Sacrificed to, Ma and Baba
..
…
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Ramrod Special Math Suggestion wb‡q wKQz wKQz K_v: K_v:
me©cÖc _g Ö_g K… ZÁZv Rvbv‡bv n‡”Q gnvb m„ wóKZ© vi cÖ wZ| K… ZÁZv Rvbv‡bv n‡”Q Team Ramrod Gi mKj †g¤^ vi ‡`i cÖ wZ hv‡`i wbijm cÖ ‡Póv I mn‡ hvwMZvq DU IBA Gi Ramrod Special Math Suggestion ‡ei Kiv m¤¢ e n‡q‡Q| K… ZÁvZv Rvbv‡bv n‡”Q Dremers Club Authority ‡K|
G 200 Most Tentative Math Exercises mshy ³ Kiv n‡q‡Q Ges me¸‡jv Math ï× evsjvq Explain Kiv n‡q‡Q| Math Suggestion
Math Suggestion G Include Kiv n‡q‡Q Ggb wKQz Math
Shortcuts ‡h ¸‡jv e¨envi Kv‡i Avcbviv 10 †_‡K 30 †m‡K‡Ûi g‡a¨ Math Ki‡Z cvi‡eb| ‡ jvg ‡ Zv † kl Ki ‡ Z cvi ‡ j 30 Uv Math Gi g ‡ a¨ me¸ ‡ jv fv a¨ wgwbgvg 20 wUi g‡Zv Math Same Pattern, Same Rules-Regulations Same Shortcuts G ‡c‡q hv‡eb| Ges Same
DU IBA, Bank Job, GRE, GMAT, SAT, BCS
Gi mKj Candidate Gi Rb¨ ïf
Kvgbv iB‡jv|
K… ZÁZvq, Md. Biplob Hossain Founder
Dreamers Club
2|Page
Ramrod Special Math Suggestion wb‡q wKQz wKQz K_v: K_v:
me©cÖc _g Ö_g K… ZÁZv Rvbv‡bv n‡”Q gnvb m„ wóKZ© vi cÖ wZ| K… ZÁZv Rvbv‡bv n‡”Q Team Ramrod Gi mKj †g¤^ vi ‡`i cÖ wZ hv‡`i wbijm cÖ ‡Póv I mn‡ hvwMZvq DU IBA Gi Ramrod Special Math Suggestion ‡ei Kiv m¤¢ e n‡q‡Q| K… ZÁvZv Rvbv‡bv n‡”Q Dremers Club Authority ‡K|
G 200 Most Tentative Math Exercises mshy ³ Kiv n‡q‡Q Ges me¸‡jv Math ï× evsjvq Explain Kiv n‡q‡Q| Math Suggestion
Math Suggestion G Include Kiv n‡q‡Q Ggb wKQz Math
Shortcuts ‡h ¸‡jv e¨envi Kv‡i Avcbviv 10 †_‡K 30 †m‡K‡Ûi g‡a¨ Math Ki‡Z cvi‡eb| ‡ jvg ‡ Zv † kl Ki ‡ Z cvi ‡ j 30 Uv Math Gi g ‡ a¨ me¸ ‡ jv fv a¨ wgwbgvg 20 wUi g‡Zv Math Same Pattern, Same Rules-Regulations Same Shortcuts G ‡c‡q hv‡eb| Ges Same
DU IBA, Bank Job, GRE, GMAT, SAT, BCS
Gi mKj Candidate Gi Rb¨ ïf
Kvgbv iB‡jv|
K… ZÁZvq, Md. Biplob Hossain Founder
Dreamers Club
2|Page
Activities of Dreamers Club Offline: 1. 2. 3. 4. 5. 6. 7. 8.
Dream Succession Campaign Dreaming Campaign Seminar Workshop Dreamer Finding Campaign / Campus Tour Career Succession Campaign Volunteery activities Extra Curricular activities
Online (Youtube) 1. 2. 3. 4. 5. 6. 7. 8.
IBA, GRE, GMAT, SAT Tutorials BCS, Bank Job Tutorials, IT based Tutorials Freelancing Tutorials Motivational Speech Student Counsultancy Career Help Tutorials Dream Share Campaign
Websites and Social Media 1. 2. 3. 4. 5.
E Books Apps Providing Learning Materials Quiz Competition Blogging e.t.c
For more Details please visit our websites: www.ourdreamersclub.com Facebook page: https://www.facebook.com/Our-Dreamers-Club412812415784365/ Facebook Group: https://www.facebook.com/groups/353664461422621/ Youtube: https://www.youtube.com/channel/UCAkQc-8gCRN2fw7pns91c7A
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Math Pattern DU IBA Gi Math Pattern wb‡q wKQz K_v:
Gi m¤¢ ve¨ 30 wU Math Gi g‡a¨ Chapter Wise Tentative Pattern ‰Zwi Kiv n‡q‡Q| GLv‡b Avmbœ GB eQ‡ii cÖ kœ ‡Z wKQz msL¨vMZ cwieZ© b n‡Z cv‡i| me© vwaK msL¨K Math Avmv Chapter ¸‡jvi cÖ wZ Priority w`‡Z Aby ‡iva Kiv n‡jv|
weMZ K‡qK eQ‡ii cÖ kœ we‡kø lY mv‡c‡ÿ
Dremers club
Math Pattern 1. Percentage, Profit-loss, Discount, Interest: 6 wU 2. Number, Divisibility, LCM, HCF: 5 wU 3. Ineqality: 3 wU 4. Average, Conscutive integers: 2 wU 5. Mixture, Roots, Ven diagram: 2 wU 6. Unitary System: 3 wU 7. Ratio: 2 wU 8. Equation, Fraction: 2 wU 9. Speed, Time, distance: 1 wU 10. Probability: 1 wU 11. Geometry: 2 wU 12. Others/IQ: 1 wU 13. Age: 1 wU
N.B: The pattern is approximately changeable to any requirement for IBA, GRE, GMAT, Bank Job. So Please forgive us if any changes happen in the admission test.
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Percentage-Profit Loss-Discount Interest 1. In redesigning a warehouse, the length is increased by 20%, the breadth is increased by 40% & the height is decreased by 25%. What is the net increase in the volume of the redesigned warehouse compared to the previous design? (A) 20% (B) 25% (C) 40% (D) 26% (E) 15% Solution: GB g¨v_ Gi g‡Zv Percentage Increase Decrease Gi Math A‡bK cwigv‡Y Av‡m|
ZvB fvjg‡Zv wk‡L wbb| GUv Multiplier System-G Ly e mn‡R †ei Kiv hvq| aiæb Starting value = 1 After increase of 20% (0.2), The value becomes = 1.2(1+0.2)
Zvn‡j ev` evwK `y BUv n‡e ?
1.4(1+0.40) Ges 0.75 (1-0.25) Gevi GB 3 Uv ¸Y w`‡jB Avgiv outcome †c‡q hv‡ev 1.2 1.4 48 12 1.68 0.75 840 1176 1.2600
Zvn‡j c~ ‡e© wQj 1 Avi GLb 1.26
†e‡o †M‡Q 1.26-1= 0.26 (26%) Ans. D 26% N:B: ‡ q † M ‡ jv, Avcbvi † Kvb value ˆZw র Ki ‡ Z n ‡ jv bv * Easily n ‡ Z n ‡ jv bv র *Avevi eo eo msL¨v wb ‡ q KvR Ki 2. Successive discounts of 20% and 25% are equal to what single discount rate? (A) 45 (B) 40 (C) 200 (D) 50 (E) None of the above Solution: Multiplier System: after 20% discount 0.8 [1-0.20] .75 [1-0.25] after 25% ” 0 .600 Zvi gv‡b eZ©gvb value 0.6 (60%) 5|Page
Zvn‡j Single Discount (1-0.6) = 0.4 (40%) Ans. C. 40% 3. A shop sold a pair of shoes for Tk. 1600.00 and a pair of sandals for Tk. 960.00. If made a profit of 20% on shoes and took a 10% loss on sandals. The shop made a________? (A) Loss of 17.8% (B) Loss of 15% (C) Gain of 32% (D) Gain of 75.3% (E) none of there Solution: Multiplier System †Kvb value `iKvi ci‡e bv After 20% Profit = 1.2 After 10% Loss = .9 1.08 myZivs jvf (1.08-1) = 0.08 (8%) †Kvb Value B cÖ ‡qvRb ci‡jv bv Ans. 8%(অথবা 8% এর কাছাকাছ ভালু হেত পাতর যমন 7%) বদ Multiplier System এ ভালু এই ধরনর মযাথ সামায assume কনর বেন হেন পানর E. None of these 4. Karim received a 10% raise each month for 3 consecutive months. If his salary after the 3 raises is 13310, what was his starting salary? (A) 9000 (B) 10000 (C) 11000 (D) 12000 (E) None of these Multiplier System: 1.1 1.1 1.21 1.1 1.3310
Now, 1.3310=13310 So Ans.
1=
13310 1.3310
=
13310 10000 13310
=10000
B 10000
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5. The sale of TV increased by 30% when the price was reduced by 10%. What will be percentage change in revenue? (DU IBA BBA: 2016-17) (A) +14% (B) +15% (C) +17% (D) +18% (E) None of these Solution: Multiplier System, †Kvb value `iKvi ci‡e bv After 30% increase = 1.3 After 10% decrease = 0.9 =1.17% myZivs increase (1.17-1) = 0.17 (17%) †Kvb Value B cÖ ‡qvRb ci‡jv bv Ans. C. +17% 6. Nipu sold 100 pens, of which 50 are red and 50 are black, at tk. 48 per pen. He made a profit of 20%. On the black pens and made a loss of 20% on the red pens. What was the net gain or net loss on this sale? (DU IBA BBA-2016-17, IBA MBA June-July, 2017) (A) 0 (B) Gain of Tk. 200 (C) Loss of Tk .200 (D) Gain of Tk. 400 (E) None of these. Solution: GB g¨v_wU IBA BBA 2016-17 Ges IBA MBA 58th Intake G wQj| Just Multiplier System G KiæY 1.2 0.8 0.96 Loss (1-0.96) = .04 (4%) Pen Gi total `vg = 48100= 4800 Loss 4% 4800 = 192 UvKv (া ২০০ টাকা এর কাছাকাবছ া একট কম িব ) বদ Multiplier System এ ভালু এই ধরনর মযাথ সামায assume কনর বেন হেন পানর Ans. (C) Loss of Tk .200 7. At a certain bookstore, the regular price of each book is 20 percent less than its listed price. If during a sale the price of each book at the store was 15 percent less than its regular price, the price of book during the sale was what percent less than its listed price? (IBA MBA-June-July, 2017) (A) 30% (B) 32% (C) 35% (D) 38% (E) None of these Solution: Multiplier System 0 .8 (20% Less) 0.85(15% loss) 0.680 Less (1-0.68) =0 .32 (32%) 7|Page
Ans. B. 32% 8. Arif bought a pen at 30% discount on listed price. Few months later, he found that the price for the same pen has increased by 15% and the discount he got in taka remained the same. How much discount did Arif get in terms of the new listed price? (MBA-June/July-17) (A) 10% (B) 15% (C) 20% (D) 22.5% (E) None of these Solution: Multiple Systems 0 .7 (30% discount) 1.15 (15% increase) 0.805 (increased value) Less (1-0.805) =0 .195 (approximately 20%) Ans. 20% Alternative: aiæb Listed Price = 100 UvKv Discount = 30 UvKv Price ‡e‡o †M‡jv 50% Now, 100+50 = 150 UvKv wKš‘ Discount tk †Z same A_© vr 30 UvKv 30 100 Discount Percentage = 150 = 20% ans. C. 20%
9. Price of paper has increased by 20%. How much paper usage must be curtailed so that expenditure for paper remains the same? (A) 8-66% (B) 12.33% (C) 16.66% (D) 24.37% (E) None of these Solution:
c~ ‡e© i `vg
eZ© gvb `vg
100
120 ejy b‡Zv, Kgv‡Z n‡e KZ? Simple, 20tk Kvi Dci †_‡K Kgv‡Z n‡e? nu ¨v, 120 Gi Dci 20 100 So, Percentage = 120 = 16.67% Ans. C. 16.67%
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10. A trader normally sells a cow at a loss of 20% on his cost . He would make a profit of 10% on cost, if he could sell the cow at a price which is Tk. 1500 more than what he got. What was the cost of the cow to the trader in taka (A) 4500 (B) 4000 (C) 5000 (D) 3600 (E) None of these Solution: GwU Ki‡eb 100x Gi wbq‡g | Selling iæY Purchasing ধ 100x 80x (100x-20x) New Selling= 110x (100x+10x) & 80x + 1500 The two selling prices are equal 110x = 80x + 1500 ev, 110x – 80x = 1500 ev, 30x = 1500
ev, x =
1500 30
x = 50 100x = 100 50 = 5,000 Ans. C. 5000
11. Last year 60 students enrolled in the business communication course . Of the enrolled students, 90% took the final exam. twothird of the students who took the final exam passed the final exam. What percentage of the enrolled students did not pass in the exam? (A) 40% (B) 45%
(C) 60%
(D) 75%
(E) Cannot be determined
Solution: Enrolled = 60 Final Exam w`‡q‡Q = 90%60 = 54
Pass K‡i‡Q =
2 3
54
= 36 Pass K‡iwb = (60-36) = 24 24 100 Percentage = 60 = 40% Ans. A. 40% 9|Page
12. The import duty on a car is 50% of its cost. An additional supplementary tax of 90% is charged on the cost plus import duty. If the total of import duty and supplementary tax is Tk. 2,8 5,000, what is the cost of the car? (A) 3,00,000 (B) 3,200,000 these Solution: Cost 100
(C) 3,75,000
Cost+impoprt duty 150(100+50)
(D) 4,00,000
(E) None of
cost+import duty +tax 195(150+30% 150)
Import duty + tax = 95 (195-100) GLb, 95 ভাগ = 285000 1 ”
=
100 ” =
2,85,000 95 2,85,000 100 95
= 3,00,000 Ans. A. 300000 13. A sales person earns a commission of 5% on all sales between Tk. 2000 and Tk. 6000 and 8% on all sales over Tk. 6000. What is his total commission in a week in which his sales total Tk. 10,000? (A) 500 (B) 540
(C) 620
(D) 720
(E) None of these
Solution: 2,000 †_‡K 6,000 Gi g‡a¨ weµq Ki‡j 5% Kwgkb cvq| ‡ i 8% Kwgkb cvq । ev`evwK ev 6,000 Gi Dc Sales= 10,000 UvKv Kwgkb 5%6000 myZivs 6,000 ch© šÍ =300 UvKv ev`evwK UvKvi = 4000(10,000-6,000) Gi Dci 8% Kwgkb cv‡e| ev`evwK UvKvi Dci Kwgkb = (4,000 8%) = 320 UvKv †gvU Kwgkb (300+320) UvKv = 620 UvKv Ans. C. 620
