ¹ ®Á¦ : 3 + ÿ Á¤´ äÀº
4 =6 5 − x
(E)
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GRE Math °-ÁÂ Set 8-2
41. A breakfast that consists of 1 ounce of corn puffs and 8 ounces of fruit X provides 257 calories. When 8 ounces of fruit Y is substituted for the 8 ounces of fruit X , the total number of calories is reduced to 185. If fruit X provides 1.8 times as many calories as fruit
Y , how many calories does 8 ounces of fruit Y alone provide? (A)
11.25
(B)
72
(C)
90
(D)
95
(E)
129.6
1 ounce of corn + 8 ounces of fruit X = 257 calories 1 ounce of corn + 8 ounces of fruit Y = 185 calories jÀ§ÀÇ µÎ k fruit
Á¶°Ç¿¡ ¼ ´ ÙÀ½ÀÇ ½ÄÀ» À¯µµÇÒ ¼ö ÀÖÁÒ: 8X − 8Y = 72
X = 1.8Y
kÀ»j¿¡ ´ ëÀÔÇÏ ¸ é
ÿ Á¤´ äÀº
Y °ª 11.25À» ±¸ÇÒ ¼ö ÀÖ°í ÀÌ °Í À» 8À» ° öÇÏ ¸ é 90ÀÌ ³ ª ¿À³ ׿ä.
(C)
42. A 2-year certificate of deposit is purchased for
k dollars. If the certificate earns interest at
an annual rate of 6 percent compounded quarterly, which of the following represents the value, in dollars, of the certificate at the end of the 2 year?
(C)
(1.06) 2 k (1.06) 8 k (1.015) 2 k
(D)
(1.015) 8 k
(E)
(1.04) 4 k
(A) (B)
Compounded Annual Interest (º ¹ ¸ ® ÀÌ ÀÚ) < principle(¿ø±Ý) × (1 + interest rate)
time
, (time = ÀÌ ÀÚ Áö±Þ Ƚ¼ö)>
an annual rate of 6% compounded quarterly´  ¿¬°£ 6%ÀÇ ÀÌ ÀÚÀ² · Î º б⺠° (1³ â¿ ¡ 4¹ ø)· Î ÀÌ ÀÚ¸ ¦ Áö±ÞÇÑ´ Ù´  Àǹ Ì ÀÔ´ Ï ´ Ù. ° ð, ¸ Å º б⺠°· Î ¿¹ ±ÝÃѾ׿¡ ´ ëÇØ 1.15%¾¿ ÀÌ ÀÚ°¡ Áö±ÞµÇ´  °Í ÀÔ ´ Ï ´ Ù. 2³ â µ¿¾È º б⸠¶´ Ù ÀÌ ÀÚ°¡ Áö±ÞµÇ¸ é 8¹ øÀÌ Áö±ÞµÇ´  °Í ÀÌ ¹ Ç· Î À§ÀÇ °ø½Ä¿¡ time = 8ÀÌ ¶ó°í ´ ëÀÔÇÏ ¸ é k (1 + 0.015) 8 ÿ Á¤´ äÀº
(D)
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GRE Math °-ÁÂ Set 8-2
43. On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent to motel actually charged for that night? (A)
$600
(B)
$800
(C)
$1,000
(D)
$1,600
(E)
$2,400
$60ÇÏ´  ¹ æÀ» ¸ ¸ ¾à¿¡ $40ÀÇ °¡ °ÝÀ¸ · Î 10° ³ · »Æ®¸ ¦ Áá´ Ù¸ é ±× ¸ ðÅÚÀÇ Àüü ¼öÀÔÀÇ 25%° ¡ °¨ ¼ÒÇÑ´ Ù°í ÇßÀ¸ ´ Ï $60°ú $40ÀÇ Â÷¾×ÀÎ $20¿¡ 10 rooms À» °öÇÑ ÈÄ ´Ù½Ã 4(25%À» Â÷ÁöÇÏ ¹ Ç· Î ) ¸ ¦ °öÇÏ ¸ é ¹ ®Á¦ ¸ ¦ Ç® ¼öµµ ÀÖ°Ú³ ׿ä: ($ 20 × 10) ×4 = $800 ÿ Á¤´ äÀº
(B)
44. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 4 miles per hour faster than the first runner’ s rate. How far apart, to the nearest mile, will they be after (A)
6
(B)
7
(C)
8
(D)
12
(E)
14
1 hour? 2
4 2 + 62 = (2 13 ) 2 ⇒ 2 13 ≈ 7 ÿ Á¤´ äÀº
(B)
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GRE Math °-ÁÂ Set 8-2
45. The rear wheels of a car crossed a certain line 0.5 second after the front wheels crossed the same line. If the centers of the front and rear wheels are 20 feet apart and the car traveled in a straight line at a constant speed, which of the following gives the speed of the car in miles per hour? (5,280 feet = 1 mile) (A)
(B) (C)
20 60 2 5,280 0.5 20 60 5,280 0.5 20 0.5 2 5 , 280 60
(D)
(20)(5,280) (60 2 )(0.5)
(E)
(20)(5,280) (60)(0.5)
¾Õ ¹ ÙÄû¿Í µÚ ¹ ÙÄû°¡ ¼±À» Áö³ ª °¡ ´  µ¥ °É¸° ½Ã°£ÀÌ 0.5ÃÊÀÌ °í µÎ ¹ ÙÄûÀÇ Á߽ɰ£ÀÇ °Å¸ ®°¡ 20feet ¶³ ¾î Á® ÀÖÀ» ¶§ ¼Óµµ¸ ¦ ¹ °¾î º ¸°í ÀÖ´ Ù. 20 feetÀÇ °Å¸ ®¸ ¦ 0.5 seconds¿¡ Áö³ ¯ ¶§ ¼Óµµ¸ ¦ ¹ °¾î º ¸ ´  ¹ ®Á¦ ¿Í °°´ Ù. ÇÑ °¡ Áö À¯ÀÇÇÒ Á¡ Àº ¹ ®Á¦ ¿¡ ¼ ´  feet¿Í second·Î ÁÖ¾ú±â ¶§¹®¿¡ feet¸ ¦ mile· Î secondÀ» hourÀÇ ´ ÜÀ§·Î ¹ Ù² Ù¾î ¾ß ÇÕ´ Ï ´ Ù. Áï Speed =
20 feet ¿¡ ¼ feet´Â 0.5 sec onds
5,280À¸ · Î ³ ª ´ ©¾î ÁÖ°í 0.5 secondsÀº 60×60À¸ · Î ³ ª ´ ©¾î ÁÖ¸ é µË´ Ï ´ Ù. ÿ Á¤´ äÀº
(A)
46. A cashier mentally reversed the digits of one customer’s correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 45 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents? (A) 14
(B) 45
(C) 54
(D) 65
(E) 83
°Å½º ¸ § µ· ÀÇ ÀÚ¸ ´ ¼ö¸ ¦ ½Ç¼ö· Î µÚÁý¾î »ý°¢ÇÏ ¿© ÁÖ¾úÀ» ¶§ 45centÀ» ´ ú ÁÖ¾ú´ Ù¸ é
½ÇÁ¦ · Î ÁÖ
¾î ¾ß Çß´ ø µ· Àº ¾ó¸ ¶¿´ ´ ÂÁö¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. 10a + b – ( 10b + a ) = 45 , ⇒ 9(a − b) = 9 ×5 ⇒ a − b = 5, ½ÇÁ¦ · Î a − b = 5ÀÎ ½ÖÀ» ±¸ ÇÏ ¸ é ( a , b) : (6,1), (7,2), (8,3), (9,4)ÀÔ´ Ï ´ Ù. ÀÌ Áß¿¡ ab − ba = 45ÀÎ °Í Àº (8, 3)ÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(E)
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GRE Math °-ÁÂ Set 8-2
47. A shipment of 1,500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived,
2 of the heads were sold, each at 25 3
percent above the cost per head. The following day the rest were sold at a price per head equal to 10 percent less than the price each head sold for on the day before. What was the gross profit on this shipment? (A) $100
(B) $115
(C) $125
(D) $130
(E) $135
2 600 1 600 × 1.25 × ×0.9) = $725 ) + (1,500 × ×1.25× 1,500 1,500 3 3 µû¶ó¼ $725 − $600 = $125 (1,500 ×
ÿ Á¤´ äÀº
(C)
48. If Sam were twice as old as he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam? (A)
20
(B)
30
(C)
40
(D)
50
(E) 60
If Sam were twice as old as he is: “SamÀÌ Áö±Ý ³ ª ÀÌ ¿¡ ¼- 2¹ è°¡ µÈ´ Ù¸ é” j2Sam
= 40 + Jim, kJim + 10 = Sam
µÎ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é SamÀÇ ³ ª ÀÌ ´  30ÀÌ µË´ Ï ´ Ù. ÿ Á¤´ äÀº
(B)
49. A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel? (A)
$1
(B)
$2
(C)
$3
(D)
$4
(E)
$12
Ÿ ¿ùÀÇ °¡ °ÝÀÌ $1ÀÎ »óµÉ °æ¿ì $120· Î ±¸ ÀÔÇÒ ¼ö ÀÖ´  Ÿ ¿ùÀÇ °³ ¼ö°¡ 10° ³ °¨ ¼ÒÇÒ ¶§ ÇöÀç Ÿ ¿ùÀÇ °¡ °ÝÀ» ±¸ÇÏ ¶ó´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. Ÿ ¿ùÀÇ °³ ¼ö: n , Ÿ ¿ùÀÇ °¡ °Ý : p¶ó ° ¡ Á¤ÇÏ ¸ é j NP
= $ 120,
k(N-10)(P+1)=$120ÀÌ
µÇ°í ¿©±â¼ 120 = 2×3×4×5ÀÔ´ Ï ´ Ù. 120ÀÇ ¾à¼ö¸ ¦ ±¸ ÇÏ °í
¹ ®Á¦ ÀÇ Á¶° ÇÀ» ¸ ¸ Á· ÇÏ ´  Á¶ÇÕÀ» ±¸ ÇÏ ¸ é µË´ Ï ´ Ù. Áï , ´ ÙÀ½°ú ° °ÀÌ , ¸ ¸ ¾à ¾ÖÃÊÀÇ °¡ °ÝÀÌ $2ÀÌ ¸ é ÆǸ ŵǴ  Ÿ ¿ùÀÇ °³ ¼ö´Â 60°³ ¿´ À» °Í ÀÌ °í °¡ °Ý ÀÌ $1 Áõ°¡ µÇ¾î $3· Î µÇ¸é ÆǸ ŵǴ  Ÿ ¿ùÀÇ °³ ¼ö´  40° ³ °¡ µÇ¾î ±¸ÀÔÇÒ ¼ö ÀÖ´  Ÿ ¿ùÀÇ °³ ¼ö°¡ 20° ³ °¨ ¼ÒÇÏ °Ô µÇ¾î Á¶°ÇÀ» ¸ ¸ Á· ÇÏ Áö ¾Ê½À´ Ï ´ Ù. ±×· ¯³ ª ¾ÖÃÊ¿¡ °¡ °ÝÀÌ $3¿¡ ¼ $4· Î Áõ °¡ ÇÏ ¸ é ÆǸ Å°³ ¼ö´  40° ³ ¿¡ ¼ 30° ³ · Î °¨ ¼ÒÇÏ °Ô µÇ¾î Á¶° ÇÀÌ ÃæÁ· µÈ´ Ù. ÿ Á¤´ äÀº
(C)
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GRE Math °-ÁÂ Set 8-2
50. A ruby and a diamond have insured values of $1,800 and $1,200, respectively, and the annual premium rate for each gem is $1.50 per $100 of insured value. If the rate and insured values of the two gems remain constant over the years, after how many years will the total of the insurance premiums on both gems for those years first exceed the insured value of the diamond? (A)
8
(B)
12
(C)
20
(D)
27
(E)
40
$3,000 ×
1.5 × x years = $1,200⇒ x years ≈ 26.6 100
µû¶ó¼ diamondÀÇ °¡ Ä¡ °¡ µÎ º ¸ ¼®ÀÇ º ¸ Çè· áº ¸ ´ Ù Å©· Á¸ é 27³ âÀÌ ÇÊ¿ä ÇÕ´ Ï ´ Ù. ÿ Á¤´ äÀº
(D)
51. A furnace service contract costs $48 per year and covers payment of 80 percent of all repair costs. The total amount paid by the owner, including the cost of the contract, will equal the payment covered by the contract when the total repair costs for the year are (A) $48 (B) $60 (C) $72 (D) $80 (E) $92 $ 48 + 0.2 ×all repair costs = 0.8 × all repair costs ⇒ all repair costs = $80 ÿ Á¤´ äÀº
(D)
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-Á Â – Se t 9 GRE Math °
Category 9 L ines and Angl es
1.
