2015 Metrobank MTAP DepEd Math Challenge Eliminations Level-Grade 5 Directions: Check your answers. Analyze the solution given in every question. Be sure you deeply understand the concepts involved. Test yourself again by answering the questions. 1.) Write the missing number: 1, 3, 2, 6, 3, 9, 4, ___. Solution: 1, 3, 2, 6, 3, 9, 4, 12. Answer: 12 2.) Using only the number 87, how many times will you use it as a factor to get a product whose ones digit is 7? Solution: 87x87x87x87x87 = 4 984 209 207 Answer: 5 3.) Write three hundred thousand twelve and 5 tenths in symbols. Answer: 300 0012. 5 4.) How many 0.001 are there in 1 000? Solution: 1 000 ÷ 0.001 = Answer: 1 000 000 5.) The ratio of two numbers is 7:9. If their difference is 24, what is their sum? Solution: 9n-7n = 24 9n= 9 x 12 = 108 2n = 24 7n= 7 x 12 = 84 n = 24 ÷ 2 108 + 84 = 192 n = 12 Answer: 192 6.) When Daria bought a glass of juice for Php 15.00 and a sandwich for Php 37.00, she still had Php 73.00 left in her wallet. How much money did Daria have at the beginning? Solution: Php15.00 + Php37.00 + Php73.00 Answer: Php 125.00
7.) How many 3 cm by 3 cm square tiles can cover a square floor with an area of 36 cm^2. Solution: Area of square tile = 3 cm x 3cm = 9 cm 2 Area of floor/ area of square tile 36 cm2 ÷ 9 cm2 = 4 Answer: 4 square tiles 8.) The volume of a rectangular block is 30, 000 cm^3. What is its volume in dm^3? Solution: 1 dm3 = 1 000 cm3 30 000 cm3 ÷ 1 000= 30 Answer: 30 dm3 9.) The product of 2 two-digit numbers is 351. What is their sum? Solution: 351 = 27 x 13; 27 + 13 =40 Answer: 40 10.) If 2 * 5 = 3, 4 * 9 = 5, and 5 * 12 = 7. What is 12 * 17? Answer: 9 A-5 11.) How many 15 thousandths are there in 3/8? Solution: = 3/8 ÷ 15/1000 = 3000/120 = 25 Answer: 25 12.) What is the sum of the digits in the product of 23 tens and 32 ones? Solution: 23 tens = 230 32 ones = 32 230 x 32 = 7, 360 Sum of the digits= 7 + 3 + 6 + 0 = 16 Answer: 16 13.) What is the sum of 3 consecutive whole numbers if the smallest of these numbers is 9? Solution: consecutive numbers are 9, 10, 11
9 + 10 + 11 = 30 Answer: 30 14.) What is 1/5 of the sum of 6 tens and 5 ones? Solution: 6 tens = 60 ; 5 ones = 5 60 + 5 = 65 1 of 65 = 1 x 65 = 65 = 13 5 5 1 5 Answer: 13 15.) Dolly had Php 155.00. She bought a glass of juice for Php 18.00 and a sandwich for Php 41.00. How much money did she have left? Solution: Total Expenses (juice + sandwich) = Php18.00 + 41.00 = Php59.00 Total Money – Expenses = Php155.00 – 59.00 = Php96.00 Answer: Php 96.00 16.) Marissa called her friend at 10:15 am. They talked for 157 min. What time did their conversation end? Solution: 157 minutes is equivalent to: 157 x 1 = 157 = 2 hours and 37 minutes 60 60 10:15 + 2 hours and 37 minutes = 12:52 Answer: 12:52 pm 17.) Liza wants to buy a cake for her mother on her birthday. She already has Php 460.00. The cake costs Php 675.50. How much more does she need to buy the cake? Solution: Php675.50 – 460.00 = Php215.50 Answer: Php 215.50 18.) How many 25-centavo coins are equal to Php 5.00? Solution: 1 peso = 4 25-centavo coins 5 pesos = 4 x 5 = 20 Answer: 20
19.) If two congruent equilateral triangles are placed side by side, what kind of shape is formed? Solution: Answer: rhombus 20.) What is the value of 15 + 3 x 2 – 6 ÷ 3 – 1 x 3? Solution: 15 + 3 x 2 – 6 ÷ 3 – 1 x 3 15 + 6 – 2 – 3 21 – 2 – 3 19 – 3 16 Answer: 16 21.) The cost of a box of chocolate decreased from Php 120.00 to Php 115.00. What percent of the original price is the amount of decrease? Solution: Php120.00 – Php115.00 = 5.00(discount) Rate of discount = discount ÷ original price = 5 ÷ 120 = 0.04166 = .04166 x 100% = 4.166% Answer: 4.166% 22.) Mark, Thea, Lota, and Lito want to divide 140 pieces of marbles in the corresponding ratio of 1:2:4:7. How many more marbles will Lota get than Mark? Solution: Partitive proportion = 1n + 2n + 4n + 7n = 14n 140 = 14n 140/14 = n 10 = n Lota = 4 x 10 = 40; Mark = 1 x 10 Lota – Mark = 40 – 10 = 30 Answer: 30 marbles 23.) A tank has a capacity of 50 liters. How many seconds will it be filled if the flow rate into it is 2.5 liters per seconds? Solution: 50 ÷ 2.5 = 20 Answer: 20 seconds.