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14. A price of a hammer is twice that of a screwdriver. If the price of a hammer is raised by 5% and the price of a screwdriver is decreased by 4%, how much or less will it cost to buy 3 screwdrivers and 3 hammers? (A) 2% more (B) 2% less (C) 4% more (D) 4% less (E) None of these Solution: bZz b GKwU kU© KvU wkLy b Ax By x y A = 1st Percentage Change B = 2nd Percentage Change y = 1 [ me mgq 1 ai‡Z n‡e] x = twice X I y cÖ_g cÖ ‡kœ i cÖ_g jvB‡b Exist Ki‡e |
Price mgvb ejv _vK‡j X I y `y BUvB 1 ai‡Z n‡e| GB g¨v _Uv‡Z, A = +5 B = -4 y=1 x=2 Ax By x y 5 2 4 1 = 2 1 10 4 6 2% = 3 3 Ans. 2% more
wet `ªt* cÖ ‡kœ i jvó jvBb Kv‡R Avm‡e bv| * djvdj () Avm‡j loss n‡e|
15. In a season, a football team has won 30 games out of 50 played. It has 46 more games to play. How many of these must the team win to make its record of wins 75% for the season? (A) 24 (B) 32 (C) 36 (D) 42 (E) 46
Solution: Ratio Equalization এ KiæY
1st Step
won
30
played 50 30 x 75% 2nd Step, 50 46
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ev, ev,
30 x
75
50 46 100 30 x 3
96 4 ev, 4(30+x) = 3 96 ev, 120+4x = 288 ev, 4x = 288-120 168 ev, x = 4 x = 42 Ans. D. 42 16. In a club, 60% members are male and 70% members are graduates also, 50% of the graduate members are male. What percent of the club members are female and not graduate? (A) 40 (B) 20 (C) 15 (D) 10 (E) 5 Solution: Box System 1st Step
Graduate Non-Graduate
Male 35 (50%70)
Female
60
40
Total 70 (100-70) 30 100
(100-60)
2nd Step Graduate Non-Graduate
Male 35 25 60
Female 35 5 40
Total 70 0 100
So, Female+Non-Graduate = 5% Ans. E. 5%
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17. In a shop 40% socks are white and rest are black. 60% socks are made of cotton & rest are made of wool. 25% white socks are made of cotton & 20 of the black socks are made of wool. How many black socks are made of cotton? (A) 100 (B) 80 (C) 60 (D) 50 (E) 25 Solution: Same Math: Box System
White Black Total Cotton 50 60 10(25%40) Wool 30 10 40 Total 40 60 100 GLv‡b mKj Value percentage-G wKš‘ As‡K e‡j‡Q, (Black+Wool) = 20 10 fvM = 20 20 1 fvM = 10 20 50 50 fvM = 10 = 100 Ans. A
18. Sixty percent members of a club are female. Fifty percent of the female members are doctors. The number of female doctors is twice the number of male non-doctors. What percent of members are doctors? (IBA BBA: 2016-17) (A) 45% (B) 55% (C) 57.5% (D) 60% (E) none of this Solution: Doctors Non Doctors Total
Male 25 15
Female 30(50%of60)
Total 55
40
60
100
Now given, The number of female doctors is twice the number of male non-doctors (Female doctors =2Male Non- Doctors) So, 30=2Male Non- Doctors) So, Male non-doctors =15 So Doctors = 55 %( 30%+25%) Ans. (B) 55% 13 | P a g e
19. In a class, 120 students are male and 100 students are female. 25% of the male students and 20% of the female students are engineering students, 20% of the male engineering students and 25% of the female engineering students passed the exam. What percent of the engineering students passed the exam? (IBA BBA: 2016-17) (A) 5% (B) 10% (C) 16% (D) 22% (E) none of this Solution:
Engineers NonEngineers Total
Male 30
Female 20
Total 50
120
100
220
Male Engineers= 25% 120 = 30 Female Engineers= 20% 100 = 20 Now, calculate the numbers of the passed students 20% 30 = 6 and 25% 20 = 5 Passed the exam = 6+5 = 11
Percentage = =
Passed Engineerin g
100
11 100 50
= 22% Ans. D. 22% 20. 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 sales 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 Solution: Multiplier System Percentage changes are = -20%, +20% .8 (1-0.20) 1.2 (1+0.20) 0.96 96 fvM = 3 million 14 | P a g e
1 100
3 96 3 100 ”= 96
”=
100 32
32100 3.1 96 40 32 8 Ans. D. 3.1 Million 21. 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%
(C) 64%
(D) 75%
(E) 100%
Solution: +25%, -20% Multiplier system 1.25 .8 1.000 Starting G 1 wQj Ending I 1 n‡q‡Q | myZivs value Gi †Kvb cwieZ© b nq bvB|
100% ev 1 wQj 100% B i‡q‡Q| Ans. E. 100% 22. In 1986 the book value of a certain car was and in 1988 its book value was
1 2
2 3
of the original purchase price,
of the original purchase price. By what
percent did the book value of this car decrease from 1986 to 1988? 1 2 (A) 16 % (B) 25% (C) 33 % (D) 50% (E) 75% 3 3 Solution: fMœ vskœ `y wUi ni 3 I 2 Gi j.mv.¸ = 6 6 †K Original price a‡i,
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1986 Gi car Gi `vg wQj
Ges 1988 ” ” ” ”
K‡g †M‡Q 4-3 = 1 Percentage Ki‡j,
1 4
1 2
2 3
6 4
6 3
100 = 25%
Ans. B.25% 23. 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 are in the same ratio of tagged fish in the second catch 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 Solution: Let N be the number of fish. Now please use ration equalization process. tagged 1 total1
ev,
=
tagged 2 total 2
50 2 N 50 N 50 50
ev, N
2 50 50
2 N = 1250 Ans. C.
24. During a two-week period, the price of an ounce of silver increased by 25 perrcent by the end of the first week and then decreased by 20 percent of this new price by the end of the second week. If the price of silver was x dollars per ounce at the beginning of the two-week period, what was the price, in dollars per ounce, by the end of the period? (A) 0.8x (B) 0.95x (C) x (D) 1.05x (E) 1.25x Solution: Please use the multiplier system Changes are: +25%, -20% Starting with 1 Multiply the change 1.25 16 | P a g e
.8 1.000 Starting G 1 wQj Ending I 1 n‡q‡Q | myZivs value Gi †Kvb cwieZ© b nq bvB| X wQj X B i‡q‡Q | Anc. C 25. Ms. Adams sold two properties, X and Y, for $30,000 each. She sold property X for 20 percent more than she paid for it and sold property Y for 20 percent less than she paid for it. If expenses are disregarded, what was her total net gain or loss, if any, on the two properties? (A) Loss of $1,250 (B) Loss of $2,250 (C) Gain of $1,250 (D) Gain of $2, 500 (E) There was neighter a net gain nor a net loss Solution: Use Multiplier System please Given: +20%, -20% 1.2 0.8 0.96 (selling) Loss (1-0.96) = 0.04 96 fvM selling Ges 4 fvM losses GLb, 96 fvM = 30,000
1 fvM =
4 fvM =
30,000 96 30,000 4 96
=
30,000 24
1250 ïay GKwU c‡Y¨i Rb¨ 2 wU c‡Y¨i 2 Loss = 1250 2 = 2500 Ans. B. Loss of 2,500 25. A union contract specifies a 6 percent salary increase plus a $450 bonus for each employee. For a certain employee, this is equivalent to an 8 percent salary increase. What was this employee’s salary before the new contract? (A) $21,500 (B) $22,500 (C) $23,500 (D) $24,300 (E) $25,000 Solution: 6% of salary + 450 = 8% That means 450 = 8% - 6% 450 = 2% Zvigv‡b, 2 fvM = 450
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1 ”
100 ” =
=
450 2
450 2
100 = 22,500
Ans. B 26. A toy store regularly sells all stock at a discount of 20 percent to 40 percent. If an additional 25 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $ 16 before any discount? (A) $5.60 (B) $7.20 (C) $8.80 (D) $9.60 (E) $15.20 Solution: Lowest possible price w`‡Z n‡j Highest percentage discount w`‡Z n‡e, 16 – 40% (16) = 9.6 Avevi discount n‡e 25% Price = 9.6 – 25% (9.6) = 9.6 – 2.4 = 7.20 Ans. B.7.20
27. Of 30 applicants for a job, 14 had at least 4 years experience, 18 had degrees, and 3 had less than 4 years experience and did not have a degree. How many of the applicants had at least 4 years experience and a degree? (A) 14 (B) 13 (C) 9 (D) 7 (E) 5 Solution: GB g¨v_wU Box system G K‡i †djy b| at least 4 year less than 4 year experience experience Degree 5 13 Not Degree 9 3 Total 14 16(30-14)
total 18 12 30
At least 4 years experience + Degree = 5 Ans. E. 5
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28. Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club? (A) 60 (B) 80 (C) 100 (D) 120 (E) 140 Solution: pass Ki‡Q = 30% pass K‡iwb = 70% G‡`i †fZi 12 Rb †Kvm© wb‡q‡Q Ges 30 Rb †bqwb Avm‡j 12 I 30 Gi †hvMdjB 70% GLb 70 fvM = 12+30
42 70 42 100 = 60 Rb 100 Ó = 70 Ans. A. 60
1 Ó
=
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Number Properties, Divisibility, L.C.M, H.CF, Function
GB P¨vÞUvi †_‡K 5-6 Uv g¨v_ Avm‡Z cv‡i| ZvB fv‡jvg‡Zv wk‡L wb‡eb| 1. If x is an integer greater than 2 then which of the following statement is not true? (A) 2x is always divisible 8 (B) 2x is always divisible by 16 (C) 2x is always divisible by 4 (D) All of these (E) none of these Solution: Given, x > 2...X (A) x = 3 n‡j mZ¨ bq (B) x = 3 n‡j mZ¨ bq (C) x = 3 n‡j mZ¨ bq Ans. D. all of these
Gi gvb a‡i wb‡q †PK KivUv me †_‡K ey w×gv‡bi KvR|
2. If m is an even integer and n is an odd integer and both are positive numbers, which of the following must be even? (A) m2+n2 (B) mn+n2 (C) m3+n2 (D) mn+m2 (E) None of these Solution: m I n Gi gvb a‡i wb‡q †PK KivUv me †_‡K ey w×gv‡bi
KvR| m=2 n=3
Gevi †PK Kiæb, (d) mn + m2 =23+ (2)2 = 6+4= 10
ev`evwK ‡PK K‡i †`Lyb me¸‡jv odd n‡e| Ans. D. mn+ m2 3. 3 and 5 are factors of F we can conclude that... (A) 35=F (B) 8 is a factor of F (C) F is a multiple of 15 (D) 3 5 are the only factors of F (E) 15 is a multiple of F. Solution: 3, 5 are factors of F
Zvigv‡b G‡`i L.C.M = 15 n‡jv G‡`i cÖ_g Multiple Av‡iv A‡bK Multiple n‡Z cv‡i †hgb 30, 45, 60... 20 | P a g e
Gevi option ¸‡jv hvPvB KiæY (A) me©mgq mZ¨ bq KviY F = 30, 45, 60... BZ¨vw` n‡Z cv‡i| (B) GBUv GK`g AmZ¨ (C) GBUv GK`g mZ¨ F = 15, 30, 45, 60..... Giv me Multiple of 15 (D) mZ¨ bq, KviY F = 30, 45, 60... BZ¨vw` n‡Z cv‡i (E) mZ¨ bq, KviY F = 30, 45, 60... BZ¨vw` n‡Z cv‡i Ans. C 4. If n is an even integer, which of the following must be an odd integer? (A) 7n-2 (B) 5(n-2) (C) (16n+24)/18 (D) (6n+12)/3 (E) None of these Solution: aiæY n =2 (A) (72) – 2 = 14-2 = 12 (which is even) (B) 5(n-2) = 0, (which is even) 16n 24 (C) 18 (16 2) 24 = 18 32 24 = 18 56 = 18 =7 (which is odd) 6 2 12 12 12 24 8 (Which is even) (D) 3 3 3 Ans. C
6. You want to make some candy using a recipe that calls for 1
1 cups of sugar, 2
1 cup of boiling water and several other ingredients. You find that you have 2 only 1 cup of sugar. How much water will you have to use? (A)
1 3
cup (B)
3 cup 4
(C) 1 cup (D)
1 6
cup
(E)
1 cup 4
Solution: Ratio Equalization System Follow Kiæb; 1 3 1 2 2 21 | P a g e
suger 1 water 1
suger 2
water 2
3
ev, ev,
2 1 1 w2 2
3 2
ev, 3
1
2
w2
1
w2 1 w2 3
Ans. A.