In the figure above, the value of y is (A) 6 (B) 12 (C) 24 (D) 36 (E) 42
2. If each of the two lines
l 1 and l 2 is
answer
parallel to line
l3 ,
which of the following must be
answer
true? (A)
Lines
l 1 , l 2 , and l 3 lie
in the same plane.
(B)
Lines
l 1 , l 2 , and l 3 lie
in different planes.
(C)
Line
l 1 is
parallel to line
(D)
Line
l 1 is
the same line as line
l2.
(E)
Line
l 1 is
the same line as line
l3 .
l2.
3. In the figure above, what is the value of x ? (A) 18 (B) 30 (C) 36 (D) 40 (E) 45
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answer
-Á Â – Se t 9 GRE Math °
4.
5.
In the figure above, what is the value of x ? (A) 28 (B) 30 (C) 32 (D) 42 (E) 48
Square RSTU shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for T to be in the position where S is now shown. The number of degrees through which RSTU is rotated is (A) 135 (B) 180 (C) 225 (D) 270 (E) 315
answer
answer
° ° ° ° °
6. In the figure above, if line (A) 20 (B) 50 (C) 110 (D) 140 (E) 160
k and n are parallel, then x =
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answer
-Á Â – Se t 9 GRE Math °
7. The figure above traces the path of a certain billiard ball on a rectangular billiard table. If the ball bounces off the side of the table at the same angle at which it hits the side, and if w = 42 , what the value of z ? (A) 42 (B) 48 (C) 52 (D) 58 (E) 60
8. In the figure above, what is the value of x ? (A) 20 (B) 30 (C) 40 (D) 50
answer
answer
(E) 70
9. The figure above shows two lines intersecting at the point O . If the lines are rotated about O at the same rate and in the directions shown until AB ⊥CD , through how many degrees must each line move? (A) 90 − θ (B)
90 −
(C)
90 +
(D) (E)
θ
2 θ
2
90 + θ 2 90 + 2θ 2
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answer
-Á Â – Se t 9 GRE Math °
10. The figure above traces the path of a certain billiard ball on a rectangular billiard table. If the ball bounces off the side of the table at the same angle at which it hits the side, and if w = 42 , what the value of z ? (A) 42 (B) 48 (C) 52 (D) 58 (E) 60
11. If each of the two lines
l 1 and l 2 is
parallel to line
l3 ,
which of the following must be
true? (A)
Lines
l 1 , l 2 , and l 3 lie
in the same plane.
(B)
Lines
l 1 , l 2 , and l 3
(C)
Line
l 1 is
parallel to line
(D)
Line
l 1 is
the same line as line
l2.
(E)
Line
l 1 is
the same line as line
l3 .
lie i n different planes. l2.
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answer
answer
-Á Â – Se t 9 GRE Math °
¼öÇÐÇؼ³
Category 9 L ines and Angl es
1. In the figure above, the value of y is (A) 6 (B) 12 (C) 24 (D) 36 (E) 42 y°ª À» ±¸ ÇÏ ±â Àü¿¡ ¸ ÕÀú xÀÇ °ª À» ±¸ ÇØ¾ß °Ú³ ׿ä. 2x¿Í 3x´  º ¸ °¢ÀÇ °ü°è· Î ÇÕÃļ- 180µµÁÒ 2x + 3x = 180 x= 36 ±× ´ ÙÀ½Àº 3x° + (y+30)° = 180 °(º ¸ °¢), ¶Ç´  2x° = y° +30 ° (¸ ² ÀÁö° ¢) µÑ Áß¿¡ ¾Æ¹ « ½Ä¿¡ x=36À» ´ ëÀÔÇÏ ¸ é y = 42¸ ¦ ±¸ ÇÒ ¼ö ÀÖÁÒ. . Á¤´ äÀº (E)
2. If each of the two lines
l 1 and l 2 is
parallel to line
l3 ,
which of the following must be
true? (A)
Lines
l 1 , l 2 , and l 3 lie
in the same plane.
(B)
Lines
l 1 , l 2 , and l 3 lie
in different planes.
(C)
Line
l 1 is
parallel to line
(D)
Line
l 1 is
the same line as line
l2.
(E)
Line
l 1 is
the same line as line
l3 .
l 1 °ú l 2 °¡
l 3 ¿¡ ÆòÇàÇÏ ´ Â
°Í Àº
l2.
l1 , l 2 ,
and
l 3 °¡
¸ ðµÎ ÆòÇàÇÔÀ» ¸ »ÇÏ ´  °Í ÀÌ Áö, ÀÌ µéÀÌ
°°Àº Æò¸é (plane)ÀÌ ³ ª ¼±(line)¿ ¡ ÀÖ´ Ù´  ¶æÀº ¾Æ´ Ï Áö¿ä . µû¶ó¼- ÀÌ·± Á¶°ÇÀ» ¸ðµÎ ¸ ¸ Á· ½ÃÅ°´  °Í Àº (C) . Á¤´ äÀº (C)
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-Á Â – Se t 9 GRE Math °
3. In the figure above, what is the value of x ? (A) 18 (B) 30 (C) 36 (D) 40 (E) 45 x¿Í 4x »çÀÌ ÀÇ °¢À» ÀÓÀÇ· Î y¶ó °¡ Á¤ÇÏ ¸ é jx + y =90(¿©°¢ÀÇ ° ü°è), k4x + y = 180(º ¸ °¢ÀÇ ° ü°è) . Á¤´ äÀº
j°úkÀ» Ç®¸ é
x = 30
(B)
4. In the figure above, what is the value of x ? (A) 28 (B) 30 (C) 32 (D) 42 (E) 48 º ¸ °¢ÀÇ °ü°è(ÇÕÃļ- 180µµ)¸ ¦ ¹ ¯´  ¹ ®Á¦ ³ ׿ä . ¹ Ù² ã ¸ »ÇÏ ¸ é 2x + 84 + x = 180, ¿©±â¼- ½ÄÀ» Á¤ ¸ ®ÇÏ ¸ é x = 32 . Á¤´ äÀº
(C)
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-Á Â – Se t 9 GRE Math °
5.
Square RSTU shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for T to be in the position where S is now shown. The number of degrees through which RSTU is rotated is (A) 135 (B) 180 (C) 225 (D) 270 (E) 315 ° ° ° ° °
Á¤»ç°¢Çü RSTU°¡ ½Ã°è¹ æÇâÀ¸ · Πȸ ÀüÇÒ ¶§, T°¡ S· Î ÀÌ µ¿ÇÏ ´ µ¥ ÃÖ¼Ò °¢ÀÌ ¾ó¸ ¶ÀÎ Áö¸ ¦ ¹ ¯´Â ¹ ®Á¦ ³ ׿ä. T¿¡ ¼- ´ ٽà T·Î µ¹ ¾Æ¿À´ µ¥ 360µµ ȸ ÀüÇÏ °í , T¿¡ ¼- U· Î ÀÌ µ¿ÇÏ ´  °Í Àº 90µµÀÔ´ Ï ´ Ù. µû¶ó¼- T¿¡ ¼- S±î Áö´  270µµ¸ ¦ ȸ ÀüÇÏ ³ ׿ä . . Á¤´ äÀº
(D)
6. In the figure above, if line (A) 20 (B) 50 (C) 110 (D) 140 (E) 160
k and n are parallel, then x =
µÎ ¼±ÀÌ ÆòÇàÇÑ ¼º Áú°ú »ï °¢ÇüÀÇ ÇÕÀÌ 180 µµ¶ó´  ¼º Áú° ú º ¸°¢ ( µÎ °¢ÀÌ ÇÕÃļ- 180 µµ)ÀÇ ¼º ÁúÀ» ÀÌ ¿ëÇÏ ¸ é ½±°Ô Ç® ¼ö ÀÖ½À´ Ï ´ Ù. 70 + 90 + (180 − x) = 180 , x = 160 . Á¤´ äÀº
(E)
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-Á Â – Se t 9 GRE Math °
7.
The figure above traces the path of a certain billiard ball on a rectangular billiard table. If the ball bounces off the side of the table at the same angle at which it hits the side, and if w = 42 , what the value of z ? (A) 42 (B) 48 (C) 52 (D) 58 (E) 60
´ 籸 ´ ë¿¡¼- ÀÔ»ç° ¢°ú ¹ Ý»ç° ¢ÀÌ °°´ Ù´  Á¶°Ç¿¡ ¼- ó À½ ÀԻ簢À» w = 42 ¶ó°í ÁÖ°í ¼- ³ ª ¸ ÓÁö ¹ Ý»ç° ¢ zÀ» ±¸ ÇÏ ¶ó´  ¹ ®Á¦ ³ ׿ä . w = 42 À» ¾Ë¾ÒÀ¸ ´ Ï ±× ´ ÙÀ½Àº y ° ª À» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. w(=42) + y + 90 = 180, ÀÌ ½ÄÀ» Ç®¸é y = 48. y=48ÀÇ ÀԻ簢ÀÌ µé¾î °¡ ¸ é ÀÌ ¹ ø¿¡ ´  ¹ Ý»ç° ¢µµ 48 µµÀÔ´ Ï ´ Ù. µû¶ó¼- zÀÇ °ª Àº 48µµ . Á¤´ äÀº
(B)
8. In the figure above, what is the value of x ? (A) 20 (B) 30 (C) 40 (D) 50 (E) 70 ù ¹ ø° ±¸ ÇÒ °¢Àº ¸ Ç À§¿¡ ÀÖ´  °¢À» y¶ó ÇÏ ¸ é 30+110+y = 180, ¿©±â¼- y = 40. ÀÌ ¹ ø¿¡ ´ Âx + y(=40) + 100 = 180 ⇒ x = 40 . Á¤´ äÀº
(C)
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-Á Â – Se t 9 GRE Math °
9. The figure above shows two lines intersecting at the point O . If the lines are rotated about O at the same rate and in the directions shown until AB ⊥CD , through how many degrees must each line move? (A) 90 − θ (B)
90 −
(C)
90 +
(D) (E)
θ
2 θ
2
90 + θ 2 90 + 2θ 2
AB ⊥CD °¡ µÇ· Á¸ é ÀÏ ´ Ü ¼±º Ð CD´  θ ÷÷⊕↑ÀÌ µ¿Çؼ- ¼±º Ð ABÀÇ À§Ä¡ · Î °¡ °í o
¼±º Ð AB´Â 90µµ ÀÌ µ¿ÇØ¾ß ¼±º Ð CD¿Í ¼öÁ÷ÀÇ °ü°è° ¡ ¼º ¸ ³ ÇÏ ÁÒ. ±×· ±µ¥ ÀÌ µÎ ¼±º ÐÀº O À» Áß½ÉÀ¸ · Î ¶È °°Àº °¢µµ· Î µ¿½Ã¿¡ ÀÌ µ¿ÇÑ´ Ù°í ÇßÀ¸ ´ Ï ¾ó¸ ¶¸ ¸ Å- ÀÌ µ¿ÇØ¾ß ÇÏ ´ ÂÁö¸ ¦ ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. ÿ Á¤´ äÀº (D)
θ
o
+ 90À» 2· Î ³ ª ´ ©¾î ÁÖ¸ é °¢ ¼±º ÐÀÌ
10. The figure above traces the path of a certain billiard ball on a rectangular billiard table. If the ball bounces off the side of the table at the same angle at which it hits the side, and if w = 42 , what the value of z ? (A) 42 (B) 48 (C) 52 (D) 58 (E) 60 ³ ² Çлýµé¿¡ °Ô ¾ÆÁÖ Ä£¼÷ÇÑ ¹ ®Á¦ ³ ׿ä . ´ 籸ÀÇ ±âº » ¿ø¸ ®ÀÎ ÀÔ»ç° ¢°ú ¹ ݻ簢ÀÌ °°´ Ù´  Á¶°ÇÀ» ÁÖ¾ú±â ¶§¹ ®¿¡ w = 42 ⇒ x = 42 ⇒ y = (180 −(90+42) = 48 ⇒ z =48 ÿ Á¤´ äÀº
(B)
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-Á Â – Se t 9 GRE Math °
11. If each of the two lines
l 1 and l 2 is
parallel to line
l3 ,
which of the following must be
true? (A)
Lines
l 1 , l 2 , and l 3 lie
in the same plane.