1 3
7. In a school with the same number of boys and girls, 1/8 th of the girls and 5/6 th of the boys are residing in the hostel. What percent of the students consists of boys who do not reside in the hostel? (A) 1/12 (B) 1/6 (C) 7/48 (D) 13/48 (E) none of these Solution: GB ai‡bi g¨v_ msL¨v a‡i wb‡q Ki‡j
me †_‡K Better
nq| Same number of boys and girls. fMœ vsk¸‡ jv ni 8 I 6 Gi j.mv.¸ = 24 aiæb Same number of boys and girls=24 1 So, girls reside K‡i 24 = 3, 8 5 i 24 = 20, And boys reside K‡ 6 Boys reside K‡i bv 24 – 20 = 4
Part =
Ans. A.
Boys who do not reside Total students
=
4 24 24
boys=24, girls=24
4 48 1
12 1 12
22 | P a g e
8. A student completed
7 the of the math problems in a chapter in 1 day, Had 9
he completed 3 more problems, he would have completed
5 6
the of the total
problems. How many problems were there in the chapter? (A) 18
(B) 36
Solution: 3 Uv Problem
(C) 54
(D) 64
†ewk Ki‡Z cvi‡j fMø vsk n‡Zv
(E) 72
5 . Zvigv‡b bZz b fMœ vsk I cy ivZb 6
fMœ vsk Gi Zdvr -B Avm‡j 3 Uv Problem Gi mgvb| 5
1 18
7
6 9 15 14 18 1 18
fvM = 3 Uv cÖ e‡jg
1 fvM = 318 = 54 Uv Problem Ans. C. 54 9. Half of the graduates of the MBA programm became members of the IBA alumni association. One third of the graduates became members of the MBA club. If 1/5th of the graduates were members of both Alumni Association & MBA club, what fraction of the graduates were members of only the MBA club? (A) 1/8 (B) 1/15 (C) 1/12 (D) 2/13 (E) None of these Solution: aiæY Graduates Gi msL¨v = x x IBA Allumini Association = 2 x MBA Club = 3 x Both = 5 x x Only MBA Club = 3 5
23 | P a g e
= =
Fraction =
5x 3x 15 2x
15
Only MBA Club Graduates
2x
15 x
2x 15 2
1 x
15
Ans. E 10. A cake is divided into three pieces so that the first piece is three times as big as the second and the second piece is three times as big as the third. What fraction of the entire cake is the smallest piece? (A) 1/8 (B) 1/12 (C) 1/13 (D) 1/16 (E) None of there Solution: aiæb, third piece = 1 2nd piece = 3 (3 ¸Y ) Ges 1st piece = 9 (3 3) Smallest
Fraction = Entire Cake
1 13
1
Ans. C.
13
11. Seventy five percent of the students entering BBA program are from Dhaka city. Two third of them majored in finance and of the finance majors
3 worked 4
in multinational companies. What fraction of the entire class worked in multinational companies? (A)
1 2
(B)
1 4
(C)
1 8
(D)
1 12
(E) None of these
24 | P a g e
75
Solution: 75% =
3
(Dhaka City)
100 4 2 3 1 So Finance Major = 3 4 2
3
1
4
2
Multinational Company †Z i‡q‡Q
3 8
Ans. E. None of these 12. In a class, 25% of the students voted for Mr. X. Two thirds of the remaining students voted for Mr Y. The remaining 11 students did n’t cast their vote. How many students are there in the class? (A) 64 (B) 44
(C) 36
Solution: 25% =
1 4
(D) 22
(E) 16
(Voted for Mr. X)
1
4 1
4
4
Remaining = 1 = 3
Now, Remaining = 1
1
=
3
3 4
1 = 4 2
Voted for M. Y =
2
1
4 2 4 1 2
4
1 4 1 ejv n‡q‡Q Remaining n‡jv 11 Rb students 4 =
ev,
1
11
4 1 = 11 4 = 44 Ans. B. 44
25 | P a g e
13. Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $3 for the first item and $1 for each additional item. Which of the following gives the total dollar amount of Kim’s purchase, including postage and handling, in terms on n? (A) 8n + 2
(B) 8n + 4
(C) 9n + 2
(D) 9n + 3
(E) 9n + 4
Solution: 8 UvKv per piece n‡e total = 8n Others charges (postage and handling) = 3 + 1 (n-1) Total charges = 8n + 3 + 1 (n-1) = 8n + 3 + n -1 = 9n + 2 Ans. C 14. A car dealer sold x used cars and y new cars during May. If the number of used cars sold was 10 greater than the number of new cars sold, which of the following expresses this relationship? (A) x > 10y
(B) x > y + 10 (C) x > y - 10
(D) x = y + 10 (E) x = y - 10
Solution: Simple, x is y + 10 x = y + 10 Ans. D
15. A certain electronic component is sold in boxes of 54 for 16.20 and in boxes of 27 for 13.20. A customer who needed only 54 components for a project had to buy 2 boxes of 27 because boxes of 54 were unavailable. Approximately how much more did the customer pay for each component due to the unavailability of the larger boxes? (A) 0.33 (B) 0.19 (C) 0.11 (D) 0.06 (E) 0.03 Solution: 27 Gi 2 Uv e· Gi `vg 13.20 2=26.40 10 .2 = 0.19 (Approximated) LiP †ewk jvM‡e 54 Ans. B
26 | P a g e
16. If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 Solution: x Gi gvb a‡i Avgiv hvPvB Ki‡Z cvwi A) X = 2 so y=8, 8 †K 4 w`‡q fvM Kiv hv‡e| [(32)+2] B) X = 1 ewm‡q nq 5... 5 †K 5 w`‡q fvM Kiv hv‡e|[(31)+2]=5 C) 6 w`‡q fvM Kiv hvq bv x Gi gvb hvB aiæb bv †Kb| D) x = 5, 3x+2 = 35 hv 7 w`‡q fvM Kiv hvq| E) x = 2, 3x+2 = 8, hv 8 w` ‡q fvM hv‡e|
17. Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.30? (A) 426
(B) 430
(C) 443
(D) 460
(E) 486
Solution : me †_‡K †ewk Envelopes cvIqv hv‡e 1.50 Gi Rate-G Envelopes purchase Ki‡j 1.54=6 UvKv ; 400(100 4) Uv Envelopes 50 Gi Uv ‡`Iqv hv‡e GKUv Pack 6+1 = 7tk GLv‡b, ($7.30-$7) = $0.30 0.30 30 =10 Uv AviI AwZwi³ Envelopes purchase Kiv hv‡e 0.03 3 Greatest Envelop number = 400+50+10 = 460 Ans. D. 460
27 | P a g e
18. If s, u, and v are positive integers and 2s = 2u + 2v, which of the following must be true? I. s = u II. u v III. s > v (A) None (B) I only (C) II only (D) III only (E) II and III Solution: “2s = 2u+2v” cv‡ib, Equation Gi w`‡K ZvKv‡j ey S‡Z (I) n‡e bv GLv‡b, S Ges U mgvb n‡Z cvi‡e bv| (II) n ‡ e bv, KviY U I V mgvb n ‡ ZI cv ‡ i Avevi bvI n ‡ Z cv ‡ i Z ‡ e Aek¨B Must be true
bq) III. S Aek¨B V Gi †_‡K eo n‡e| (KviY U I V 2 w`‡q ¸b K‡i †hvM Ki‡j S Gi mgvb n‡e| Zvi gv‡b S Aek¨B eo)| Ans.D. III only. 19.If x * y = xy – 2 (x + y) for all integers x and y, then 2 * (-3) = (A) -16 (B) -11 (C) -4 (D) 4 (E) 16 Solution: Given function, x*y = xy-2(x+y) 2*(-3) = 2 -3 – 2 (2 - 3) [x = 2, y = -3] = -6 – (2-1) = -6 + 2 = -4 Anc. C 20. In a certain class consisting of 36 students, some boys and some girls, 1 1 exactly of the boys and exactly of the girls walk to school. What is the 3 4 greatest possible number of students in this class who walk to school? (A) 9 (B) 10 (C) 11 (D) 12 (E) 13 Solution: aiæY Boys Gi msL¨v = x Girls Gi msL¨v = (36-x)
Now,
1 3
= = =
x +
1 (36-x) 4
4 x 3(36 x) 12
4 x 108 3x 12 x 108 12 28 | P a g e
= =
x
12 x
12
108 12
9
cvwi 9 Gi mv‡_ GB Equation Uv †`L‡j Avgiv ey S‡Z GLb x hw` 36 Zvn‡j, 9 Gi mv‡_ girls I i‡q‡Q|
x 12
†hvM n‡e|
36 = 3 †hvM n‡e| wKš‘ boys 36 n‡e bv| KviY †mLv‡b 12
24 2 GUv n‡e Maximum 12 9+2 = 11 Ans. C. 11
21.If m is an integer such that (-2) 2m = 29-m, then m = (A) 1 (B) 2 (C) 3 (D) 4 (E) 6 Solution: (-2) 2n ‡`Ly b GUv‡K wKfv‡e GKUz †PBÄ K‡i wb‡Z nq, (-2)2m = {(-2)2}m = (-2-2)m = (4)m = (22)m = 22m GLb, 22m = 29-m ev, 2m = 9-m [Base same excluded] so, m=3 ans: C 22. A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x? (A)
9 4
(B)
3 2
(C)
4 3
(D)
2 3
(E)
1 2
Solution: depending on the conditions x
2 x 3 29 | P a g e
2 x x 2 3 2x 2 x 3
ev, 3 x2 = 2 x ev, 3 x = 2 x
2
[ Dfq cÿ‡K x w`‡q fvM K‡i ]
2 3
Ans. D.
2 3
23. If a, b, and c are nonzero numbers and a + b = c, which of the following is equal to 1? bc ab ac ba (A) (B) (C) (D) b c b c cb (E) a Solution: 1 n‡Z †M‡j je I ni‡K mgvb n‡Z n‡e Given.........a+b = c aiæb, 1 +1 = 2 GLb, GB gvb ¸‡jv w`‡q option check Kiæb ‡ KvbwU র je I ni mgvb c b 2 1 1 1 E. 1 1 a Ans. E. 24. If x, y, and z are positive integers such that x is a factor of y, and x is multiple of z, which of the following is NOT necessarily an integer? yz y z x y x z xy (A) (B) (C) (D) (E) x x z z z Solution: First of all, please understand what Factors and multiples are.. Just See the example: 6 2(Factors) = 12 (Multiple)
GLb GUv‡Z e‡j‡Q, x is a factor of y aiæb, x = 6 30 | P a g e
y = 12 Avevi, x is a multiple of z aib, z = 3 [32=6 nq ev 6 †K fv½‡j 3 I 2 cvIqv hvq| Gevi, x = 6, y = 12 z = 3 GB gvb¸‡jv Option ¸‡jv‡Z ewm‡q †`Ly b †KvbwU fvM Kiv hvq bv| y z 12 3 15 [GBUv fvM Kiv hvq bv|] Option B. 6 6 x
ev` evKx me¸‡jv fvM Kiv hvq| Ans. B 25. The positive integer n is divisible by 25. If n the following could be the value of ? 25 (A) 22 (B) 23 (C) 24 Solution:
n
is greater than 25, which of
(D) 25
(E) 26
n > 25
ev, n > (25)2 [Dfq cÿ‡K square K‡i] ev, n > 625 2
ev, n
25
625 n [Dfq cÿ‡K 25 w` ‡q fvM K‡i] > 25 25
> 25
Option নার েভনর শধু GKUv value ই 25 এর উপনর রন ‡ Q Ans. E. 26 26.Which of the following CANNOT yield an integer when divided by 10? (A) The sum of two odd integers (B) An integer less than 10 (C) The product of two primes (D) The sum of three consecutive integers (E) An odd integer Solution: Option A.
Ó
B.
Ó
C.
Ó
D.
10 10 5 2 10
73 10
1; integer n‡e,
1; integer n‡e
10 10
1; integer
9 10 11 10
30 10
3 integer
31 | P a g e
But E GKUv odd integer KL‡bv 10 w`‡q fvM Kiv hvq bv| Ans. E 27. For all numbers s and t, the operation * is defined by s * t = (s – 1) (t+1). If (-2) * x = -12, then x = (A) 2 (B) 3 (C) 5 (D) 6 (E) 11 Solution: Function w`‡q‡Q, s*t = (s-1) (t+1) Ges GKB function follow K‡i, (-2) * x = -12 ev, (-2-1) (x+1) = -12 ev, -3(x+1) = -12 12 4 ev, (x+1) = 3 ev, x = 4-1 x = 3 Ans. B. 3 28. at a certain pizzaria, were mushroom and
1 8 1
of the pizzas sold in one week of the remaining pizzas sold were pepperoni. If n of
3 the pizzas sold were pepperoni, how many were mushroom? 3 7 3 7 n (D) n (E) 3n (A) n (B) n (C) 16 7 8 8 Solution: 1 8
= mashroom 1
7
8
8
Remaining = 1 Pepperoni =
1 7
7
3 8
24
7 n 24
1
24n 7
[1 fvM মান m¤ú~ Y © Ask]
1
24n
8
7
Mashroom Gi msL¨v =
32 | P a g e
= Ans. B.
3n 7
3n . 7
29. A collection of books went on sale, and
2 of them were sold for $2.50 each. 3
If none of the 36 remaining books were sold, what was the total amount received for the books that were sold? (A) $180 (B) 135 (C) $90 (D) $60 (E) $54
Solution: Remaining books fraction =
2 = 1 3
1 3
1 fvM = 36 n‡j 3
1 fvM = 363 = 108
2 Sold n‡qwQj 108 3 = 72 Amount = 72 2.5 = 180 Ans. A. 180 30. Three machines, individually, can do a certain job in 4, 5 and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates? 11 3 11 5 9 (A) (B) (C) (D) (E) 30 5 15 6 20 Solution: 3 Machines Gi cÖ wZw`‡bi job Gi 1 1 1 part , , 4 5 6 1 1 eo `y BUv n‡jv 4 5 1 hour G greatest part n‡e 1 1 = 9 4 5 20 33 | P a g e
Ans. B.
9 20
Average & Consecutive integers: 1. After 2 quizzes, Ap u had an average of 15 marks per quiz. In order to increase the average by n marks, what should be his score in the 3rd quiz? (DU IBA BBA: 2016-17) (A) 3n (B) 30+3n
(C) 15n
(D) 15+3n
(E) None of these
Solution: 2 Uv quiz Gi †hvMjdj = 152 = 30 n marks average G †hvM n‡j (15+n) 3 bs quiz Gi ci total n‡e (15+n)3 = 45+3n 3rd quiz G Obtain K‡i‡Q {(45+3n) – 30} = 3n+15 Ans: D 2. Average mark of 10 students is x. If 5 other students each earned 84 marks, find the average grade of the centre group?
34 | P a g e
(A) (10x+420)/15 (B) (10x+84)/15
(C) (x+420)/5 (D) (x+84)/2 (E) None
Solution: 10 Students Gi total mark = 10x AwZwi³ 5 R‡bi total mark = 584 = 420 10 x 420 Average of entire group = 10 5 10 x 420 = 15 Ans: A 3. Average of 17 even consecutive integers is 42. What is the third integer from the beginning of the series when the integers are arranged in an increasing sequence? (A) 28 (B) 30 (C) 28 (D) 34 (E) 36 Solution: 17 Uv b¤^ ‡ii Middle point n‡jv average 17 2
+ 0.5 = 9th number
9th number n‡jv average 9th 8th 7th 6th 5th 4th 3th 2nd 1st 42 40 38 36 34 32 30 [ ‡h‡nZz even conswcutive integers) Ans. B. 30 4. Francis had an average of 75 on her first four geography tests. After taking the next test, her average dropped to 72. How much did she get in the fifth text? (A) 54 (B) 56 (C) 58 (D) 60 (E) 73.5 Solution: 4 Uvi total 754 = 300 5 Uvi total 725 = 360 5th test G obtain K‡i‡Q 360-300 = 60 Ans: D. 60 5. Average weight of 8 persons is 120 lb. One person leaves the group and a new person comes in & the new average weight becomes 122 lb. If the weight of the outgoing person is 110 lb. What is the weight of the incoming person? (A) 118 (B) 120 (C) 122 (D) 126 (E) None of these 35 | P a g e
Solution: Average weight cÖ wZ Person †e‡o †M‡Q (122-120) =2 †gvU weight †e‡o‡Q = 28= 16 lb Zvi gv‡b New Person 16 lb †ewk IRb wb‡q G‡mwQj| Incoming person Gi weight = Outgoing person + 16 = (110+16) lb = 126 lb Ans. D. 126 6. If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5, and 5K + 1 is 63, what is the value of K? 3 3 (A) 11 (B) 15 (C) 22 (D) 23 (E) 25 10 4 Solution:
k (2k 3) (3k 5) (5k 1)
4 ev, k + 2k+3+3k-5+5k+1 = 252 ev, 11k -1 = 252 ev, 11k = 253 253 ev, k = 11 = 23 Ans. D
63
7. 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 N could equal (A) 16 (B) 32 (C) 41 (D) 54 (E) 68 Solution: Series Uv †`Ly b Red, Green, White, Blue, Yellow (5 numbers) Avevi Repeat Ki‡j Red, Green White, Blue, Yellow ‡h‡nZz white 3 b¤^ ‡i †kl nq| Zvn‡j option Gi †KvbUv 3 gvBbvm Ki‡j 5 w`‡q fvM Kiv hv‡e| E. 68 †K GiKg Kiv hv‡e| Ans. E
36 | P a g e
8. On 3 sales John has received commission 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 4 th commission must be (A) $164 (B) $170 (C) $175 (D) $182 (E) $185
240 80 110 x
Solution:
4 ev, 430+x = 150 4 ev, x = 600-430 x = 170 Ans: B. 170
150
9. A club sold an average (arithmetic mean) of 92 raffle tickets per members. 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 Solution: cÖk g‡Z, 84f + 96m = 92 (f+m) œ ev,84f+96m = 92 f + 92m ev,96m – 92 m = 92f – 84f ev,4m = 8f ev, 2m = 4f
ev,
m f
4 2
2 1
M: f = 2: 1 Ans. D
Mixture, Ven diagram, Roots and Exponents 1. Box 1 contain of 500 marbles 24% of which are black. Box 2 contains some markble of which 10% are black. You put the marble together in another box and found that the percentage of black marbles is 20%. How many markbles were there in box 2? (DU IBA MBA: June-July, 2017) (A) 100 (B) 150 (C) 200 (D) 250 (E) None of these Solution: Mixture Gi m~ ÎwU jÿ Kiæb
1g wgkÖY + 2q wgkÖY = Ultimate Rate (R1Q1) + (R2Q2) = RuQt or total amount Where,
R1 = Rate1 37 | P a g e
R2 = Rate2 Q1 = Quantitity1 Q2 = Quantitity2 Ru = Ultimate Rate Qt = Total Quantity
GLb g¨v_ Kiæb, (R1Q1) +(R2Q2) = RuQt (24500) +(10X) = 20(500+x) ev, 12,000+10x = 10,000+20x ev, 120,000-10,000=20x-10x ev, 2,000 = 10x ev, 10x = 2,000 2,000 10 x = 200 Ans. C. 200
ev, x=
2. Coffee a normally costs 100 taka per pound. It is mixed with coffee B, which normally costs 70 taka per pound, to form a mixutre which costs 88 taka per pound. If there are 10 pounds of the mix, how many pounds of coffee A are used in the mix? (A) 4
(B) 5
(C) 6
(D) 7
(E) None
Solution: (R1 Q1) + (R2Q2) = (RuQt) or total amount (100X) + {70(10-x)} = 88 10 ev, 100x +700 70x = 880 30x = 880-700 30x = 180 180 x= 30 6 x = 6 Ans. C
38 | P a g e
3. In 24 kg of salt water 80% is salt of another mixture, 40% is salt. How many kg of the 2 nd solution must be added to the first mixture to get a solution that is 5% salt? (A) 24 (B) 36 (C) 48 (D) 72 (E) 96 Solution: (R1 Q1) + (R2Q2) = RuQt (8024) + 40 x = 50 (24+x) ev, 1920 + 40x = 1200 + 50x ev, 1920 – 1200 = 50x – 40x ev, 720 = 10x ev, 10x = 720
ev, x =
720 10
x = 72 Ans. D
4. In a box, there are equal numbers of 10 paisa, 25 paisa and 50 paisa coins. If it contains Tk. 170 in total of the three coin denominations, then what is the number of 10 paisa coins? (A) 2 (B) 20 (C) 200 (D) 2000 (E) 80 Solution: 170 tk = (170 100) paisa = 17,000 paisa Assume Equal number paisa = x (R1Q1) + (R2Q2) + (R3Q3) = total (10x) + (25x) + (50x) = 17,000 ev, 10x+25x + 50x = 17,000 ev, 85x = 17000 17 ,000 200 ev, x = 85 x = 200 Ans. C. 200
39 | P a g e
5. A trader purchased some pens for Tk. 8 and some pencils for tk. 4.5 per piece respectively. If he purchased a total of 12 pens and pencils for Tk. 82, how many pens did he purchase? (A) 6 (B) 7 (C) 8 (D) 9 (E) None Solution: (R1 Q1) + (R2Q2) = total 8 x + 4.5 (12-x) = 82 ev, 8x + 54 – 4.5x = 82 ev, 3.5x = 82 – 54 28 ev, x = 3.5 2 28 10 ev, x = 35 7 x = 8 Ans. C 6. Arif bought 17 pens of three color-black, green and red, which cost Tk. 5, Tk. 10 and Tk. 25 each. The total amount that Arif paid was Tk. 205. If Arif bought twice as many green pen, red pens, how many black pens did he buy? (DU IBA BBA: 2016-17) (A) 4 (B) 5 (C) 7 (D) 8 (E) None
Solution: Assume, The numbers Green Per = x Red = 2x Black = 17 – x – 2x = 17 – 3x Now, (R1Q1) + (R2Q2) + (R3Q3) = total 5 (17-3x) + 10 2x + 25 x=205 ev, 85 – 15x + 20x + 25x = 205 ev, 30x = 205 – 85 120 ev, x = 30 x = 4 Ans. A. 4
40 | P a g e
Unitary System 1. A ferry can carry 20 buses or 32 cars. If there are 15 buses on the ferry, how many cars can be loaded into it? (A) 6 (B) 8 (C) 12 (D) 15 (E) None Solution: 20 buses = 32 cars ev, 54 buses = 46 cars ev, 5 buses = 6 cars Ferry †Z evm i‡q‡Q 15 Uv, AviI 5 Uv bus Gi RvqMv i‡q‡Q AviI 6 Uv car load Kiv hv‡e †h‡nZz 5 buses= 6 cars © Ans. A. 6 2. A man and a boy together can complete a job in 81 days. Two men and three boys together can complete the same job in 36 days. In how many days can four men together complete the same job? (A) 21 (B) 27 (C) 30 (D) 36 (E) 38 Solution: 1 man + 1 boy together K‡i 31 days G Iw`‡K 2 man + 3 boys K‡i 36 days G cÖ_g condition Uv‡K hw` Avgiv 3 man + 3boys Ki‡Z cvwi Zvn‡j c‡ii condition minus Ki‡j ïay 1 man Gi KvR †ei
n‡e| 1g condition, 1 man + 1 boys K‡i 81 days G 3 man + 3 boys ”
81 3
”G
= 27 w`b
G‡`i Rate
1 27
2nd condition G Rate =
1 36
1 1 Ask 27 36
1 man 1 w`‡b K‡i 43 108 1 = 108 =
41 | P a g e
1 Ask 108 1 1 4 ” ” 4= 27 108 27 days (inverse of part of work=day) Ans. 27 days 1 man K‡i
3. In a hostel there was food supply for 20 students for 25 days. After 5 days, some students left the hostel and rest of the food lasted for 25 days. How many students left hostel? (104) (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 Solution: 25 w`‡b †L‡q †d‡j 1 Ask food 1 1 ” ” ” ” ” 25 1 ” ” 5 ” 5 ” ” 25 1
=