(B)
Lines
l 1 , l 2 , and l 3 lie
in different planes.
(C)
Line
l 1 is
parallel to line
(D)
Line
l 1 is
the same line as line
l2.
(E)
Line
l 1 is
the same line as line
l3 .
l 1 °ú l 2 °¡
l 3 ¿¡ ÆòÇàÇÏ ´ Â
°Í Àº
l2.
l1 , l 2 ,
and
l 3 °¡
¸ ðµÎ ÆòÇàÇÔÀ» ¸ »ÇÏ ´  °Í ÀÌ Áö, ÀÌ µéÀÌ
°°Àº Æò¸é (plane)ÀÌ ³ ª ¼±(line)¿ ¡ ÀÖ´ Ù´  ¶æÀº ¾Æ´ Ï Áö¿ä . µû¶ó¼- ÀÌ·± Á¶°ÇÀ» ¸ðµÎ ¸ ¸ Á· ½ÃÅ°´  °Í Àº (C) . Á¤´ äÀº
(C)
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- ÁÂ Set-10 GRE Math °
Category 10 Tr iangles
1.
2
3.
In ∆ ABC above, what is (A) z + 73 (B) z − 73 (C) 70 − z (D) z − 70 (E) 73 − z
For what value of (A) 2 (B) 3 (C) 6 (D) 9 (E) 12
x in terms of z ? answer
x will the triangle above be equilateral?
In the figure above, the perimeter of shaded region? (A) 2 + 2 (B) 6 (C) 8 2
answer
∆ MNP is how much greater than the perimeter of the
6+ 3 2 (E) 6 + 8 2 (D)
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- ÁÂ Set-10 GRE Math °
4. The figure above shows the dimensions of an isosceles triangle in terms of area of the triangle? (A) 24 (B) 30 (C) 48 (D) 60 (E) 96
5. In the figure above, if AB || CE , (A) 45 (B) 60 (C) 67.5 (D) 112.5 (E) 135
x . What is the
CE = DE , and y = 45 , then x =
6. On the map above, if the segment that joins cities P and Q represents 6 kilometers, how many kilometers does the segment that joins cities Q and R represent? (A) (B) (C) (D) (E)
answer
3 3 6 9
6 3 It cannot be determined from the information given
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answer
answer
- ÁÂ Set-10 GRE Math °
7. If the perimeter of RT ? (A) 21 (B) 19 (C) 17 (D) 15 (E) 13 .
8.
∆ RST above is 40, which of the following could NOT be the length of
In ∆ RST above, if the measure of (A)
∠ R equals the measure of ∠T , then RT =
1 2
(B)
1
(C)
3 2
(D)
2
(E)
5 7
answer
answer
Note : Figure not drawn to scale. 9. In the figure above, if the sum of the perimeters of the three triangles is 37, what is the perimeter of pentagon ABCDE ? (A) 32 (B) 27 (C) 25 (D) 22 (E) 17
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- ÁÂ Set-10 GRE Math °
Note : Figure not drawn to scale. 10. The figure above shows the dimensions of a stepladder that stands on a floor. How high is the top of the ladder from the floor? (A) 4 ft (B) 5 ft (C) 6 ft (D) 4 3 ft (E)
2 15 ft
11. In the figure above, CE = 5 , BD = 8 , and the area of quadrilateral ABCD is 36. What is the area of ∆ ABD ? (A) 4 (B) 9 (C) 16 (D) 20 (E) 56
12.
answer
In the figure above, If PQRS is a square and QT = TR , which of the following statements is NOT true? (A) PT = TS (B) x = y (C) u = v (D) r = y (E) The area of ∆ PQT is equal to the area of ∆ SRT .
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answer
answer
- ÁÂ Set-10 GRE Math °
Note : Figure not drawn to scale. 13. In City R , streets run either east-west or north-south, as shown on the map above. Blocks along east-west streets are 400 feet long and blocks along north-south streets are 200 feet long. If the width of the streets is ignored, what is the straight-line distance, in feet, from X to Y ? (A) 200 5 (B) 1,000 (C) 1,200 (D) 400 (E) 1,600
answer
10
14. If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side? I. 5 II. 8 III. 11 (A) II only (B) III only (C) I and II only (D) II and III only (E) I, II, and III
15. The length of each side o f a triangle is an even number. If no two of the sides are equal, what is the smallest perimeter the triangle could have? (A) 18 (B) 16 (C) 14 (D) 12 (E) 6
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answer
- ÁÂ Set-10 GRE Math °
16. The lengths of two sides of a right triangle are
d d and . If one of these sides is the 3 4
answer
hypotenuse, what is the length of the third side of the triangle?
5d 12 d (B) 7 d (C) 5 d (D) 12 d 7 (E) 12 (A)
17. If each side of ∆ ACD above has length 3 and if AB has length 1, what is the area of region BCDE ? (A)
18. In
9 4
(B)
7 3 4
(C)
9 3 4
(D)
7 3 2
answer
(E) 6 + 3
∆ PQS above, if PQ = 3 and PS = 4 , then PR =
9 4 12 (B) 5 16 (C) 5 15 (D) 4 20 (E) 3 (A)
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- ÁÂ Set-10 GRE Math °
19. In the figure above, square region ABCE and triangular region ACD each have area 36. What is the perimeter of triangle ACD ? (A) 24 (B) 12 + 12 2 (C) 36 (D) 18 + 18 2 (E) 36 2
answer
Note : Figure not drawn to scale. 20. The figure above shows the relative positions of a projection lens L , a film F , and a screen S . The film is 6 inches from the lens and is parallel to the screen. How many feet from the screen is the lens if a 0.3 -inch figure on F projects a 6-foot image on S ? (1 foot = 12 inches) (A) 0.3 (B) 10 (C) 12 (D) 100 (E) 120
21. In the figure above, if A1 , A2 , and A3 are the areas of the respective semicircular regions, what is the value of (A)
1
A1 + A2
A3 3 (B) 2
? (C)
π
2
(D) 2
(E)
3π 2
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answer
- ÁÂ Set-10 GRE Math °
D R Y LAND 22. A cable is being laid from one side of a swamp, at point A , to the other side, at point D . If laying cable costs $500 per mile on dry land and $800 per mile in the swamp, how much is saved by laying the cable on the ABD route rather than the ABCD route? (A) $700 (B) $1,000 (C) $1,500 (D) $3,200 (E) $4,700
23. A ladder that is 13 feet long is placed against a vertical wall so that the top of the ladder is 5 feet below the top of the wall. If the bottom of the ladder rests on level ground and is 5 feet out from the base of the wall, what is the height of the wall, in feet? (A) 12 (B) 13 (C) 17 (D) 19 (E) 23
24. A ladder 25 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip? (A) 4 (B) 5 (C) 8 (D) 9 (E) 15
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answer
answer
answer
- ÁÂ Set-10 GRE Math °
25. A rope hangs from the top of a vertical pole, leaving 4 feet of slack on the floor. When fully extended, the rope touches the floor at a point 12 feet away from the pole. How many tall is the pole? (A) 4 (B) 12 (C) 13 (D) 16 (E) 20
² ÀÁö° ¢ <<Âü° í -ÀÌ µî º ¯»ï ° ¢ÇüÀǼº Áú>> ¨ ç µÎ ¹ Ø° ¢ÀÇ Å©±â´  ¼- · Î °° ´ Ù. ¨ è µÎ ³ »° ¢ÀÇ Å©±â° ¡ °°Àº »ï ° ¢ÇüÀº ÀÌ µî º ¯ »ï ° ¢ÇüÀÌ ´ Ù. ¨ é ² ÀÁö° ¢ÀÇ ÀÌ µî º м±Àº ¹ غ ¯À» ¼öÁ÷ ÀÌ µî º ÐÇÑ´ Ù. ¨ ê ÀÌ µî º ¯»ï ° ¢ÇüÀDz ÀÁö° ¢ÀÇ ÀÌ µî º м±Àº ¹ غ ¯À» ¼öÁ÷ ÀÌ µî º ÐÇÏ ´  ¼º ÁúÀÌ ÀÖ½À´ Ï ´ Ù.
¹ Ø°¢
<<Á÷»ï ° ¢ÇüÀÇÇÕµ¿Á¶° Ç>> ¨ çº øº ¯ÀÇ ±æÀÌ ¿Í ÇÑ ¿¹ ° ¢ÀÇ Å©±â° ¡ °¢°¢ °° ´ Ù. ¨ èº øº ¯ÀÇ ±æÀÌ ¿Í ´ Ù¸ ¥ ÇÑ º ¯ÀÇ ±æÀÌ°¡ °¢°¢ °° ´ Ù. <<»ï ° ¢ÇüÀÇ ÇÕµ¿Á¶° Ç>> ¨ ç ´ ë ÀÀÇÏ ´  µÎ º ¯ÀÇ ±æÀÌ ° ¡ °¢°¢ ° ° ° í , ±× ³ ¢ÀÎ ° ¢ÀÇ Å©±â° ¡ °° ´ Ù. ¨ è ´ ë ÀÀÇÏ ´  ÇÑ º ¯ÀÇ ±æÀÌ ° ¡ ° ° ° í , ±× ¾ç ³ ¡ ° ¢ÀÇ Å©±â° ¡ °¢°¢ °° ´ Ù. ¨ é ´ ë ÀÀÇÏ ´  ¼¼ º ¯ÀÇ ±æÀÌ ° ¡ °¢°¢ °° ´ Ù. <<»ï ° ¢ÇüÀÇ ´ àÀ½Á¶° Ç>> ¨ ç ¼¼ ½ÖÀÇ ´ ë ÀÀÇÏ ´  º ¯ÀÇ ±æÀÌ ÀÇ º ñ° ¡ °° ´ Ù. ¨ è µÎ ½ÖÀÇ ´ ëÀÀÇÏ ´  º ¯ÀÇ ±æÀÌ ÀÇ º ñ°¡ ° ° ° í , ±× ³ ¢ÀÎ ° ¢ÀÇ Å©±â° ¡ °° ´ Ù. ¨ é µÎ ½ÖÀÇ ´ ëÀÀÇÏ ´  ° ¢ÀÇ Å©±â° ¡ °° ´ Ù.