25 1 4 Lvevi evwK Av‡Q 1 Ask 5 5 2 eviB 25 days nIqv‡Z Benchamark mgvb| Avjv`v Avi Day Calculate Ki‡Z n‡e bv| 1 Ask Lvq 20 Rb 4 20 4 ” Lv‡e 4 5 5 = 16 Rb Leave K‡iwQj (20-16) = 4 Rb Ans: A. 4 4. An empty water tank can be filled in 40 minutes by opening one pipe and the full tank can be emptied in 120 minutes by opening the other pipe. If both pipes are opened together while the tank is empty, in how many hours time will the tank be completely filled. (A) 1.5 (B) 1.2 (C) 1.0 (D) 2.0 (E) 1.6 1 Solution: cÖ_g Pipe Gi Rate = 40
wØZxq Ó Ó Rate =
1 120 42 | P a g e
1 1 40 120 3 1 = 120
= =
2 120 1 60 1
60 days (inverse of ) 60
Ans. 1 hour 5. A team of 2 men and 5 women completed one forth of a job in 3 days. After 3 days another man joined the team and they took 2 days to complete another onefourth of the job. How many men can complete the whole job in 4 days? (A) 4 (B) 6 (C) 8 (D) 9 (E) None Solution: 2m + 5w Gi
1 4
1
As‡ki Rate (Inverse of day) 4
Avevi bZz b GKRb add nIqv‡Z 1 1 As‡ki Rate (Inverse of day) 4 2 1 1 One man Gi Kv‡Ri part 2 3 3 2 1 = = 6 6 1 6 days (inverse of part) 6 3m + 5w Gi
GLb, 1 Ask K‡i 6 w`‡b 4 1 ” 1 ” ” 6 4 ” = 24 w`b 24 w`‡b K‡i 1 Rb 1 Ó Ó 124 Ó 1 24 4 Ó Ó 4 = 6 w`b 1 man
43 | P a g e
Ans. B.6 days 6. 6 men or 8 women can do a work in 18 days. How many days will it require to complete the work if 3 men and 5 women work together? (A) 10 (B) 12 (C) 14 (D) 16 (E) 18 Solution: 6 men = 8 women 3 man = 4 women jvó jvB‡bi (3 men and 5 women) GUv‡K ïay women convert Ki‡Z n‡e (3 men + 5 women) = (4 women+ 5 women) [ †h‡nZz 3m = 4 w] =9w GLb 8w K‡i 18 w`‡b 1w ” 188 ” 18 8 ” 9 ” ” 9 = 16 w`‡b| Ans. D. 16 w`b 7. Alam starts working on a job and works on it for 12 days and complete 40% of the work. Then Babu joins Alam and together the complete the rest of the work in 12 days. How long will it take Babu to complete the job if he works alone? (DU IBA BBA: 2016-17) (A) 24 days (B) 30 days Solution: 40% =
40
”
(D) 60 days
(E) None of these
2
100 5
Alam, 12 w`‡b K‡i
1 ”
=
(C) 45 days
2 5
Ask KvR 2
1
5 12 30 awi, Babu x w`‡b K‡i 1 wU KvR 1 1 ” ” ” ” x 2 3 ‡Ri cvU© evwK i‡q‡Q = 1 = Kv 5 5
`y R‡b GKmv‡_ 12 w`‡b K‡i
3 5
Ask
Ask KvR 44 | P a g e
” ”
1 ” ”
3 5 12
” ”
GLb, Alam Gi Rate + Babu Gi Rate = 1
30
ev, ev, ev,
1
x 1 x 1 x 1 x
1 20
1 20
1
1
20 30 3 2 60 1 60
ev, x = 60 Ans. D. 60 days 8. If 20 men or 24 women or 40 boys can do a job in 12 days, how many men working with 6 women and 2 boys can complete the same work in 32 days? (IBA, BBA-16/17) (A) 4 (B) 5
(C) 10
(D) 12
(E) None of these
Solution: 12 w`‡b K‡i GKwU KvR 20 Rb Men ” 2012” ” 1 ” ” ” 20 12 ” 32 ” ” ” 32
=
15 2
= 7.5 ev, 8 (approximated) Ges women Ges Boys †K Men G Convert Kwi 24 women = 20 men 20 1 ” = men 24 20 6 = 5 men 6 ” = 24 40 boys = 20 men 20 men 1 boy = 40 45 | P a g e
2 boy =
20 2
men
40 = 1 man ‡gvU Men jvM‡e = 8 Already KvR K‡i‡Q (5+1) Rb men = 6 men AwZwi³ Men jvM‡e = (8 – 6) Rb men = 2 Men Ans. E. 2 Men
Ratio 1. The ratio of boys to girls in a class is 2/5. If 2 boys
1 leave and 4 girls join the class, the ratio of the boys to the girls becomes . 4 Originally how many girls were in the class? (A) 16 (B) 20 (C) 21 (D) 24
(E) None
Solution: Use Ratio Equalization System Boys 2 Girls
=
Now =
5 2x 2
1
5x 4 4 ev, 4(2x-2) = 5x ev, 8x – 8 = 5x + 4 ev, 8x – 5x = 4+8 ev, 3x = 12
ev, x =
12 3
46 | P a g e
x = 4 Boys Gi msL¨v = 2x = 24 =8 Girls ” ” = 5x = 54 = 20 Ans. B. 20 2. 2 partners, x and y have 60% and 40% shares in a business. After sometime, a 3rd partner z joined the business by investing five lakh taka and thus having 20% share in the business. What is y’s share now in the business? (A) 32% (B) 48%
(C) 36%
(D) 50%
(E) None of these
Solution: x:y = 60: 40 = 3: 2 3rd Party †h UvKv Uv wb‡q Avmj Avm‡j †mUvB 20% Gi mgvb evwK _v‡K (100-20) = 80% v‡Z fvM K‡i w`‡j nq = 48:32 80 †K 3:2 Abyc y cv‡”Q 32% ‡Kvb value B cÖ ‡qvRb cij bv Ans. A. 32% 3. A jar contains white, red and green marbles in the ratios 2:3:4. Five more green balls are added to the jar and so the ratios become 2:3:5. How many white balls are there in the jar? (A) 40 (B) 6 (C) 8 (D) 10 (E) None Solution: †`Ly b Ratio †Z ïay cwieZ© b n‡q‡Q Green marble. Gi KviY Green marble add
n‡q‡Q Ab¨ `y BwU AcwieZ© bxq 2:3:4 2:3:5 (5-4) = 1 fvM GB 1 fvMB 5 Uv green marble Gi mgvb 1 fvM = 5 n‡j 2 fvM = 52 = 10 Ans. D. 10
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4. The ratio of boys and girls in a class is 1:2 and the classroom has 24 students. How many boys would have to be admitted to make ratio of boys to girls 1:1? (A) 6 (B) 8
(C) 10
(D) 12
(E) 16
Solution: The ratio of Boys and girls = 1:2 and their total = 24 myZivs Ratio †Z fvM K‡i w`‡j nq 24 1 8 Boys = 3 24 2 16 Girls = 3 GLb Ratio Equalization Apply KiæY Boys 8 x 1 = Girls 16 1 ev, 8 + x = 16 ev, x = 16 – 8 x = 8 Ans. B. 8 5. A certain pole casts a shadow 24 ft long. At the same time another pole which is 3 feet high costs a shadow 4 feet long. How high is the first pole, given that the heights and shadows are in proportion? (A) 17 (B) 13
(C) 20
(D) 21
(E) None
Solution: Ratio Equalization Pole1 Pole 2 Shadow1 Shadow2 x 3 24 4 3 24 ev, x = 4 x = 18 Ans. 18 6. If the area of a square increases by 69%, then the side of the square increases by. (A) 13% (B) 30% (C) 20% (D) 69% (E) 130% Solution: Multiplier System 48 | P a g e
Backward c×wZ‡Z Answer Check up Ki‡Z n‡e| Option Gi †Kvb increase Gi Kvi‡Y multiplier system G ¸Y †`Iqvi ci Value 1.69 (1+69% e„ w×) nq ? Check it…. 1.3
B. 30% Zvigv‡b
1.3 1.69
Ans. B 7. If the side of a square increase by 20% then its area increases by what percent? (A) 40% (B) 44% (C) 400% (D) 80% (E) None Solution: Multiplier System Square Gi GKevû †e‡o hvIqv gv‡bB Aci evû e„ w× cvIqv; 1.2
1.2 1.44
†e‡o †M‡Q (1.44-1) = (0.44) 44% Ans. B 8. A, B and C can complete a job individually in 6, 8 and 12 hours respectively. If all three of them work together to complete a job and earn Tk. 3600, what will be c’s share of the earnings? (DU IBA BBA: 2016 -17) (A) 800 (B) 820 (C) 875 (D) 950 (E) none of these Solution: †h‡Kvb UvKv Day Gi Ratio †Z fvM Kiv hvq bv| Kv‡Ri Part Gi Ratio †Z fvM
Ki‡Z nq| Day †K Dwë‡q w`‡j Kv‡Ri Part cvIqv hvq| A: B : C Day’s Ratio 6 : 8 : 12 1 1 1 Kv‡Ri Part Gi Ratio : : 6 8 12 1 1 1 = 72: 72: 72 8 12 6 = 12 : 9 : 6 Gevi, 3,600 UvKv fvM K‡i w`‡j 3600 6 c cv‡e 27
2 12, 8, 6 3 6, 4, 3 2 2, 4, 3 1, 2, 3 =72
49 | P a g e
=
3600 3
9 = 1200 Ans. E. none of these
9. A 60 litre mixture of sugar and water contains sugar and water in the ratio 2:3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1:1? (IBA, BBA-2016-2017) (A) 6 (B) 10 (C) 15 (D) 20 (E) None Solution: 60 wjUvi fvM Kiæb 2:3 †Z Sugar : Water = 27 : 36 Equalization GLb Ratio Equalization s 24 x 1
36 x 1 36 – x x ev, 24+x = 36 – 36 – 24 24 ev, x + x = 36 – ev, 2x = 12 x = 6 Ans. A. 6
w
10.The ratio ra tio of two t wo quantities quantitie s is 3 to 4. If each of the quantities is increased by 5, what is the ratio of these two new quantities? 23 18 8 3 (A) (B) (C) (D) 19 24 9 4 (E) It cannot be determined from the information given Solution: x 3 y 4 So,
x 5 y 5
35 45
8 9
Again the ratio can also be
6( x) 5 11 8( x) 5 13
So it varies from value to value Ans. E
50 | P a g e
11.The annual budget of a certain college c ollege is to be shown on a circle c ircle graph. graph . If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 15 percent of the budget? (A) 150 (B) 360 (C) 540 (D) 900 (E) 1500 Solution: GKwU circle G total degree _v‡K 3600 100 fvM = 3600 360 0 1 Ó = 100 360 0 15 15 fvM = 100 = 54 Ans. 540 12.The amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5. If they worked a combined total of 112 hours, how many hours did the secretary who worked the longest spend on the project? (A) 80 (B) 70 (C) 56 (D) 16 (E) 14 Solution: GUv GK`g mnR| 112 hours † Ratio ে fvM K Ratio fvM Kiæb 112 112 5 8(1 2 5) 112 5 8 = 70 Ans. B. 70 13. In a certain company, the ratio of the number of managers to the number of production-line production-line workers is 5 to 72. If 8 additional additional production-line production-line workers workers were to be hired, the ratio of the number of managers to the number of production-line production-line workers would be 5 to 74. How many managers does the company have? (A) 5 (B) 10 (C) 15 (D) 20 (E) 25 Manager Mana ger 5 Solution: Given, Wor ker ker 72 5 x 5 Now, 72 x 8 74 ev, 745x = 5(72x+8) ev, 370x = 360x + 40 51 | P a g e
370x – 360x 360x = 40 ev, 370x – ev, 10x = 40
40 10
ev, x = x = 4
So managers=5x=5 managers=5x=54=20 ans. D.20
Equation 1. If x/y = -1, and xy = -1 then x-y=? (A) 2 (B) 1 (C) 0 (D) -2
Solution:
x y
(E) A or D
1 Ges xy = -1
GB `y BwU Equation †`L‡j †evSv hvq x = 1 y = 1 x – y y 1 – (+1) (+1) x – A_ev, - 1 – = 1 – 1 – (-1) (-1) =2 2 A_ev -2 Ans. E
= -1 – -1 – 1 1 = = -2
2. What is 10% of
y
3 (C) 3
(A) 1 (B) 2
, if
2 y
is 10% of 600? 3 (D) 4 (E) None
Solution: Given, 2y is 10% of 600 3 2y ev, =10%600 3 2 y 10 600
ev, ev,
3 2y 3
ev, y =
=
100
= 60
60 3 2
=60
52 | P a g e
10% of
y
3 10
=
100 =2 Ans. B. 2
xy
3. If
z
3
= 27 and
2
y 2 zx
3
3 (B)
(A)
60
=
1 3 3
(C) 1/3
3
what is the ratio of z toy? (D) 3 3
(E) None of these
Equation ¸Y K‡i cvq Solution: `y BUv xy z
ev,
2
y
y 2 zx
3
z 3
27
3 3
y 3 z 3
y z
3 3
27
2
ev,
1
=
3 3
z to y = Ans. B.
3
3: 3
3 3
4. 3 friends invested equals share in a business. After careful calculation, they realized that each of them would have invested Tk. 3000 less if they had found 2 more friends with equal shares. Find the total investment in the business (A) 7500 (B) 7,000 (C) 22,500 (D) 6000 (E) Can not be determined Solution: 2 Rb AwZwi³ Avmv‡Z ev`evwK 3 R‡bi Per Person Kg c‡i 3,000 UvKv 3 R‡bi total Kg jv‡M = 3,0003= 9,000 UvKv GB 9,000 UvKv-B 2 R‡bi UvKv 9,000 1 R‡bi UvKv = 2 = 4,500 UvKv 5 R‡bi UvKv Investment = 4,500 5= 22,500 Ans. C. 22,500 53 | P a g e
5. There are 200 questions in a 3-hour examination. Among questions are 50 mathematical problems. It is suggested that twice as much time be allowed for each mathematics as for each of the other questions. How many minutes should be spent in the mathematics mathematics problems? problems? (A) 36 (B) 60 (C) 72 (D) 100 (E) 120 Solution: Mathematical Problems = 50 Uv ” = (200-50) (200-50) Other =150 Uv x UvKv awi, Other Problem G per question G UvBg †`q x Mathematical cÖ kœ time time †`q 2x 2x UvKv cÖ wZ Mathematical Now, Mixture Mixture System R1Q1 + R2Q2 = total time 2x50 + x150 = 180 ev, 100x+150x = 180 ev, 250x = 180 180 180 ev, x = 250 250 Mathematical cÖ kœ time jv‡M = 502x 18 = 502 = 72 25 Ans. (C) 72 6. If
x z
is 1 more than
(A) x-1 (B) zn-1
œ Solution: cÖk g‡Z, ev, ev,
y z y z
+ 1= =
x z
x z
y z
, then y =?
(C) x-z
=
y z
(IBA, BBA-16/17)
(D) (x-1)/z
(E) none
+1
x z
1
x ev, y = z 1 z
ev, y =
zx
z
z = x – x – z z Ans. C. x – x – z
54 | P a g e
7. If x is an integer and y= -4x+17, what is the least value of x for which y is less than 1? (IBA, MBA-June/July) MBA-June/July) (A) 2 (B) 3 (C) 4 (D) 5 (E) None of these Solution: y = - 4x + 17 check Pjy b Avgiv Answer option ¸‡jv check A. 2, y = -42+17 = -8+17 = 11 B. 3, y = -43 + 17 = -12+17 =5 C. 4, y = -4 4+17 = -16+17 =1 D. 5, y = -4 5+17 = -20 + 17 = -1 [GUv Less than 1] Ans. D. 5 8. Raju has x number of books, which is 3 times as many as siam and
1 as many as payel. How many books do the 2
three of them have all together in terms of x? (IBA, MBA-June/July) 7 x 5 x 10 x 7 x (A) (B) (C) (D) (E) None of these 6 3 3 2
Solution: Raju x
Siam x
3
Raju Siam Gi 3 3 ¸Y gv‡b Siam Siam Raju Gi
Payal 2x
1 ¸Y| 3
1
Raju n‡jv Raju 2 2 ¸Y Payel Raju Gi 2 Books they have all together x = x 2 x 3
Avevi, Payal Gi
55 | P a g e
=
3 x x 2 x 3 6 x
=
3 = 2x Ans. E. None 9. A restaurant buys fruit in cups containing 3 restaurant uses
1 2
1 cups of fruit each. If the 2
cup of the fruit in each serving of its fruit compote, what is
the least number of cans needed to prepare 60 servings of the compote? compote? (A) 7 (B) 8 (C) 9 (D) 10 (E) 12 Solution: The restaurant uses fruit
1 2
60
= 30 Uv
cÖ wZUv Cup G Av‡Q =
Cup jvM‡e = 3
=
30 1 3 2
1 2
30 7 2
= closes to 9 Ans. C. 9 10. In a nationwide nationwide poll, N people people were interviewed. If to question 1, and of those,
1
1 4
of them answered “yes”
answered “yes” to question 2, which of the
3 following expressions represents the number of people interviewed who did not answer “yes” to both questions? 6 N 5 N 7 N 11 N N (A) (B) (C) (D) (E) 12 7 7 7 12
Solution: Yes to question 1 = n/4
56 | P a g e
G‡`i †fZi yes to question 2 = =
1 3
N
4
N
12
did not answer yes to both question = N –
N
12
=
11 N 12
Anc. C.
2 ) = 0 and b 3, then b=? b 1 1 (A) -8 (B) -2 (C) (D) (E) 2 2 2 2 Solution: (b-3) (4+ ) = 0 b 11.If (b-3) (4+
Either, b-3 = 0 ev, b = 3
or 4 +
ev, ev,
2 =0 b
2 = -4 b 2
4
=b
b =
wKš‘, b is not equal to 3 b =
1 2
1 2
Ans. C.
1 2
12. The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria? (A) 10 (B) 12 (C) 14 (D) 16 (E) 18 57 | P a g e
Solution: 2 n (1000) = 5, 00,000
ev, 2n =
5,00,000 1000
ev, 2n = 500 ev, 2n = 222222222 (2)n = (2)9 [9 Approximately] Time jvM‡e 29 = 18 Ans. E. 18 13. Marion rented a car for $18.00 plus $0.10 per mile driven. Craig rented a car for $25.00 plus $0.05 per mile driven. If each drove d miles and each was charged exactly the same amount for the rental, then d equals (A) 100 (B) 120 (C) 135 (D) 140 (E) 150 Solution: Marion Gi charge = 18+0.10 d Ges craig Gi 25 + 0.05d
cÖ kœ g‡Z `y BR‡bi PvR© mgvb 18+0.10d = 25+0.05d ev, 0.10d – 0.05d=25-18 ev, 0.05d=7 ev, 0.05d=7
ev, d =
7 0.05
D=140 miles 14. Tickets for all but 100 seats in a 10,000 seat stadium were sold. Of the tickets sold, 20 percent were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales? (A) $15,840 (B) $17,820 (C) $18,000 (D) $19,800 (E) $21,780 Solution: 100 seats sold nq bvB, ev`evwK sold n‡q‡Q ? (10,000-100) = 9900 Revenue (total) ( 0.2 9,900 $1 )+( 0.8 9,900 $2 )
= 1980+15840 = 17820 Ans. B. 17,820 15. Rene earns $8.50 per hour on days other than Sundays and twice that rate on Sundays. Last week she worked a total of 40 hours, including 8 hours on Sunday. What were her earnings for the week? 58 | P a g e
(A) $272
(B) $340
(C) $398
(D) $408
(E) $476
Solution: Other days Gi rate = 8.5 Sunday Gi Rate = 8.52 = 17 Total earning 178+8.5 (40-8) =136+8.5 32 = 136+272 =408 Ans. D 16. A certain grocery purchased X pounds of the produce for P dollars per pound. If Y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for S dollars per pound, which of the following represents the gross profit on the sale of the produce? (A) (x – y)s - xp (B) (x – y)p - ys (C) (s – p)y - xp (D) xp - ys (E) (x-y) (s – p) Solution: Purchasing price = xp if y pounds discarded = (x-y) Selling price = (x-y) S Gross profit = selling price – purchasing price = (x-y) S - xp Ans. A.
17. Jan lives x floors above the ground floor of a high-rise building. It takes her 30 seconds per floor to walk down the steps and 2 seconds per floor to ride the elevator. If it takes Jan the same amount of time to walk down the steps to the ground floor as to wait for the elevator for 7 minutes and ride down, then x equals (A) 4 (B) 7 (C) 14 (D) 15 (E) 16 Solution: cÖwZ floor mgqjv‡M 30 seconds. Total floor i‡q‡Q x Uv †gvU mgq jvM‡e 30x Uv 7 minutes = 420 seconds elevator Gi Rb¨ AwZwi³ jv‡M Zvn‡j GLv‡b †gvU mgq = (2x+420) cÖ kœ g‡Z, 2 Uv mgq same 30x = 2x+420 ev, 30x-2x = 420 ev, 28x = 420
59 | P a g e
ev, x =
420
28 x = 15 Ans. D.
18. A dealer originally bought 100 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, them, in terms of q, for how many dollars was each battery sold? 3q 3q (A) (B) (C) 150q 200 2 q 150 (D) +50 (E) 200 q Solution: Battery Gi total cost q dollar Battery i‡q‡Q = 100 Uv q cÖ wZ Battery Gi `vg = 100 150% = 1.5 q `vg evovi ci n‡e= 1.5 100 1.5 q
= = =
100 15 q 100 10 3q 200
Ans.A a 2 19. If , which of the following NOT true? b 3 b ab 1 ab 5 3 (A) (B) (C) 3 b 3 ba b 2a 4 a 3b 11 (D) (E) 3b 9 b 2 a 2 20. b 3 a Gi gvb = 2 Ges b ” ” = 3 a‡i me¸‡jv Ackb †PK K‡i †`Ly b 60 | P a g e
ïay c b¤^ i wgj‡e bv|] Ans. C 21. The weights of four packages are 1, 3, 5 and 7 pounds, respectively. Which of the following CANNOT be the total weight, in pounds, of any combination of the packages? (A) 9 (B) 10 (C) 12 (D) 13 (E) 14 Solution: Option A = 9 (1+3+5) ” B = 10(3+7) ” C = 12 (5+7) ” D = 13 (1+5+7) but ” E evbv‡bv hvq bv Ans. E 22. If x and y are different integers and x 2 =xy, which of the following must be true? I. x = 0 II. y = 0 III. x = -y (A) I only (B) II only (C) III only (D) I and II (E) II and III Solution: x 2 = xy x = y x x = y GRb¨ (iii) x = -y n‡e bv (ii) y = 0, x = 2 n‡j 22 = 20 4=0 n‡e bv (I) x = 0 Ges y Gi †h‡Kvb gvb n‡jI O2 = 0.2 O = 0, it must be true Ans. A. I only 2
23.If X and Y are sets of integers, X Y denotes the set of integers that belong to set X or set Y, but not both If X consists of 10 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X Y consists of how many integers? (A) 6 (B) 16 (C) 22 (D) 30 (E) 174 Solution: xy denotes only x A_ev y wKš‘ both bq| Avmy b Avgiv GwU venn diagram w`‡q K‡i †dw j 61 | P a g e
x
y
4
6
12
x = 10 y = 18 both = 6 both = 6 only x = 4 only y = 12 X or y = 4+12 Xy = 16 25. A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10 4, what was the number in the population 1 hour later? (A) 2(104) (B) 6(10 4) (C) (26) (104) (D) (106) (104) (E) (104)6 Solution: 10 minutes G Double n‡j, 60 6 times 1 hour n‡e double n‡e = 10 (26) (104) [104 = initial] Ans: E 26. During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played? (A) 180 (B) 170 (C) 156 (D) 150 (E) 105 Solution: aiæb Total game played =x 0.80 100 +0.50 (x-100) = 0.70x 80 + 0.50x -50= 0.70x ev, 0.70x – 0.50x = 30 ev,0.20x = 30 30 ev, x = 0.20 ev,x = 150 Ans. D.150 62 | P a g e
27. A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 130,000 and variable cost averaging $8 per item. If the manufacturing selling price is $15 per item, how many items must the manufacturer produce and sell to earn an annual profit of $150,000? (A) 2,858 (B) 18,667 (C) 21,429 (D) 35,000 (E) 40,000 Solution: Profit = Revenue – Cost (fixed+variable) Profit = 1,50,000 Let the number of items = x Revenue = 15x cost = fixed cost + variable cost = 1,30,00 + 8x profit = Revenue – cost ev, 1,50,000 = 15x – (1,30,000+8x) ev, 1,50,000 = 15x – 1,30,000 - 8x ev, 1,50,000+1,30,00 = 15x-8x ev, 2,80,00 = 7x 2,80,000 ev, x = 7 x = 40,000 Ans. E. 40,000
Age Problem: 1. 7 years ago, Samir was 3 times as old as Sourav. In 4 years, Samir will be twice as old as Saurav. What is Saurav’s present age? (DU IBA MBA June July, 2017) (A) 40 years (B) 18 years (C) 30 years (D) 20 years (E) None of these Solution:
7 years ago Now, In 4 years
Samir 3x 3x+7 3x+7+4
Sourav x x+7 x+7+4
So, 3x+7+4 = 2(x+7+4) X=11 So Saurav’s present age= 11+7=18 Ans. (B) 18 years 2. Today is Arif’s 12 th birthday and his father’s 40 th birthday. How many years from today will Arif’s father be twice as old as fir st at that time? 63 | P a g e
(A) 12 (B) 16
(C) 18
(D) 24
(E) None of these
Solution: Depending on the condition,
40+X = 2(12+X) X=16 Ans. 16 3. Mr. Rahim who is 28 years of age has a son who is 4 years old. In how many years will Mr. Rahim be 4 times as old as his son? (A) 10 (B) 12 (C) 13 (D) 14 (E) 15 Solution: Depending on the condition,
28+X = 4(4+X) X=12 Ans. B. 12 4. Rahim is 10 years older than his brother Sabbir. However, P years ago Rahim was twice as old as Sabbir. If Sabbir is now n years old and n>p, find the value of (n-p). (A) 10 (B) 15 (C) 20 (D) 30 (E) 25 Solution:
Rahim Now, n+10 P years ago n+10-p Depending on the condition, n+10-p= 2(n-p) ev, n+10-p=2n-2p ev, 10=2n-2-n+p ev, 10=(n-p) (n-p) =10
Sabbir n n-p
ans. A. 10 5. If man was r years old s years ago, how many years old will he be t years from now? (A) s+r+t (B) rs+t (C) s-r+t (D) r-s+t (E) none 64 | P a g e
Solution: A man was r years old s years ago . so now the present age of the man = r+s So the age will be after T years= r+s+t ans. A
6. Today Rose is twice as old as Sam and Sam is 3 years younger than Tina. If Rose, sam and Tina are all alive 4 years from today, which of the following must be true on that day? I. Rose is twice as old as Sam II. Sam is 3 years younger than Tina III. Rose is older than Tina (A) I only (B) II only (C) III only (D) I and II (E) II and III Solution: Math Uv GKUz critical Pjy b cÖ_‡g (i) bs option Uv Avgiv hvPvB Kwi, “today rose is twice as old as sam” ejv Av‡Q today but fwel¨‡Z Rose, Sam Gi wظY bvI n‡Z cv‡i| †hgb, today sam = 3 rose = 6 3 eQi c‡i, sam 3 +3 = 6 Rose, 6 +3=9, not twice © fwel¨Z memg‡qi Rb¨B cÖ ‡hvR¨ gvb, (ii) Sam is 3 years younger than tina GUv eZ (iii) R = 2s, s = (t-3) R = 2(t-3) R = 2t-6 myZivs Rose, tina Gi †_‡K eo bq| Ans. Only (ii) ev B 7. The sum of the ages of Doris and Fred is y years. If Doris is12 years older than Fred, how many years old will Fred be y years from now, in terms of y? y 3 y 5 y (A) Y – 6 (B) 2y – 6 (C) – 6 (D) – 6 (E) – 6 2 2 2 Solution: D+F = y Given, D = F + 12 F+12+F= y ev, 2F+12 = y ev, 2F = y – 12
65 | P a g e
ev, F =
y 12
2
y years c‡i n‡e,
= = = =
y 12
y 12 2 y
2
y
2 3 y 12
2
3 y 2 3 y
2
12 2
6
Ans. D.