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answer
- ÁÂ Set-10 GRE Math °
¼öÇÐÇؼ³
Category 10 Tr iangl es
1. In ∆ ABC above, what is (A) z + 73 (B) z − 73 (C) 70 − z (D) z − 70 (E) 73 − z
x in terms of z ?
»ï °¢ÇüÀÇ ³ »ÇÕÀÇ ÇÕÀº 180µµ ÀÔ´ Ï ´ Ù. X + 37 + Z + 70 = 180, ÀÌ ½ÄÀ» z °ª À¸· Î x À» Ç¥ÇöÇÏ ¸ é 73 − z . Á¤´ äÀº
(E)
2. For what value of (A) 2 (B) 3 (C) 6 (D) 9 (E) 12
x will the triangle above be equilateral?
»ï °¢ÇüÀÌ Á¤»ï °¢ÇüÀÌ µÇ±â À§Çؼ ´  ¼¼º ¯ÀÌ ¸ ðµÎ °°¾Æ¾ß ÇÕ´ Ï ´ Ù. µû¶ó¼ 2x = x +3, ¿©±â¼ x = 3 . Á¤´ äÀº
(B).
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3. In the figure above, the perimeter of shaded region? (A) (B) (C) (D) (E)
∆ MNP is how much greater than the perimeter of the
2+ 2
6
8 2 6+ 3 2 (E) 6 + 8 2
ÇÇŸ °í ¶ó½º ÀÇ Á¤¸ ® --- ¼¼ º ¯ÀÇ ±æÀÌ °¡ a, b, cÀÎ »ï °¢Çü¿¡ ¼ b 2 aÀ» º øº ¯À¸ · Î ÇÏ ´  Á÷°¢ »ï °¢ÇüÀÌ ´ Ù. Å« »ï °¢ÇüÀÇ º øº ¯Àº 8 2
+ 8 2 = (8 2 ) 2 , ÀÛÀº
»ï °¢ÇüÀº 5 2
+ c 2 = a 2 ℵ⊂÷ , ÀÌ
»ï °¢ÇüÀº
+ 5 2 = (5 2 ) 2
Å« »ï °¢ÇüÀÇ µÑ· ¹ ´ Â16 + 8 2 , ÀÛÀº »ï °¢ÇüÀÇ µÑ· ¹ ´ Â10 + 5 2 ±× Â÷ÀÌ ¸ ¦ ±¸Çغ ¸ ¸ é 6 + 3 2 . Á¤´ äÀº
(D)
4. The figure above shows the dimensions of an isosceles triangle in terms of area of the triangle? (A) 24 (B) 30 (C) 48 (D) 60 (E) 96
x . What is the
ÀÌµî º ¯»ï °¢Çü(isosceles)ÀÇ ¼º Áú µÎ º ¯ÀÌ °°°í ¾Æ· ¡ ¹ غ ¯ÀÌ °°´ Ù´  °Í À» ÀÌ ¿ë ÇÏ ¸ é µÇÁÒ. 2x − 2 = 3x − 8, ¿©±â¼ x = 6. µû¶ó¼ ³ ôÀÌ ´  6ÀÌ°í ¹ غ ¯ÀÇ ±æÀÌ ´  16ÀÔ´ Ï ´ Ù. »ï °¢ÇüÀÇ ¸éÀûÀº
1 (6 × 16) = 48 2 . Á¤´ äÀº
(C)
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5. In the figure above, if AB || CE , (A) 45 (B) 60 (C) 67.5 (D) 112.5 (E) 135
CE = DE , and y = 45 , then x =
ÀÏ ´ Ü AB || CE ÀÌ ¹ Ç· Î B ° ¢° úC°¢ÀÌ µ¿ÀÏ ÇÏ ÁÒ. µû¶ó¼ C° ¢µµ xµµÀÔ´ Ï ´ Ù. ´ ÙÀ½Àº CE = DE ÀÌ ¹ Ç· Î C°¢°ú D°¢ÀÌ ¶È°° À¸ ¹ Ç· Î D = xµµ ÀÔ´ Ï ´ Ù. ÀÛÀº »ï °¢ÇüÀÇ °¢À» º ¸ ¸ é µÎ °¢Àº xÀÌ °í ³ ª ¸ ÓÁö´  y=45¶ó ÇßÀ¸ ´ Ï ±î 2x + 45 = 180, ¿©±â¼ x = 67.5ÀÔ´ Ï ´ Ù. . Á¤´ äÀº
(C)
6. On the map above, if the segment that joins cities P and Q represents 6 kilometers, how many kilometers does the segment that joins cities Q and R represent? (A) (B) (C) (D) (E)
3 3 6 9
6 3 It cannot be determined from the information given
PÀÇ °¢Àº 30µµ, Q ¹ Ù±ùÂÊ °¢Àº 60µµÀÌ ¹ Ç· Î ¾ÈÂÊ °¢Àº 120µµÀÔ´ Ï ´ Ù. ±×·¯¸ é ³ ª ¸ ÓÁö RÀº 180 − (120 + 30) = 30µµÀÔ´ Ï ´ Ù. µû¶ó¼ QP¿Í QRÀº µÎ º ¯ÀÇ ±æÀÌ °¡ °°°í µÎ º ¯ÀÇ ±æÀÌ °¡ °°Àº ÀÌ µî º ¯ »ï °¢ÇüÀÔ´ Ï ´ Ù. QRÀÇ ±æÀÌ ´  6km. . Á¤´ äÀº
(B)
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7. If the perimeter of RT ? (A) 21 (B) 19 (C) 17 (D) 15 (E) 13
∆ RST above is 40, which of the following could NOT be the length of
»ï ° ¢ÇüÀÇ Á¤ÀÇ --- µÎ º ¯ÀÇ ÇÕÀº ³ ª ¸ ÓÁö º ¯ÀÇ ÇÕº ¸ ´ Ù Ç×»ó Å©´ Ù ÀÌ ¼º ÁúÀ» ¾Ë°í ÀÖÀ¸ ¸ é ¹ ®Á¦ °¡ ½±°Ô Ç®¸ ®³ ׿ä . À§ÀÇ »ï °¢ÇüÀº ¾Æ· ¡ º ¯ÀÌ ¸ ðµÎ X ÀÌ ¹ Ç· Î ÀÌ µî º ¯ »ï °¢ÇüÀÔ´ Ï ´ Ù. µû¶ó¼ ÀÌ ÇÑ º ¯À» a ¶ó °¡ Á¤ÇÏ ¸ é 2a > RT Ç×»ó ¼º ¸ ³ ÇØ¾ß ÇÕ´ Ï ´ Ù. ÇÏ ³ ª ¾¿ ´ ëÀÔÇغ ¸ ¸ é RT = 21 ÀÏ ¶§ »ï °¢Çü µÑ· ¹ ÀÇ ±æÀÌ ´  40 ÀÌ ¹ Ç· Î 40 – 21 = 19. ¿©±â¼ 19 Àº µÎ º ¯ ÀÇ ÇÕ(2a)ÀÌ ÁÒ, ±×· ±µ¥ 19 > 21(RT)¿¡ ¼º ¸ ³ ÇÏ Áö ¾ÊÀ¸ ¹ Ç· Î (A)°¡ Á¤´ äÀÔ´ Ï ´ Ù. . Á¤´ äÀº
(A)
8. In ∆ RST above, if the measure of
(A)
∠ R equals the measure of ∠T , then RT =
1 2
(B)
1
(C)
3 2
(D)
2
(E)
5 7
R ° ¢°ú T°¢ÀÌ °°´ Ù°í ÇßÀ¸ ´ Ï ±î ÀÌ °Í Àº ÀÌ µî º ¯»ï °¢ÇüÀÇ ¼º ÁúÀ» ¸ »Çß³ ׿ä . ÀÌ µî º ¯»ï °¢ÇüÀº ¾Æ· ¡ ¹ غ ¯ÀÌ °°°í µÎ º ¯ÀÇ ±æÀÌ °¡ °°ÁÒ. Áï 2x –1 = x + 1/2 ¿©±â¼- x = 3/2 . Á¤´ äÀº
(C)
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Note : Figure not drawn to scale. 9. In the figure above, if the sum of the perimeters of the three triangles is 37, what is the perimeter of pentagon ABCDE ? (A) 32 (B) 27 (C) 25 (D) 22 (E) 17 ÀÏ´ Ü AB=a BC=b CD=c DE=d EA=e¶ó °¡ Á¤ÇÏ ¸ é ¼¼ »ï °¢ÇüÀÇ µÑ· ¹ ´  (a+b+5) + (5+5+c) + (5+d+e) = 37, ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é a + b + c + d + e = 17ÀÔ´ Ï ´ Ù. µû¶ó¼ ÀÌ ´ Ù°¢ÇüÀÇ µÑ· ¹ ´  a + b + c + d + eÀÌ ¹ Ç· Î 17ÀÔ´ Ï ´ Ù. . Á¤´ äÀº
(E)
Note : Figure not drawn to scale.
10. The figure above shows the dimensions of a stepladder that stands on a floor. How high is the top of the ladder from the floor? (A)
4 ft
(B)
5 ft
(C)
6 ft
(D)
4 3 ft
(E) 2 15 ft
x 8ft
2ft
À§ÀÇ »ï °¢ÇüÀ» ÀÌ µî º ÐÇؼ x °ª À» ±¸ ÇÒ ¼ö ÀÖÁÒ. 8 2 . Á¤´ äÀº (E)
− 2 2 = (2 15 ) 2
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11. In the figure above, CE = 5 , What is the area of ∆ ABD ? (A) 4 (B) 9 (C) 16 (D) 20 (E) 56
BD = 8 , and the area of quadrilateral ABCD is 36.
1 2
ÀÌ ´ Ù°¢ÇüÀº µÎ °³ ÀÇ BCD¿Í ABD»ï °¢ÇüÀ¸ · Î ³ ª ´ ©¾î ÁöÁÒ. ÀÏ ´ Ü BCDÀÇ ¸ éÀûÀº 20(= (5 × 8) ) ÀÌ ÁÒ. µû¶ó¼ ³ ª ¸ ÓÁö »ï °¢ÇüÀÇ ¸ éÀûÀº Àüü »ç°¢ÇüÀÇ ¸ éÀû 36¿¡ ¼ 20À» »©¸ é 16ÀÌ ³ ׿ä. . Á¤´ äÀº
12.
(C)
In the figure above, If PQRS is a square and QT = TR , which of the following statements is NOT true? (A) PT = TS (B) x = y (C) u = v (D) r = y (E) The area of ∆ PQT is equal to the area of ∆ SRT .