3 y 6 2
Motion:( Speed, time, distance) 1. A plane travelling at 600 miles per hours is heading for Chittagong Airport at 3:58 p.m it is 30 miles from the airport. At what time will it arrive at the airport? (A) 3:59 pm (B) 4:00 pm (C) 4:01 pm (D) 4:02 pm (E) 4:03 pm
Solution: 600 miles hvq 60 minute G 60 ” ” ” 1 600 60 30 ” ” ” 1 600
= 3 minutes G 3 minutes ci †cŠQv‡e 4 : 01 p.m G †cŠQv‡e Ans. C. 4:01 p.m 2. Two cars start towards the same destination at the same time. One car is 5 km behind the others. If the speed of the car at the front is 750 meter per minute and that of the other car is 1000 meter per minute, after how many minutes will the two cars meet? (A) 20 (B) 24 (C) 25 (D) 30 (E) None
66 | P a g e
Solution: 5km = 5000 mter The difference between speed of the two cars is = (1000-750) = 250
They will meet =
5,000 250
= 20
Ans. A. 20 3. Two cars start towards each other from points 200 km apart. One car travels at 40 km/hr and the other travels at 35 km/hr. How far apart will the two cars be after four hours of continuous travelling? (A) 100km (B) 75km (C) 40km (D) 20km (E) 160km 100
Solution: x 140
y
160
200 km Gi †fZ‡i 1g car 4 N›Uvq hvq 404 = 160 k.m 2 q car 4 N›Uvq hvq 354 = 140 k.m Suppose, they meet at = 100 km. which is half 200. Distance Zv‡`i g‡a¨ eZ© gvb (160-100) = 60 (140-100) = 40 (60 + 40) = 100 Ans. A 4. The mile meter of a car misses every mile being travelled. After a certain time the meter shows that 1251 miles were travelled. How many miles were actually travelled? (A) 1291 (B) 1325
(C) 1376
(D) 1424
(E) None
Solution: 11 th mile G wgm Kivi gv‡b n‡jv 10 mile G meter G show K‡i| 10 mile meter G show Kivi gv‡b n‡jv 11 mile travel 11 ” 1 ” ” ” ” 10 ” ” ” = (111251)/10 1251 ” = 1376 5. Mr. x starts from his house at 9:10 a.m. towards IBA, which is 10 miles away from his house. He must reach IBA by 9:30 a.m. If he covers half the distance at 67 | P a g e
a speed of 20 miles per hours, his speed for the remainder of the distance must be (in miles per hours): (A) 50 Solution:
(B) 60 1 2
Distance =
(C) 45 1 2
(D) 55
(E) None
10 = 5 mile hvq 20 kmp †Z
5 60 minutes 20 = 15 minutes mgq evwK Av‡Q (20-15) = 5 minute Avevi distance evwK Av‡Q = (10-5) = 5 mile 5 Speed = 60 5 = 60 m/h Ans.B. 60 mile per hour
time jv‡M =
9:10
†_‡K
9:30 = 20 minutes
Speed =
Distance Time
6. Asif riding his bike at 24 km/hr reaches his office 5 minutes late. If he would have reached the office 4 minutes earlier than the scheduled time by travelling 25% faster, how far is his office from his house in kms (IBA, BBA-16/17) (A) 18
(B) 24
(C) 36
(D) 40
(E) None
Solution: Distance = D 24 km/h Avm‡j 5 minute late Avevi; 30(24+25% 24) km/h Avm‡j 4 minute earlier Av‡m| D GLb, time1 = 24 D Avevi time2 = 30 GB `y BUv time Gi Difference B (5+4) = 9 minute 9 = hours 60 D D 9
24 30
60 68 | P a g e
ev,
5D 4D
D=
120 9 120
9 60
60 = 18 Ans. A. 18
7. Car X and car Y traveled the same 80-mile route. If car X took 2 hours and car Y traveled at an average speed that was 50 percent faster than the average speed of car X, how many hours did it take car Y to travel the route? 1 2 3 (A) (B) 1 (C) 1 (D) 1 (E) 5 3 5 3 Solution: x Gi speed =
80 2
= 40 y Gi speed = 40+50%40 = 40+20 = 60 1 80 4 y Gi time jvM‡e 1 3 60 3 Ans. C 8. One hour after Yolanda started walking from X to Y, a distance of 45 miles; Bob started walking along the same road from Y to X. If Yolanda’s walking rate was 3 miles per hour and Bob’s was 4 miles per how many miles had Bob walked when they met? (A) 24 (B) 23 (C) 22 (D) 21 (E) 19.5 Solution: `y BRb opposite direction G G‡m wgwjZ n‡j, `yBR‡bi AwZµvšÍ distance Gi †hvMdjB Avm‡j 45 kilometer Let Bob distance be D 1 and Yolanda D 2
D1+D2 = 45 (speed 1 time1)+ (speed 2 time2) = 45 [Distance = speed time] ev, (4 t) + {3 (t+1)} = 45 ev, 4t+3t+3 = 45 ev, 7t = 45-3 ev, 7t = 42 42 6 ev, t = 7 69 | P a g e
t = 6 Bob mgq †bq 6 hours Bob Distance AwZµg K‡i‡Q 4T = 46 = 24 Ans. A 9. Machine A produces bolts at a uniform rate of 120 every 40 seconds, and machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts? (A) 22 (B) 25 (C) 28 (D) 32 (E) 56
‡i Solution: Machine A per second G K Machine B per second G K‡i
120 40
= 3 bolts
100
= 5 bolts 20 Simultaneously produce K‡i (3+5) = 8 bolts per second 200 = 25 †m‡K‡Û 200 bolts produce Ki‡e 8 Ans. B. 25 10. Bill’s school is 10 miles from his home. He travels 4 miles from school to football practive, and then 2 miles to a friend’s house. If he is then x miles from home, what is the range of possible values for x? (A) 2 x 10 (D) 4 x 16
(B) 4 x 10 (E) 6 x 16
(C) 4 x 12
Solution: m‡e© v”P distance n‡Z cv‡i straight line distance G 10 H
4
S F x = 10+4+2 = 16
2 FH
me© wb¤œ Distance n‡Z cv‡i, 2
4 70 | P a g e
H
FH F 10 (H to S)
S
x = 10 – 4 – 2 =4 Ans. D. 4 x 16 11. A Furniture store sells only two models of desks, model A and Model B. The selling price of model A is $120, which is 30 percent of the selling price of model B. If the furniture store sells 2000 desks, ¾ of which are model B, what is the furniture stor e’s total revenue from the sale of desks? A. 114000 B. 186000
C. 294000
D. 380000 E. 660000
Solution: Model A Rate = 120 tk. Model B, Rate =
120 0.30
Model B number =
3 4
= 400
2000
= 1500 Model A number =2000-1500 = 500 Total revenue = R 1 Q1 + R 2Q2 = 120500+400 1500 = 60,000+6,00,000 = 6,60,00 Ans. E
Inequality 1. If x, y and z are consecutive negative integers and x>y>z, which of the following must be a positive odd integer? (DU IBA BBA: 2016-17) (A) xyz (B) (x-y)(y-z) (C) x-yz (D) x(y+z) (E) None of these Solution: aiæb, x> y> z = -1 > -2 > -3 (a) -1-2-3 = -6, negative (b) Let’s see, (x-y) (y-z) {-1-(-2)} {-2-( -3)} =1 (Which is positive odd) (c) x – yz = -1 – (-2-3) = -1 – 6 = -7, negative 71 | P a g e
(d) -1(-2-3) = 5 positive odd Av‡m But, x>y>z=-2>-3>-4 ধরন , { -2(-3-4)}=14 (positive even), হন া Ans. B 2. If x<10 and 5y-2x = 0 which of the following must be true. (IBA BBA: 201617) (A) y>-2 (B) y<4 (C) y> 2 (D) y>4 (E) None of these Solution: x< 10 nIqv‡Z, a‡i wbjvg, x = 9.9 5y – 2 9.99 = 8 ev, 5y = 19.8 19 .8 y = 5 = 3.96 (at least not equal 4 and must be less than 4) y < 4 Ans. B 3. If x and y are integers 13
Ans. B 5. If x -1 and x x3 which of the following must be true? (MBAJune/July,2017) (A) x1 (B) 0
0 (E) None of these Solution: x -1; Zvi gv‡b x Gi value -1, -0.5, 0, 1, 2 G¸‡jv n‡Z cv‡i wKbÍ y, xx3, 2 n‡Z cvi‡e bv KviY, 2 (2)3 = 28, n‡e bv x x3 †K (-0.5), 0, 1 ewm‡q mwVK cÖgvY Kiv hvq| Zvn‡j x Gi gvb -1 eo A_ev mgvb wKbÍ y 1 Gi †_‡K †QvU A_ev mgvb A_© vr -1 x 1 hv option G bvB Ans. E. None of these 6. If x is an integer such that 5
7. If ab<0 then all the following must be true EXCEPT (DU IBA MBA: JuneJuly, 2017) (A)
a b
<0 (B) a2+b2>0
(C) a3+b3<0
(D)
b a
<0
(E) None of these
Solution: ab < 0 nIqv‡Z, ab Gi ¸bdj 0 †_‡K †QvU| a A_ev b †h‡Kv‡bv GKUv‡K negative n‡ZB n‡e| [-a b<0 A_ev a-b < 0] a a (a) <0; Gi gvb 0 †_‡K †QvU n‡eB, Kvib †h‡Kv‡bv GKU v negative b b (b) a2+b2>0, a A_ev b †h‡Kv‡bv Uv square n‡j value cwRwUf Avm‡e| (c) a3+b3<0 me mgq negative Avm‡e hv 0 †_‡K †QvU| (Ña)3
73 | P a g e
b < 0 b, a ‡h‡Kv‡bv GKwU negative nIqv‡Z GUvI 0 †_‡K †QvU n‡e| a (e) None of these Ans. E (d)
8. x, y & z are consecutive integers. If 0
9. If 0x5 and y<10 which of there can be a value of xy? I. 2 II. 0 III. 50 (A) I only (B) II only (C) III only (D) I and II only (E) I and III only Solution: (I) 2 [x = 1, y =2 xy = 12 = 2] (II) 0 [x =0 I y = ‡h‡Kvb value xy = 0] (III) 50 [x = 5 but y = 10 bq xy 50] Ans. D. I and II only
10. If ab>0 and a<0, which of the following is negative? (A) -a (B) b (C) -b (D) (a-b) (E) – (a+b) Solution: ab > 0 and a<0 a = gvBbvm values Iw`‡K abGi value 0 Gi eo n‡Z n‡j b ‡KI gvBbvm value n‡Z n‡e| Ans. B. b 11. How many integers n are there such that 1 < 5n + 5 < 25? (A) Five (B) Four (C) Three (D) Two (E) One Solution: 1 < 5n +5 < 25 74 | P a g e
n Gi gvb n‡e, n = 0; l < 0+5<25 n = 1; 1 < 10 < 25 n = 2; 1 < 15 < 25 n = 3; 1 < 20 < 25 n = 4 n‡e bv 4 Uv (0,1,2,3) Ans. 4 12. Which of the following describes all values of x for which 1 – x2 0? (A) x 1 (B) x -1 (C) 0 x 1 (D) x - 1 or x 1 (E) -1 x 1 Solution:1 – x2 0 x Gi value n‡Z cv‡i, ‡`Lyb, 0, 1, - 1 1- 02 0 1-(1) 2 0 1-(-1) 2 0 ev, 1 > 0 ev, 1-1 0 ev, 1-1 0 ev, 0 = 0 ev, 0 = 0 So the value of x could be 0, 1, -1 which satisfies the equation of (E) -1 x 1 Ans. E 13. If a basketball team scores an average (arithmetic means) 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 game? y nx y y n( x y) x ny (A) (B) x (C) x (D) (E) n 1 n 1 n n 1 n 1 Solution: n game ch© šÍ total = nx next game Gi msL¨v = n+1-n [{total numbers (n+1)-n}] =1 next game ¸‡ jvi total = y 1 = y 2 Uv total Gi wgwjZ dj = nx+y nx y Average = n 1 Ans. A. 14. If 0 x 4 and y < 12, which of the following CANNOT be the value of xy? 75 | P a g e
(A) -2
(B) 0
(C) 6
(D) 24
(E) 48
Solution: just option †PK KiæY
Pjy b †`wL, A) xy = 2-1 = -2 [x = 2, y = -1] B) xy = 010 = 0 [x = 0, y = ‡h‡Kv‡bv value] C) xy = 32 = 6 [x = 3, y = 2] D) xy = 46 = 24 but (E) 48 evbv‡bv hvq bv| Kvib x Gi gvb 12 Gi †ewk n‡Z cv‡i bv| \ Ans. E 15. If a, b, c are consecutive positive integers and a
II. abc is an even integer
(A) I only (B) II only (E) I, II and III
III.