Á¤»ç°¢ÇüÀÇ ÇÑ º ¯ÀÇ °¡ ¿î µ¥¸ ¦ ±âÁØÀ¸ · Î ³ ª ´ ©¾î º ¸ ¸ é 4°³ ÀÇ Á÷°¢»ï °¢ÇüÀ¸ · Î ÀÌ · ç¾î Á® ÀÖÁÒ. ³ × °³ ÀÇ Á÷°¢»ï °¢ÇüÀº ¸ ðµÎ ¶È ° °Àº °¢°ú º ¯ÀÇ Å©±â· Î ±¸¼º µÇ¾î ÀÖÁÒ. ÇÏ Áö¸ ¸ ÀÌ »ï °¢ÇüÀº ÀÌ µî º ¯»ï °¢ÇüÀÌ ¾Æ´ Ñ °Í Àº È®½ÇÇÏ ´ Ï ±î r = y ´  °ÅÁþÀÎ °Í ÀÌ Æ² ¸ ² ¾øÁÒ. . Á¤´ äÀº
(D)
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Note : Figure not drawn to scale. 13. In City R , streets run either east-west or north-south, as shown on the map above. Blocks along east-west streets are 400 feet long and blocks along north-south streets are 200 feet long. If the width of the streets is ignored, what is the straight-line distance, in feet, from X to Y ? (A) 200 5 (B) 1,000 (C) 1,200 (D) 400 10 (E) 1,600 ¿©±â¼ Æ÷ÀÎ Æ®´  ÇÑ blockÀº °¡ · Î 400 feet ¼¼· Î 200 feet ¶ó´Â Àǹ Ì Áö Àüü blocksÀÇ ±æÀÌ °¡ 400 feet 200 feet¶ó´  Àǹ Ì ´  ¾Æ´ Ï Áö¿ä. BlockÀÇ Àǹ Ì ¸ ¦ ¾î ¶»°Ô Çؼ®ÇØ¾ß ÇÏ´Â Áö° ¡ ÀÌ ¹ ®Á¦ ÀÇ ÇÔÁ¤ÀÌ ³ ׿ä . µû¶ó¼ x¿¡ ¼ y´  °¡ · Î 2 blocks ¼¼·Î 3 blocks ¸ ¸ Å ¶³ ¾î Á® ÀÖ³ ׿ä . ÀÌ °Í À» ÇÇŸ °í ¶ó½º °ø½ÄÀ» ÀÌ ¿ëÇؼ Á÷¼±°Å¸ ®¸ ¦ ±¸ Çغ ¸ ¸ é 800 2 + 6002 = 1000 2 . Á¤´ äÀº
(B)
14. If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side? I. 5 II. 8 III. 11 (A) II only (B) III only (C) I and II only (D) II and III only (E) I, II, and III »ï °¢ÇüÀÌ µÇ±â À§Çؼ µÎ º ¯ÀÇ ±æÀÌ ÀÇ ÇÕÀº ³ ª ¸ ÓÁö ÇÑ º ¯ÀÇ ±æÀÌ º ¸ ´ Ù Å®´ Ï ´ Ù. µû¶ó¼ , ¸ ¸ ¾à »ï °¢ÇüÀÇ µÎ º ¯ÀÇ ±æÀÌ °¡ 3, 8ÀÌ ¶ó¸é ³ ª ¸ ÓÁö ÇÑ º ¯ÀÇ ±æÀÌ ´  5¿Í (3°ú ´ õÇÏ ¸ é 8) 11ÀÌ(3°ú 8À» ´ õÇÏ ¸ é 11) µÉ ¼ö ¾ø½À´ Ï ´ Ù. ÿ
´ äÀº (A)ÀÔ´ Ï ´ Ù.
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15. The length of each side of a triangle is an even number. If no two of the sides are equal, what is the smallest perimeter the triangle coul d have? (A) 18 (B) 16 (C) 14 (D) 12 (E) 6
»ï °¢ÇüÀÌ µÇ±â À§Çؼ µÎ º ¯ÀÇ ±æÀÌ ÀÇ ÇÕÀº ³ ª ¸ ÓÁö ÇÑ º ¯ÀÇ ±æÀÌ º ¸ ´ Ù Å®´ Ï ´ Ù. µû¶ó¼ , º ¯ÀÇ ±æÀÌ °¡ ¸ ðµÎ ¦ ¼öÀÌ ¸ é¼ »ï °¢ÇüÀÌ µÇ±â À§ÇÑ º ¯ÀÇ ±æÀÌ ´ Â4, 6, 8ÀÔ´ Ï ´ Ù. ÿ
´ äÀº (A)ÀÔ´ Ï ´ Ù.
16. The lengths of two sides of a right triangle are
d d and . If one of these sides is the 3 4
hypotenuse, what is the length of the third side of the triangle?
5d 12 d (B) 7 d (C) 5 d (D) 12 d 7 (E) 12 (A)
d d d ¿Í Áß °¡ º øº ¯ÀÌ ¶ó´  °Í À» ¾Ë ¼ö 3 4 3
Á÷°¢»ï °¢Çü¿¡ ¼ º øº ¯Àº ±æÀÌ °¡ °¡ Àå ±ä º ¯ÀÌ ¹ Ç· Î
ÀÖ½À´ Ï ´ Ù. µû¶ó¼ ÇÇŸ °í ¶ó½º ÀÇ Á¤ÀǸ ¦ »ç¿ëÇÏ ¿© ´ Ù¸ ¥ ÇÑ º ¯ÀÇ ±æÀÌ ¸ ¦ ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. 2
d 3 ÿ
2
d = + x 2 4
´ äÀº (E)ÀÔ´ Ï ´ Ù.
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17. If each side of ∆ ACD above has length 3 and if AB has length 1, what is the area of region BCDE ? (A)
9 4
(B)
7 3 4
(C)
9 3 4
(D)
7 3 2
(E)
6+ 3
∆ ACD ´  ÇÑ º ¯ÀÇ ±æÀÌ °¡
3ÀÎ Á¤»ï °¢ÇüÀÔ´ Ï ´ Ù. Á÷»ï °¢ÇüÀÇ º ¯ÀÇ º ñÀ² ¿¡ µû¶ó AB ÀÇ ±æÀÌ °¡ 1À̸ é BE ÀÇ ±æÀÌ °¡ 3 ÀÌ ¶ó´ Â°Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. µû¶ó¼ BCDE ÀÇ ¸ éÀûÀº ∆ ACD ÀÇ ¸ éÀû¿¡ ¼ ∆ ABE ÀÇ ¸ éÀûÀ» »©ÁÖ¸ é ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù.
1 1 = 7 3 × 3 × 3 3 − × × 1 3 2 2 2 4
( ∆ACD ÀÇ ³ ôÀÌ ¶ÇÇÑ Á÷»ï °¢ÇüÀÇ º ¯ÀÇ º ñÀ² ¿¡ µû¶ó ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù.) ÿ
´ äÀº (B)ÀÔ´ Ï ´ Ù.
18. In (A)
∆ PQS above, if PQ = 3 and PS = 4 , then PR = 9 4
(B)
12 5
(C)
16 5
(D)
15 4
(E)
20 3
∆ PQR °ú ∆ PQS µÎ
½ÖÀÇ ´ ëÀÀÇÏ ´  °¢ÀÇ Å©±â° ¡ °°À¸ ¹ Ç· Î ´ àÀ½ ² ÃÀÔ´ Ï ´ Ù. µû¶ó¼ ´ ÙÀ½ÀÇ º ñ· ʽÄÀ» ° è»êÇÏ ¸ é PR ÀÇ ±æÀÌ ¸ ¦ ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù.
3:5 = x : 4 ÿ
´ äÀº (B)ÀÔ´ Ï ´ Ù.
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- ÁÂ Set-10 GRE Math °
19. In the figure above, square region ABCE and triangular region ACD each have area 36. What is the perimeter of triangle ACD ? (A) 24 (B) 12 + 12 2 (C) 36 (D) 18 + 18 2 (E) 36 2 Á¤»ç°¢Çü ABCE ÀÇ ¸ éÀûÀÌ 36ÀÌ ¹ Ç· Î ÇÑ º ¯ÀÇ ±æÀÌ ´  6ÀÌ ¶ó´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. »ï °¢Çü ACD ÀÇ ¸ éÀûµµ 36ÀÌ ¶ó°í Ç߱⠶§¹ ®¿¡ ´ ÙÀ½ÀÇ ½ÄÀ¸ · Î AD ÀÇ ±æÀÌ ¸ ¦ ¾Ë ¼ö ÀÖÀ¸ ¸ ç ÇÇŸ °í ¶ó½º ÀÇ Á¤¸ ®¿¡ µû¶ó AC ÀÇ ±æÀÌ ¸ ¦ ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù.(¶Ç´Â Á÷»ï °¢ÇüÀÇ º ¯ÀÇ º ñ¸ ¦ ÀÌ ¿ëÇÏ ¿© ¾Ë ¼ö µµ ÀÖ½À´ Ï ´ Ù ¡ æ1 :1 : 2 )
1 × 6 × x = 36 2 ÿ
´ äÀº (B)ÀÔ´ Ï ´ Ù.
Note : Figure not drawn to scale. 20. The figure above shows the relative positions of a projection lens L , a film F , and a screen S . The film is 6 inches from the lens and is parallel to the screen. How many feet from the screen is the lens if a 0.3 -inch figure on F projects a 6-foot image on S ? (1 foot = 12 inches) (A) 0.3 (B) 10 (C) 12 (D) 100 (E) 120 ´ ëÀÀÇÏ ´  °¢ÀÇ Å©±â°¡ ¸ðµÎ °°À¸ ¹ Ç· Î µÎ µµÇüÀº ´ àÀ½ ² ÃÀÔ´ Ï ´ Ù. µû¶ó¼ ´ ÙÀ½ÀÇ º ñ· ʽÄÀ» ¸ ¸ Á· ÇÕ´ Ï ´ Ù.
0.3 : 72(= 6 feet × 12inches) = 6 : x ÿ
´ äÀº (E)ÀÔ´ Ï ´ Ù.
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21. In the figure above, if A1 , A2 , and A3 are the areas of the respective semicircular regions,
A1 + A2 ? A3 3 (B) (C) 2
what is the value of (A)
¹ Ý¿ø
1
A1 ,
π
2
A2 , A3 ÀÇ ¹ ÝÁö¸ §À» ° ¢°¢
(D) 2
(E)
3π 2
a1 , a2 , a 3 ¶ó ÇÏ ¸ é
¹ Ý¿øÀÇ
¸ éÀûÀº
(a1 )2 π (a2 )2 π (a3 )2 π 2 2 (a3 )2 ℵ™×∉×∧ ÀÔ´ Ï ´ Ù , , . ÇÇŸ °í ¶ó½º ÀÇ Á¤¸ ®¿¡ ÀÇÇÏ ¸ é (a1 ) + ( a2 ) = . 2 2 2 2
A1 + A2 (a1 )2 π (a 2 )2 π (a 3 ) = + A3 2 2 2 ÿ
π
´ äÀº (A)ÀÔ´ Ï ´ Ù.
D R Y LAND 22. A cable is bei ng laid from one side of a swamp, at point A , to the other side, at point D . If laying cable costs $500 per mile on dry land and $800 per mile in the swamp, how much is saved by laying the cable on the ABD route rather than the ABCD route? (A) $700 (B) $1,000 (C) $1,500 (D) $3,200 (E) $4,700 ÇÇŸ °í ¶ó½º ÀÇ Á¤ÀÇ¿¡ µû¶ó BD ÀÇ °Å¸ ®°¡ 5 milesÀÌ ¶ó´  °Í À» ¾Ë ¼ö Àֱ⠶§¹ ®¿¡ ABD ÀÇ °Å¸ ®°¡ 15 milesÀÌ ¶ó´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù. ABCD ÀÇ °Å¸ ®´  17milesÀÔ´ Ï ´ Ù.10 milesÀÇ °Å ¸ ®´  °øÅëÀÌ ±â ¶§¹®¿¡ ABCD ÀÇ °Å¸ ®¿Í ABD °Å¸ ®´  º ñ±³ ÇÒ ¶§ swampÁö¿ª ÀÇ 1mile° ú dry landÀÇ 3miles¸ ¸ º ñ±³ ÇÏ ¸ é µË´ Ï ´ Ù. ÿ
´ äÀº (A)ÀÔ´ Ï ´ Ù.
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- ÁÂ Set-10 GRE Math °
23. A ladder that is 13 feet long is placed against a vertical wall so that the top of the ladder is 5 feet below the top of the wall. If the bottom of the ladder rests on level ground and is 5 feet out from the base of the wall, what is the height of the wall, in feet? (A) 12 (B) 13 (C) 17 (D) 19 (E) 23 Áö¸ é° ú ¼öÁ÷À» ÀÌ · ç´ Â º®¿¡ ±æÀÌ 13feetÀÇ »ç´ Ù¸ ®°¡ ±â´ ë¾î Á® ÀÖ´ Ù°í ÇÕ´ Ï ´ Ù. »ç´ Ù¸ ®ÀÇ »ó´Ü º Î º ÐÀº º ®ÀÇ Á¦ ÀÏ ³ ôÀº º Î º к ¸ ´ Ù 5 feet ¾Æ· ¡ ÂÊ¿¡ À§Ä¡ ÇØÀÖÀ¸ ¸ ç »ç´ Ù¸ ®ÀÇ ÇÏ ´ ܺ Î º ÐÀº º ®À¸ · Î º Î ÅÍ 5feet ¶³ ¾î Á® ÀÖÀ» ¶§ º ®ÀÇ ³ ôÀÌ ¸ ¦ ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. ÇÇŸ °í ¶ó½º ÀÇ Á¤¸®¿¡ µû¶ó »ç´ Ù¸ ®ÀÇ »ó´Üº Î º ÐÀÌ Áö¸ éÀ¸ · Î º Î ÅÍ 12feet°¡ ¶³ ¾î Á® ÀÖ´ Ù´  °Í À» ¾Ë ¼ö ÀÖ½À´ Ï ´ Ù.
(13)2 − (5)2 = (12) 2 ´ äÀº (C)ÀÔ´ Ï ´ Ù.
ÿ
24. A ladder 25 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip? (A) 4 (B) 5 (C) 8 (D) 9 (E) 15 Áö¸ é° ú ¼öÁ÷À» ÀÌ · ç´ Â º®¿¡ ±æÀÌ 25feetÀÇ »ç´ Ù¸ ®°¡ ±â´ ë¾î Á® ÀÖ´ Ù°í ÇÕ´ Ï ´ Ù. »ç´ Ù¸ ®ÀÇ ÇÏ ´Ü º Î º ÐÀÌ º ®À¸ · Î º Î ÅÍ 7 feet° ¡ ¶³ ¾î Á® ÀÖ½À´ Ï ´ Ù. »ç´ Ù¸ ®ÀÇ »ó´Ü º Î º ÐÀÌ 4feet ¾Æ· ¡ ÂÊÀ¸ · Î Èê· ¯ ³ »· ÈÀ» ¶§ »ç´ Ù¸ ®ÀÇ ÇÏ ´ ܺ Î º ÐÀÌ ¾ó¸ ¶³ ª ¹ и ®´ ÂÁö ¹ °¾î º ¸ °í ÀÖ½À´ Ï ´ Ù. »ç´ Ù¸ ®ÀÇ ÇÏ ´ ܺ Î º ÐÀÌ º ®À¸ · Î º Î ÅÍ 7feet¶³ ¾î Á® ÀÖ¾úÀ» ¶§ »ó´Ü º Î º ÐÀº Áö¸ éÀ¸ · Î º Î ÅÍ 24feet 2
( (25 )
− (7)2 = (24)2 )¶³ ¾î Á® ÀÖ½À´ Ï ´ Ù.
»ç´ Ù¸ ®ÀÇ »ó´ ܺ Î º ÐÀÌ 4feet ¾Æ· ¡ ÂÊÀ¸ · Î Èê· ¯ ³ »¸ ®
¸ é »ç´ Ù¸ ®ÀÇ »ó´ ܺ Î º ÐÀº Áö¸éÀ¸ · Î º Î ÅÍ 20feet°¡ ¶³ ¾î Á® ÀÖ½À´ Ï ´ Ù. µû¶ó¼ ÇÏ ´ Ü º Î º ÐÀº º ®À¸ 2
· Î º Î ÅÍ 15feet ¶³ ¾î Áö°Ô µË´ Ï ´ Ù. (25) ÿ
− (20)2 = (15)2
´ äÀº (C)ÀÔ´ Ï ´ Ù.
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- ÁÂ Set-10 GRE Math °
25. A rope hangs from the top of a vertical pole, leaving 4 feet of slack on the floor. When fully extended, the rope touches the floor at a point 12 feet away from the pole. How many tall is the pole? (A) 4 (B) 12 (C) 13 (D) 16 (E) 20 ¼öÁ÷À¸ · Î ¼¼¿öÁ® ÀÖ´  Àå´ ëÀÇ ² À´ ë±â¿¡ ´ Þ·Á ÀÖ´  ¹ åÁÙÀ» ¹ Ù´ Ú¿¡ ´ êµµ· Ï Àâ¾Æ ´ ç±â¸ é Àå´ ë · Î º Î ÅÍ 12feet ¶³ ¾î Áø °÷¿¡ ¹ åÁÙÀÇ ³ ¡ º Î º ÐÀÌ ´ ê° í Àâ¾Æ ´ ç±âÁö ¾ÊÀ» ¶§´  ¹ Ù´ Ú¿¡ 4feetÀÇ ¹ åÁÙÀÌ ³ ² ´ ´ Ù°í ÇÕ´ Ï ´ Ù. À̸¦ ±×¸ ² À¸ · Î ±×· Áº ¸ ¸ é ´ ÙÀ½°ú °°À¸ ¸ ç ÇÇŸ °í ¶ó½º ÀÇ Á¤ÀǸ ¦ »ç¿ë ÇÏ ¿© ¸ · ´ ë±âÀÇ ±æÀÌ ¸ ¦ ±¸ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù.
¹ åÁÙ x + 4
¸·´ë±â x 12 feet
x 2 + 12 2 = ( x + 4 )2 ⇒ x = 16 ÿ
´ äÀº (D)ÀÔ´ Ï ´ Ù.
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Categor y 11 Quadri later al & Other Polygons 1.
What is the area of a square with perimeter P ? (A)
16 P 2
(B)
4 P
(C) (D) (E)
answer
P 2 4 P 16 P 2 16
2. If the area of a square region having sides of length 6 centimeters is equal to the area of a
answer
rectangular region having width 2.5 centimeters, then the length of the rectangle, in centimeters, is (A)
8.5
(B)
9.5
(C)
9.6
(D)
10.5
(E)
14.4
3. In the figure above, if PQRS is a parallelogram, then y − x (A) 30
(B) 35
(C) 40
(D) 70
=
answer
(E) 100
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4. A rectangular circuit board is designed to have width area (A) (B) (C) (D) (E)
w inches, perimeter p inches, and
k square inches. Which of the following equations must be true? w 2 + pw + k = 0 w 2 − pw + 2k = 0 2 w 2 + pw + 2k = 0 2 w 2 − pw − 2k = 0 2 w 2 − pw + 2 k = 0
5. The size of a television screen is given as the length of the screen’ s diagonal. If the screens
answer
answer
were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen? (A)
2
(B)
4
(C)
16
(D)
38
(E)
40
6. If the figure above is a parallelogram, what is the value of y in terms of x ? answer
x 2 (B) 2 x (C) 90 − x (A)
x 2 180 − x (E) 2 (D) 180 −
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Note : Not drawn to scale. 7. The figure above represents a square plot measuring x feet on a side. The plot consists of a
answer
rectangular garden, 48 square feet in area, surrounded by a walk that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of x ? (A)
8
(B)
10
(C)
12
(D)
16
(E)
18
8. What is the area of the region enclosed by the figure above? (A)
116
(B)
144
(C)
176
(D)
179
(E)
284
9. The sum of the interior angles of any polygon with n sides is 180(n − 2) degrees. If the sum of the interior angles of polygon P is three times the sum of the interior angles of quadrilateral Q , how many sides does P have? (A)
6
(B)
8
(C)
10
(D)
12
(E)
14
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answer
answer
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10. The perimeter of a rectangular flower bed is 100 feet. What is the area of the flower bed, in answer
square feet, if its length is 10 feet greater than its width? (A)
400
(B)
500
(C)
600
(D)
900
(E)
2,400
11. In the figure above, the shaded rectangular portion of the square region has perimeter 20.
answer
What is the perimeter of the unshaded portion? (A)
28
(B)
34
(C)
36
(D)
40
(E)
68
12. In the figure above, x (A)
75
(B)
90
(C)
100
(D)
105
(E)
150
=
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answer
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13. A square picture frame has an outer perimeter of 36 inches and is 1 inch wide on all sides.
answer
What is the inner perimeter of the frame, in inches? (A)
27
(B)
27
(C)
28
(D)
31
(E)
32
1 2 1 2
14. The figure shown above has area A . If the length of each side were doubled, what would then be the area in terms of A ? (A)
2 A
(B)
4 A
(C)
6 A
(D)
8 A
(E)
20 A
15. The area of a rectangular rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet? (A)
600
(B)
525
(C)
375
(D)
300
(E)
225
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answer
answer
– S e t 1 1
16. The figure above represents a window, with the shaded regions representing the openings for
answer
the glass. If all line segments segment s in the figure are either horizontal or vertical ad the openings are all the same size, what are the dimensions, in inches, of each opening? (1 foot = 12 inches) (A) (A)
12.0 by 18.0
(B)
10.5 by 16.5
(C)
9.0 by 15.0
(D)
8.0 by 10.0
(E)
7.5 by 13.5
Q
R
P
S
17. The figure above shows a rectangular parcel of undeveloped land partitioned into four regions, the area of square region Q is x 2 , the area of P , Q , R , and S . In square meters, the rectangular region R is 5 x , and the area of rectangular region P is 4 x . What is the area, in square meters, of rectangular region
S ?
(A) x 2 − x (B) x 2
+ 9 x
(C) 20 x − x 2 (D) 9 (E) 20
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answer
– S e t 1 1
18. A rectangular-shaped rectangular-shaped carpet remnant that measures
x feet by y feet is priced at $50. answer
What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard) (A) (B) (C) (D) (E)
50 xy 450 xy xy 9 xy 50 450 xy
19. A rectangular circuit board is designed to have width
w inches, perimeter p inches, and
answer
following equations must be true? true? k square inches. Which of the following (A) w 2 + pw + k = 0 (B) w 2 − pw + 2k = 0 (C) 2 w 2 + pw + 2k = 0 (D) 2 w 2 − pw − 2k = 0 (E) 2 w 2 − pw + 2 k = 0 area
20. The size of a television screen screen is given as the length of the screen’ s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen? (A)
2
(B)
4
(C)
16
(D)
38
(E)
40
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answer
– S e t 1 1
21. The dimensions of a rectangular floor are 16 feet by 20 feet. When a rectangular rug is
answer
placed on the floor, a strip of floor 3 feet wide is exposed on all sides. What are the dimensions of the rug, in fee? (A) (A)
10 by 14
(B)
10 by 17
(C)
13 by 14
(D)
13 by 17
(E)
14 by 16
22. A square board that has an area of 25 square inches is to be cut into pieces, pieces, each of which is a
answer
square with sides of length 1, 2, or 3 inches. What is the least number of such square pieces into which the board can be cut? (A)
5
(B)
6
(C)
7
(D)
8
(E)
9
23. In rectangle QRST above, RU = SU . What is the ratio of the perimeter of
∆QUT
answer
the perimeter of rectangle QRST ? (A)
3 8
(B)
1 2
to
(C)
5 8
(D)
3 4
(E)
9 11
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24. The area of each of the 16 square regions in the figure above is T . What is the area area of the shaded region? (A) (B) (C) (D) (E)
answer
13T 13T 3 5T 16T 16T 3 11T 11T 2 7T
25. Rectangular region PQRS shown shown above is partitioned into ten identical smaller rectangular regions, each of which has width x . What is the perimeter of PQRS in in terms of x ? (A) 15 x (B) 25 x (C) 30 x (D) 50 x (E) It cannot be determined from the information given.