abc
3
(C) I and II
is an integer. (D) II and III
Solution: †h‡ nZz consecutive integers a < b
Zvn‡j,
(i) c – a = a+2 – a = 2 mZ¨ (ii) 123 = 6 234 = 24 me mgq even a a 1 a 2 3a 3 3(a 1) (a 1) which is always an integer (iii) 3 3 3 Ans. E. 16. If u > t, r > q, s >t and t > r, which of the following must be true? I. u > s II. s > q III. u > r (A) I only (B) II only (C) III only (D) I and II (E) II and III Solution: Given, u>t, r>q, s>t, and t>r Zvn‡j †KvbwU must be true ? 1g Uvi Inequality Gi mv‡_ 4th Uvi inequality Gi m¤úK© add Kwi; u>t>r 2nd inequality e‡j‡Q r>q Zvigv‡b, u>t>r>q 3rd inequality e‡j‡Q s > t A_ev, s>t>r>q 76 | P a g e
‡ j t ‡_‡ K s ও u Dfq B eo| Zvn ‡hLv‡b, s, u Gi †QvU n‡Z cv‡i Avevi eo n‡Z cv‡i Avevi mgvbI n‡Z cv‡i wKš‘ DfqB t †_‡K eo | Gevi Option ¸‡jv †`Ly b: (i) U>s may be mZ¨ wKš‘ must be mZ¨ bq| (ii) S>q must be true [s>t>r>q] (iii) U>r must be true [u>t>r>q] Ans. E. 17.If b< 2 and 2x-3b = 0, which of the following must be true? (A) X > -3 (B) x <2 (C) x = 3 (D) x < 3 (E) x > 3 Solution: 2x-3b = 0 ev, 2x = 3b ev, 3b = 2x
ev, b =
2 x 3
‡h‡nZz b < 2 2 x <2 3 ev, 2x < 2 3 23 ev, x < 2 x < 3
Ans. D 18. If the product of the integers w, x, y, and z is 770, and if 1 < w < x < y < z, what is the value of w + z? (A) 10 (B) 13 (C) 16 (D) 18 (E) 21 Solution: w xvyz = 770 wxyz = 25711 (factors of 770) w+z = 2+11 = 13 Ans. B
19. If the quotient (A) a > 0
a
is positive, which of the following must be true?
b (B) b > 0
(C) ab > 0
(D) a – b > 0
(E) a + b > 0 77 | P a g e
Solution:
a b
is positive
gvb a‡i wb‡q †PK Kiæb, Avevi, but,
4
2 4 2
4 = positive 2
= positive
= negative
Zvi gv‡b 2 UvB positive A_ev 2 UvB negative n‡Z n‡e; ab (42) > 0 ab (-4-2)>0 Ans. C. ab>0
Geometry:
78 | P a g e
1. Referring to the figure below,
B
C D
(A) 3 (B) 4
(C) 5
(D) 5 2
(E) None
A
Solution:
B
D
C
w`‡q GKwU e„ Ë AvKv hv‡e hvi e¨vm < BAC = 900, ABC Gi kxl© we›`y BC 1 AD = BC 2 1 = 10 = 5 2 Ans. C 2. In the figure,
B
C
E
D
79 | P a g e
(A) 8 (B) 8
2
Solution:
(D) 12 2
(C) 12
(E) None
A 4
C 450
450
B
4
D
E
42 42 CD = 16 16 = 32 AE = CD =
Area of BCE = =
1 2
BECD
1 4 2
32
= 2 32
= 2 16 2 = 24 2 =8 2 Ans. B. 8 2 3. In the figure below, what is the sum of the angles labled g, h and c? a b d f (A) 1800 (B) 2400
(C) 3600
A
B
g (D) 900
c C
e
h i (E) Cannot be determine
Solution: (g+h+c) = (180-B) + (180 – C) + (180 – A) = 1803 – B – C – A = 540 – (A+B+C) = 540-180 =3600 80 | P a g e
Ans. 3600 Ans. C
4. ABCD is a rectangle, find the area of DEBC, given that AD = 6-unit, CD=8 unit and AE = m unit. A
E
B
D (A) 48-3m (B) 3m+16
(C) 24+3m
C (D) 48+3m
(E) 24-3m
Solution: Area of Rectangle ABCD = 6 8 = 48 1 Now, Area of ADE = ADAE 2 =
1 2
6m
= 3m Area of BCDE = Area of ABCD-Area of ADE =48 – 3m Ans. A. 48 – 3m 5. A semicircle is attached to a rectangle whose length is 2a and width is a as shown below. A formula for finding the area of the whole figure is-
a
2a (A) 3 a2 (B) 2a2+ a2
(C) 2a2+( a2)/2
(D) 2 a2
(E) 2a2+2 a2
81 | P a g e
Solution: Circle Gi Radius =
1 2
Length
1 2a= a 2 2 a Semi Circle Gi Area 2
=
And Rectangle Area = 2aa = 2a2
The area of the whole figure = 2a + 2
a2
2
Ans. C 6. Area of the following right angle PQR is 36 units If PQ = 4 and SQ = 5m, what is the area of SQR? Q
R
(A) 30 (B) 24
(C) 20
S
(D) 18
P
(E) 16
Solution: Area of PQR = 36 PQ = 4, SQ = 5 (SQ)2 = (QP)2 + (PS)2 ev, (5)2 = (4)2 + (PS) 2 ev, 25 = 16 + (PS) 2 ev, 25 – 16 = (PS)2 ev, (PS)2 = 9
PS =
9 = 3
Area of SPQ =
1
34
2 =6 Area of SQR = 36 – 6 = 30 Ans. A. 30
82 | P a g e
7. A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true? (A) w2 + pw + k = 0 (B) w2 – pw + 2k = 0 (C) 2w2 – pw – 2k = 0 (D) 2w2 – pw – 2k = 0 (E) 2w2 – pw + 2k = 0 Solution: We know, 2(Width+Length) = perimeter ev, 2(W+L) = p p ev, W+L = 2 p L = w 2 p Area w w k 2 p Now, w w k 2 wp w2 k ev, 2
ev, ev,
wp
2
w2 k 0
wp 2w2 2k
2
0
ev, wp 2w2 2k 0 ev, -1(-wp+2w^2+2k)=0*-1 [ Dfq cÿ‡K -1 w`‡q ¸Y K‡i ] ev , 2w^2-wp+2k=0 Ans. E 8. 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 Solution: wÎfz ‡Ri `y B evûi †hvMdj Aci evû †_‡K eo n‡e
Gevi hvPvB Kiæb I. 5, 3+5 = 8 n‡e bv KviY Aci evûi mgvb, so n‡e bv| II. GUv n‡e| III. (8+3) = 11 hv Aci evûi mgvb, so n‡e bv| Ans. A. 8 only 83 | P a g e
Special Model Test Math Model Test:
1. If a>b in the figure below, (the figure is not drawn to scale,) then which of the following must be true?
A. x<0 B. x=0 C. x>0 D. There is no x that fits the information in the question. E. The information in the question is not sufficient to determine which of the answers A-C is true. 2. What is sum of the eighty-third and eighty-fourth digits to the right of the decimal point when the fraction is written as a repeating decimal? (A) 16 (B) 14 (C) 12 (D) 7 3. Andrew started saving at the beginning of the year and had saved $240 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year? A. 11% B. 25% C. 44% D. 56% E. 125% (E) 5
84 | P a g e
4. If 2^x*3^y*7^z is divisible by 168 and 441. What is the least value of x*y*z if we consider x, y and z integers? A. 3 B. 4 C. 5 D. 6 E. 12 5. If x and y are positive integers, what percent of three more than y is twice the value of x? A 1/200x(y + 3) B y + 3/200x C 100(y + 3)/2x D (200x/y) + 3 E 200x/(y + 3) 6. A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 6/7 times their arithmetic mean, what is the value of x? A. 16 B. 15 C. 14 D. 13 E. 12 7. In the expression 51840/x^4, for which of the following values of x will the expression NOT be an integer? A 1/2 B) 1 C) 2 D) 3 E) 5 8. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ? A. 15 B. 16 C. 17 D. 18 E. 19 9. Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 5H, which of the following represents the amount that Roberta paid? (A) D + 40 (B) D + H – 1 (C) D + 2H (D) 5.95H (E) 1.21D
85 | P a g e
10. If a rectangular picture that measures 4 feet from side to side is hung exactly in the middle of a rectangular wall that measures 13 feet from side to side, then the left edge of the picture is how many feet from the left edge of the wall? (A) 2.0 (B) 3.0 (C) 4.5 (D) 6.5 (E) 9.0 11. If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n? A. 10 B. 11 C. 12 D. 13 E. 14
12. In the figure above, LMNO and GHJK are rectangles where GH = 1/2 LM and HJ = 1/2 MN. What fraction of the region bounded by LMNO is NOT shaded? (A) 1/4 (B) 1/3 (C) 1/2 (D) 2/3 (E) 3/4 13. If x+ (1/x) =4, X^2+ (1/x^2) =? A. 10 B. 12 C. 14 D. 16 14. A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ? A. 10:00am B. 10:45am 86 | P a g e
C. 12:00pm D. 12:30pm E. 1:30pm E. 18 15. If m pencils cost the same as n pens, and each pencil costs 20 cents, what is the cost, in dollars, of 10 pens, if each pen costs the same amount? (100 cents = 1 dollar) A. 200n/m B. 2n/100m C. 2m/n D. 2n/m E. 200nm 16. (The average of five consecutive integers starting from m) – (the average of six consecutive integers starting from m) = (A) – 1/4 (B) – 1/2 (C) 0 (D) 1/2 (E) 1/4 17. The remainder when the positive integer m is divided by n is r. What is the remainder when 2m isdivided by 2n ? (A) r (B) 2r (C) 2n (D) m – nr (E) 2(m – nr) 18. If 1 < p < 3, then which of the following could be true? (I) p^2< 2p (II) p^2= 2p (III) p^2> 2p (A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III
19. If 42.42 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k+m? (A) 6 (B) 7 (C) 8 87 | P a g e
(D) 9 (E) 10
20. The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of (A) 45 (B) 40 (C) 35 (D) 32.5 (E) 30 21. In a certain village, m litres of water are required per household per month. At this rate, if there are n households in the village, how long (in months) will p litres of water last? (A) p/mn (B) mn/p (C) mp/n (D) np/m (E) npm 22. 6 pints of a 20 percent solution of alcohol in water are mixed with 4 pints of a 10 percent alcohol in water solution. The percentage alcohol in the new solution is (A) 16 (B) 15 (C) 14 (D) 13 (E) 12 23. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps? A) 5:1 (B) 10:5 (C) 15:2 (D) 20:2 (E) 25:2 24. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set? (A) 4 (B) 7 (C) 8
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(D) 12 (E) Can not be determined 25. If n ≠ 0, which of the following must be greater than n? I 2n2 II n² III 2 - n (A) I only (B) II only (C) I and II only (D) II and III only (E)None
1. A, 2. B, 3. B, 4. E, 5. E, 6. A, 7. E, 8. C, 9.E, 10. C, 11. B, 12. E, 13.C, 14. D 15. E, 16.B, 17.B,18.E, 19.E, 20. B, 21. A, 22. A,23.E 24.D 25.E
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Vocabulary Practice Book.
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GRE Math Bible Solutions by Team Ramrod.
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Official GMAT Math Solutions by Team Ramrod.
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