STOP
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answer
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¼öÇÐÇؼ³
Catego Cate gorr y 11 Quadri late laterr al & Othe Otherr Polygons Polygons
1. What is the area of a square with perimeter P ? (A)
16 P 16 P 2
(B)
4 P
(C) (D) (E)
P 2 4 P 16 P 2 16
p p 2 p 2 Á¤» ¤»çç ° ¢Ç ¢ÇüÀ üÀÇ Ç µÑ· ¹ ° ¡ PÀ PÀÌÌ ¸ é ÇÑ ÇÑ º ¯ÀÇ ±æÀÌ ´  , µû¶ó¼ ¸ é ÀûÀ ûÀºº ( ) = 4 4 16 . Á¤´ Á¤´ äÀ äÀºº
(E)
2. If the area of a square region having sides of length 6 centimeters is equal equal to the area of a rectangular region having width 2.5 centimeters, then the length of the rectangle, in centimeters, is (A)
8.5
(B)
9.5
(C)
9.6
(D)
10.5
(E)
14.4
ÇÑ º ¯À ¯ÀÌÌ 6À 6ÀÎÎ Á¤»ç°¢Ç ¤»ç°¢ÇüÀ üÀÌ ÇÑ º ¯À ¯ÀÌÌ 2.5 centimeters ÀÎ Á÷»ç° »ç°¢Ç ¢Çü°ú ¸ é ÀûÀ ûÀÌÌ °° °°À À» ¶§, ÀÌ Á÷» ÷»ç° ç° ¢Çü ÀÇ ´ Ù¸ ¥ ÇÑ º ¯ÀÇ ±æ ±æÀ ÀÌ ¸ ¦ ±¸ ±¸Ç ÇÏ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. 36 = 2.5 × P ⇒ P = 14.4 .
Á¤´ ä Àº (E)
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3. In the figure above, if PQRS is a parallelogram, then y − x (A) 30
(B) 35
(C) 40
(D) 70
=
(E) 100
ÆòÇà»çº ¯ÇüÀÇ ¼º Áú Áß¿¡ PQ ¿Í RS´  ÆòÇàÇÏ ¸ ç ±æÀÌ µµ °° ½À´ Ï ´ Ù. 2y¿Í x´  ¼ · Î º ¸ °¢(ÇÕÃļ 180µµ)ÀÇ ° ü°èÀÌ °í 2y = 140, x = 40ÀÌ ÁÒ. ´ ٽà Á¤¸ ®ÇÏ ¸ é y = 70ÀÌ ³ ׿ä. y − x . Á¤´ äÀº
=
30
(A)
A
B
EEE C
D
l
AB || CD, AC || BD
l
AB = CD, AC = BD
l
∠ A = ∠ D, ∠ B = ∠ C
l
AE = ED, CE = EB
l
∠ A + ∠ B = 180, ∠ B + ∠ D = 180, ∠ D + ∠ C = 180, ∠ C + ∠ A = 180
4. A rectangular circuit board is designed to have width area (A) (B) (C) (D) (E)
w inches, perimeter p inches, and
k square inches. Which of the following equations must be true? w 2 + pw + k = 0 w 2 − pw + 2k = 0 2 w2 + pw + 2k = 0 2 w2 − pw − 2k = 0 2 w2 − pw + 2 k = 0
¸ éÀû = length × width(=w) = k , kÁ÷»ç°¢ÇüÀÇ µÑ· ¹ = 2length + 2w jÁ÷»ç°¢ÇüÀÇ lengthÀ» L¶ ó °¡ Á¤ÇÏ ¸ é L × w = k, 2L + 2w = P. ÀÌ ½ÄÀ» L¿ ¡ ÀÇÇØ Á¤¸ ®ÇÏ ¸ é L = 2 w2
− pw + 2 k =
. Á¤´ äÀº
0
(E)
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5. The size of a television screen is given as the length of the screen’ s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen? (A)
2
(B)
4
(C)
16
(D)
38
(E)
40
Television screenÀÇ Å©±â´  Á¤»ç° ¢ÇüÀÇ ´ ë°¢¼±ÀÇ ±æÀÌ · Î Á¤ÇØÁø´ Ù°í ÇÒ ¶§, ´ ë°¢¼±ÀÇ ±æÀÌ °¡ 21 inchÀÎ Á¤»ç° ¢ÇüÀÇ ¸éÀûÀÌ ´ ë° ¢¼±ÀÇ ±æÀÌ °¡ 19 inchÀÎ Á¤»ç°¢Çüº ¸ ´ Ù ¸ éÀûÀÌ ¾ó¸ ¶³ ª
Å©³ Ä
¸ ¦ ¹ ¯´  ¹ ®Á¦ ³ ׿ä. ÀÏ ´ Ü 21ÀÎ Ä¡ ÀÇ ÇÑ º ¯ÀÇ ±æÀÌ ¸ ¦ x¶ó ÇÏ ¸ é ¸ éÀû( x 2 )Àº : 2 x 2 = 212 ⇒ x 2 = 441 2
19ÀÎ Ä¡ ÀÇ ÇÑ º ¯ÀÇ ±æÀÌ ¸ ¦ y ¶ó ÇÏ ¸ é ¸ éÀû( y 2 )Àº : 2 y 2 = 19 2 ⇒ y 2 = 361 2
µÎ Á¤»çÇÐÇüÀÇ ¸éÀûÀÇ Â÷ÀÌ = 441 − 361 = 40 2 2 . Á¤´ äÀº
(E)
6. If the figure above is a parallelogram, what is the value of y in terms of x ?
x 2 (B) 2 x (C) 90 − x (A)
x 2 180 − x (E) 2 (D) 180 −
ÆòÇà»çº ¯ÇüÀÇ ¼º Áú Áß¿¡ “¸ °¢Àº °°´ Ù”¶ó´  °Í ÀÌ ±â¾ï ³ ª ½ÃÁÒ. Áï x = 2yÀÌ ÁÒ. ÀÌ °Í À» ´Ù½Ã y¿¡ ÀÇÇØ Á¤¸ ®ÇÏ ¸ é y = . Á¤´ äÀº
x 2
(A)
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Note : Not drawn to scale. 7. The figure above represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walk that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of x ? (A)
8
(B)
10
(C)
12
(D)
16
(E)
18
ÇÑ Á÷»ç°¢ÇüÀÇ ÀÛÀº ¶¥(plot) ÀÇ ¸ éÀûÀº 48 square feet ÀÌ ¸ ç, ±× ÀÛÀº ¶¥Àº ÆøÀÌ 3 feet ÀÌ°í ¶Ç ´ Ù¸ ¥ ÂÊÀº 2 feet ÀÎ »êÃ¥·Î °¡ µÑ· ¯½Î °í ÀÖÀ» ¶§ x ° ª À» ±¸ ÇÏ ¶ó´  ¹ ®Á¦ ³ ׿ä . ÀÏ ´ Ü ÀÛÀ» ¶¥ ÀÇ °¡ · Î a ¼¼· Î ¸ ¦ b ¶ó ÇÏ ¸ é ab = 48 . ±× ´ ÙÀ½Àº ¹ Ù±ùÂÊÀº Á¤»ç° ¢ÇüÀ¸ · Î °¡ · Î · Î 6 , ¼¼· Î · Î 4 ¸ ¸ Å Áõ°¡ ÇßÀ¸ ¸ ç Á¤»ç° ¢ÇüÀÌ ´ Ï ±î º ¯ÀÇ ±æÀÌ °¡ °°ÁÒ. ´ ٽà ¸ »ÇÏ ¸ é a + 6 = b + 4 ⇒ a b = 48 ka ja ×
b= 2
b = 2 j°úkÀ» ¿¬¸³ ¹ æÁ¤½ÄÀ¸ · Î Ç®¸ é a = 6 , b = 8
´Ù½ à a ³ ª b Áß¿¡ ÇÏ ³ ª ¸ ¦ a + 6 À̳ ªb + 4 ¿¡ ´ ëÀÔÇÏ ¸ é x ° ªÀ» ±¸ ÇÒ ¼ö ÀÖÁÒ. . Á¤´ äÀº
(C)
<¿©· ¯ °¡ Áö »ç°¢Çü> Quadrilaterals(»ç°¢Çü) > Trapezoid(»ç´ Ù¸ ®² Ã) > Parallelogram( ÆòÇà»çº ¯Çü) > Rectangle(Á÷»ç°¢Çü)
>
Square(Á¤»ç°¢Çü)
Rhombus(¸ ¶¸ §¸ ð) Á÷»ç°¢Çü : µÎ ´ ë° ¢¼±ÀÇ ±æÀÌ ° ¡ ° ° ° í , ¼- · Î ´ Ù¸ ¥ °ÍÀ» ÀÌ µî º ÐÇÑ´ Ù. ¸ ¶¸ §¸ ð : ³ × º ¯ÀÇ ±æÀÌ ° ¡ ¸ ðµÎ °°Àº »ç°¢Çü Á¤»ç°¢Çü : µÎ ´ ë° ¢¼±ÀÇ ±æÀÌ ° ¡ °° ´ Ù
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8. What is the area of the region enclosed by the figure above? (A)
116
. Á¤´ äÀº
(B)
144
(C)
176
(D)
179
(E)
284
(C)
9. The sum of the interior angles of any polygon with n sides is 180(n − 2) degrees. If the sum of the interior angles of polygon P is three times the sum of the interior angles of quadrilateral Q , how many sides does P have? (A)
6
(B)
8
(C)
10
(D)
12
(E)
14
¹ ®Á¦ ¿¡ ¼ 180(n − 2) ´  ÇÑ »ç°¢ÇüÀÇ ³ »° ¢ÀÇ ÇÕÀÇ 3¹ è¶ ó ÇßÀ¸ ´ Ï
180(n − 2) = 3(360) e n = 8 . Á¤´ äÀº
(B)
10. The perimeter of a rectangular flower bed is 100 feet. What is the area of the flower bed, in square feet, if its length is 10 feet greater than its width? (A)
400
(B)
500
(C)
600
(D)
900
(E)
2,400
È ´ ÜÀÇ length = L, width = W¶ó °¡ Á¤ÇÏ ¸ é µÑ· ¹ ´ Â2L + 2W = 100feet. ÀÌ ¹ ø¿¡ ´  L = W + 10ÀÇ Á¶°ÇÀ» ÁÖ¾úÁÒ. ÀÌ °Í À» À§ÀÇ ½Ä2L + 2W = 100feet¿¡ ´ ëÀÔÇÏ ¸ é W = 20, L = 30. ´ 翬È÷ ¸ éÀûÀº 600ÀÌ ³ ׿ä. . Á¤´ äÀº
(C)
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11. In the figure above, the shaded rectangular portion of the square region has perimeter 20. What is the perimeter of the unshaded portion? (A)
28
(B)
34
(C)
36
(D)
40
(E)
68
Á¤»ç°¢Çü¿¡ ¼ shaded º Î º ÐÀÇ ³ ôÀÌ ´  2ÀÌ °í µÑ· ¹ °¡ 20ÀÏ ¶§ ¹ غ ¯Àº 8 °ª ÀÌ ³ ª ¿ÀÁÒ. ¹ غ ¯ÀÌ 8 ÀÌ ¶ó´  ¸ »Àº ÀÌ µµÇüÀÌ Á¤»ç°¢ÇüÀÌ ±â ¶§¹ ®¿¡ ´ Ù¸ ¥ º ¯ÀÇ ±æÀÌ µµ 8ÀÌ °í
unshaded º Î º ÐÀÇ ³ ô
ÀÌ ´  8 − 2 = 6. µû¶ó¼ unshadedÀÇ µÑ· ¹ ´ Â8+ 8+ 6+ 6 = 28 . Á¤´ äÀº
(A)
12. In the figure above, x (A)
75
(B)
90
(C)
100
(D)
105
(E)
150
=
»ç´ Ù¸ ®² ÃÀº µÎ °³ ÀÇ Á÷°¢»ï °¢Çü°ú ÇÏ ³ ª ÀÇ Á÷»ç° ¢ÇüÀ¸ · Î ³ ª ´ ¼ö ÀÖÁÒ. ÀÌ »ï °¢Çü¿¡ ¼ µÎ º ¯ ÀÇ ±æÀÌ ´  50° ú 40ÀÌ ¹ Ç· Î ³ ª ¸ ÓÁö ÇÑ º ¯Àº 50 2 x = 30 + 45 + 30 = 105 . Á¤´ äÀº
= 40
2
+
a 2 . ÀÌ ½ÄÀ» Á¤¸ ®ÇÏ ¸ é a = 30.
(D)
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13. A square picture frame has an outer perimeter of 36 inches and is 1 inch wide on all sides. What is the inner perimeter of the frame, in inches? (A)
27
1 27 2
(B)
(D) 31
(C) 28
1 2
(E) 32
9
9
1
7 7
Inner frameÀÇ µÑ· ¹ ±æÀÌ ´  4×7 = 28 . Á¤´ äÀº
(C)
14. The figure shown above has area A . If the length of each side were doubled, what would then be the area in terms of A ? (A) 2 A
(B) 4 A
(C) 6 A
(D) 8 A
(E) 20 A
À§ÀÇ »ç°¢ÇüÀº ¾Æ· ¡ ¿Í °°ÀÌ ³ ª ´ ¼ö ÀÖ°í ¸ éÀûÀº cd + ab = A °¡ µË´ Ï ´ Ù. ³ ª ´ « ÈÄ¿¡ °¢ º ¯ÀÇ ×2c = 4dc° ×2b =4ab° ¡ µÇ°í 2a ¡ µÇ¹ Ç· Πó À½ ¸ éÀû A¿¡ 4 ±æÀÌ °¡ 2¹ è· Î Áõ°¡ ÇÏ ¹ Ç· Î ¸ éÀûÀº 2d
¹ è° ¡ Áõ°¡ Çß½À´ Ï ´ Ù. d
+ c
a b
c ÿ Á¤´ äÀº
(B)
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15. The area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet? (A)
600
(B)
525
(C)
375
(D)
300
(E)
225
Áõ°¡ ÇÏ ±â Àü Á¤¿øÀÇ area(¸ éÀû)À» A, length(¼¼· Î )À» L,±×¸ ®°í width(° ¡ · Î )À» W¶ó ° ¡ Á¤ÇÏ ¸ é: j (L
+ 7.5)(W) = A + 150,
k
L× ( W + 5) = A + 150
W = A¿Í ½ Å¿¡ A¸ ¦ ´ ëÀÔÇؼ Ç®¸ é L = 20, W=30À» À§ÀÇ ½Ä¿¡ ¼ L× µ¿ÀÏ ÇÏ ¹ Ç· Î L× W ´ë ±¸ÇÒ ¼ö
ÀÖ°í ¸ éÀûÀº 600ÀÌ µË´ Ï ´ Ù. ÿ Á¤´ äÀº
(A)
16. The figure above represents a window, with the shaded regions representing the openings for the glass. If all line segments in the figure are either horizontal or vertical ad the openings are all the same size, what are the dimensions, in inches, of each opening? (1 foot = 12 inches) (A)
12.0 by 18.0
(B)
10.5 by 16.5
(C)
9.0 by 15.0
(D)
8.0 by 10.0
(E)
7.5 by 13.5
ÀÏ´ Ü ¼¼· Î º Î ÅÍ °è»êÇÏ ¸ é 3ft = 36 inches°¡ µÇ°í 36 inches − (3+3+3) = 27 inchesÀ» 2· Î ³ ª ´ ©¸ é 13.5 inches°¡ ³ ª ¿À³ ׿ä. ¹ ®Á¦ Áß¿¡ ¼ 13.5°¡ ÀÖ´  °Í Àº (E) »ÓÀÌ ¹ Ç· Î Á¤´ ä! À¯¸ ®Ã¢ÀÇ °¡ · Î ÀÇ ±æÀÌ µµ À§¿Í µ¿ÀÏ ÇÑ ¹ æ¹ ýÀ¸ · Î Ç®¸ é µË´ Ï ´ Ù. ÿ Á¤´ äÀº
(E)
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Q
R
P
S
17. The figure above shows a rectangular parcel of undeveloped land partitioned into four regions,
P , Q , R , and S . In square meters, the area of square region Q is x 2 , the area of rectangular region R is 5 x , and the area of rectangular region P is 4 x . What is the area, in square meters, of rectangular region
S ?
(A) x 2 − x (B) x 2
+ 9 x
(C) 20 x − x 2 (D) 9 (E) 20
S ÀÇ ¸ éÀûÀ» ±¸ ÇÏ · Á¸ é °¡ · Î ¿Í ¼¼· Î ÀÇ ±æÀÌ ¸ ¦ ¾Ë¾Æ¾ß ÇÕ´ Ï ´ Ù. ±×· ±µ¥ S ÀÇ ° ¡ · Î ´  R °ú °° °í ¼¼· Î ´  P ¿Í °°½À´ Ï ´ Ù.
5 x ÀÌ ¹ Ç· ΰ ¡ · Î ´  5 °¡ µÇÁÒ. µ¿ÀÏ ÇÑ ¹ æ¹ ýÀ¸ · Î P ÀÇ ¼¼· Î ÀÇ ±æÀÌ ´  4° ¡ µË´ Ï ´ Ù. µû¶ó¼ S ÀÇ ¸ éÀûÀº 20. ÀÏ ´ Ü Q ÀÇ ÇÑ º ¯ÀÇ ±æÀÌ ´  x ÀÌ ¹ Ç· Î R ÀÇ ¼¼· Î µµ x ÀÌ °í R ÀÇ ¸ éÀûÀÌ
ÿ Á¤´ äÀº
(E)
18. A rectangular-shaped carpet remnant that measures
x feet by y feet is priced at $50.
What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard) (A)
50 xy
x × yfeet = 50 dollars 1 square yard =
ÿ Á¤´ äÀº
(B)
⇒ 1
450 xy
square feet =
(C)
xy 9
(D)
xy 50
(E)
450 xy
1 square yardÀ» ¿ÞÂÊ¿¡ ´ ëÀÔÇÏ ¸ é 9
450 xy
(E)
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19. A rectangular circuit board is designed to have width area (A) (B) (C) (D) (E)
w inches, perimeter p inches, and
k square inches. Which of the following equations must be true? w 2 + pw + k = 0 w 2 − pw + 2k = 0 2 w 2 + pw + 2k = 0 2 w 2 − pw − 2k = 0 2 w 2 − pw + 2 k = 0
Á÷»ç° ¢ÇüÀÇ ¼¼· Î ¸ ¦ LÀÌ ¶ó ÇÏ ¸ é j 2W +
k À§ÀÇ µÎ ½ÄÀ¸ · Î L°ª À» ±¸ ÇÏ ¸ é 2 w2 − pw + 2 k = 0 ÿ Á¤´ äÀº
2 L = p
k L × W =
(E)
20. The size of a television screen is given as the length of the screen’ s diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 19-inch screen? (A)
2
(B)
4
(C)
16
(D)
38
(E)
40
TV Å©±â´  ½º Å©¸ °ÀÇ ´ ë°¢¼±ÀÇ ±æÀÌ · Î ÁÖ¾î Áø´ Ù°í Çß° í , ½º Å©¸ °ÀÌ Æò¸ éÀÌ ¶ó°í Çß½À´ Ï ´ Ù. ÇÑ Á¤»ç°¢Çü ½º Å©¸ °ÀÌ 21-inch ÀÏ ¶§ ¸ éÀû°ú , ¶ Ç ´Ù¸¥ Á¤»ç°¢Çü ¸ ð¾çÀÇ ½º Å©¸ °ÀÌ 19-inchÀÏ ¶§ µÎ ¸ éÀûÀÇ Â÷ÀÌ ¸ ¦ ±¸ ÇÏ ´  ¹ ®Á¦ ÀÔ´ Ï ´ Ù. ÀÏ ´ Ü ½º Å©¸ ° Å©±â
21-inch´  ÇÑ º ¯À» a¶ó °¡ Á¤ÇÏ ¸ é a 2 = 441/2
¸ éÀûÀº
a 2 À» ±¸ÇÏ ¸ é µË´ Ï ´ Ù.
2a 2 = ( 21) 2 ⇒ b2 µµ a¸ ¦ ±¸ ÇÑ ¹ æ¹ ý°ú µ¿ÀÏ ÇÏ °Ô ±¸ ÇÏ ¸ é b2 = 361/2 a 2 − b2 = 80/2 = 40 ÿ Á¤´ äÀº
(E)
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21. The dimensions of a rectangular floor are 16 feet by 20 feet. When a rectangular rug is placed on the floor, a strip of floor 3 feet wide is exposed on all sides. What are the dimensions of the rug, in fee? (A)
10 by 14
(B)
10 by 17
(C)
13 by 14
(D)
13 by 17
(E)
14 by 16
° ¡ · Î 16 ¼¼· Î 20ÀÎ ¹ Ù´ Ú¿¡ rugÀ» ±ñ ÈÄ ¹ Ù´ Ú °¡ ÀåÀÚ¸ ®¿¡ 3 feet°¡ ³ ² À» ¶§ ÀÌ rugÀÇ Ä¡ ¼ö¸¦ ±¸ ÇÏ · Á¸ é °¡ · Î ´  16 − 6 =10ÀÌ °í ¼¼· Î ´  20 − 6 = 14ÀÔ´ Ï ´ Ù. ÿ Á¤´ äÀº
(A)
22. A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2, or 3 inches. What is the least number of such square pieces into which the board can be cut? (A)
5
(B)
6
(C)
7
(D)
8
(E)
9
À§ÀÇ Å×ÀÌ º í ¿¡ ¼ ÇÑ ¼¿ÀÇ Å©±â´  °¡ · Î 1 inch ¼¼· Î 1inch ÀÌ °í °¢ º ¯ÀÇ ±æÀÌ ´ Â5 inches ÀÏ ¶§, °¢ º ¯ÀÌ 1, 2, or 3 inches Áß¿¡ ¼ ÇÑ ¼öÄ¡ ¸ ¦ ¼±ÅÃÇؼ Á¤»ç° ¢Çü ¸ ð¾çÀ¸ · Î ³ ª ´ ¶§ °¡ Àå ÀÛÀº °æ¿ì ÀÇ ¼ö´  8 °¡ ÁöÀÔ´ Ï ´ Ù. À§ÀÇ ±×¸ ² À» Âü° í ÇÏ ¼¼¿ä! ÿ Á¤´ äÀº
(D)
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23. In rectangle QRST above, RU = SU . What is the ratio of the perimeter of
∆QUT
to
the perimeter of rectangle QRST ? (A)
3 8
(B)
1 2
(C)
5 8
3 4
(D)
(E)
9 11
(QU ) 2 = (UT ) 2 = 4 2 + 3 2 = 52 ∆QUT ÀÇ µÑ· ¹ = 8 + 5 + 5 = 18 QRST ÀÇ µÑ· ¹ = 8 + 8 + 3 + 3 = 22 µû¶ó¼ the ratio of
ÿ Á¤´ äÀº
∆QUT
9 11
to QRST = 18 : 22 = 9 : 11 =
(E)
24. The area of each of the 16 square regions in the figure above is T . What is the area of the shaded region? (A)
13T 3
(B)
5T
(C)
16T 3
(D)
11T 2
(E)
7T
°¢°¢ÀÇ Á¤»ç °¢ÇüÀÇ ¸éÀûÀÌ T ÀÌ ¹ Ç· Î Àüü ¸ éÀûÀº 16 T °¡ µÇ°í 16 T ¿¡ ¼ unshaded regionÀÇ ¸ éÀûÀ» »©ÁÖ¸ é shaded regionÀÇ ¸ éÀûÀ» ±¸ ÇÒ ¼ö ÀÖ½À´ Ï ´ Ù. 16 T − ( 4 T + 6 T + T ) = 5 T ÿ Á¤´ äÀº
(B)
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