24.) What is the missing number in the sequence? 1, 3, 5, 10, 18, 32, ___. Solution: 1 + 3 = 4 + 1 = 5 3 + 5 = 8 + 2 = 10 5 + 10 =15 + 3 = 18 10 + 18=28 + 4 = 32 18 + 32=50 + 5 = 55 Answer: 55 25.) What is the sum of all the numbers in the set {2 3,32,43,34}? Solution: 23 = 2x2x2= 8 32 = 3 x3 = 9 43 = 4x4x4 = 64 34 = 3x3x3x3 =81 (8+9+64+81) = 162 Answer: 162 26.) An airplane arrived at 10:45 am. It was delayed for 1 hour and 25 minutes. If the flight time is 1 hour and 30 minutes, what time was the airplane supposed to depart? Solution: 10:45 am 9:20 - 1:25 - 1:30 9:20 7:50 am Answer: 7:50 am 27.) On 6 December 2014, Risa bought a load worth Php 300.00 for her cellphone. If the load is valid for 75 days, until when is the load available if December 6 is included in the 75 days? Solution: Dec.6- Dec. 30 = 26 days Jan. 1–Jan. 31= 31 days (26 + 31 = 57 days) 75 days – 57 days = 18 days, Answer: February 18, 2015 28.) The average of one set of 3 numbers is 25 and the average of another set of 5 numbers is also 25. What is the average of the 8 numbers? Solution: 3 x 25 = 75 ÷ 3 = 25 5 x 25 = 125 ÷ 5 = 25
8 x 25 = 200 ÷ 8 = 25 Answer: 25 29.) Lina’s weekly transportation expenses reduced by 75% when she joined her aunt in going to school. If she used to spend Php 140.00 a week, how much does she spend now for transportation? Solution: Php140.00 x .75 = Php105.00 Php140.00 – Php105.00 = Php35.00 Answer: P 35.00 30.) 34 – 6 ÷ 3 + 8 x 4 is ___ Solution: 34– 6 ÷ 3 + 8 x 4 34 – 2 + 32 32 + 32 = 64 Answer: 64 31.) If 50% of a number is 500, how many percent of the number is 250? Solution: Base= percentage/ Rate Rate= P/B =500 ÷ 50% =250 ÷ 1000 =500 ÷ .50 =0.25 =1000 =25% Answer:25% 32.) Observe the pattern: 2, 5, 8, 11, 14, … If the pattern continues, what is the 30th number? Solution: (n-1) x interval+ the first number =(30-1) x 3 + 2 =29 x 3 + 2 =87 + 2 = 89 Answer: 89 33.) What number is 2/3 between 7 and 13? Answer: 11
34.) An airplane departed at 2:15 pm and flew for 1 ½ hours. It arrived 25 minutes earlier than the scheduled arrival. What should have been its scheduled arrival? Solution: 2:15 + 1 ½ hour = 3:45 pm 3:45 pm + 25 minutes = 4:10 pm Answer: 4:10 pm 35.) The vertex of an isosceles triangle is 36 degrees. What is the measure of its base angle? Solution: Isosceles Triangle = 1800 =1800 - 360 = 1440 Isosceles means two sides are equal so; 1440 ÷ 2 = 720 Answer: 72 degrees 36.) The perimeter of an equilateral triangle and a rhombus are both equal to 45 cm. How many cm shorter is a side of the rhombus than a side of the triangle? Solution: Perimeter = 45 cm = 45 cm ÷ 3 = 15 cm each side of triangle Perimeter = 45 cm = 45 cm ÷ 4 = 11.25 cm each side of rhombus = 15 cm – 11.25 cm = 3.75 cm Answer:3.75 cm 37.) The sum of 2 numbers is 80. Their difference is 16. What is the quotient when the bigger number is divided by the small number? Solution: = 80–16 = 64 = 64 ÷ 2 = 32 smaller number = 32 + 16 = 48 bigger number =48 ÷ 32= 1.5 Answer: 1.50 38.) A tray of salted eggs contains 30 pieces. Each piece costs Php 11.00. Liza sells each egg at Php 11.75. How much is her profit if she sold 6 ½ trays of salted eggs? Solution: 6 ½ x 30 = 195 195 x 11 = Php2 145.00
195 x 11.75 = Php2 291.75 Php2 291.75- 2 145.00= 146.75 gain Answer:Php146.25 39.) Ernesto is weighing his school bag. He says “if I add 725 grams, it will weigh 2 kilograms”. How many grams does his bag weigh? Solution: 2 kilograms = 2000 grams 2000 grams – 725 grams = 1,275 Answer: 1, 275 grams 40.) There are 36 packs of candies in a box. The packs of candies are divided equally among 4 children. How many packs will each child receive? Solution: 36 packs ÷ 4 children = 9 Answer: 9 packs 41.) Twenty seven apples are put in box. There are 6 boxes. How many boxes contain exactly the same number of apples? Answer: 5 boxes 42.) Liza has read 4/5 of the total number of pages of a book. Today, she reads 21 pages. She still needs to read 1/10 of the total number of pages to finish reading the book. How many pages does the book have? Solution:Change 4/5 and 1/10 in similar fractions 4/5 is 8/10 and 1/10 is 1/10, therefore to complete 1 whole 21 is 1/10 of the number. Find the base: base = percentage/ rate = 21÷1 = 210 = 210 10 1 Answer: 210 pages 43.) Alice has 47 apples. She is going to give them equally to 6 children. How many more apples are needed so that each child will receive 9 apples? Solution: 6 children x 9 apples = 54 = 54-47 =7
Answer: 7 apples 44.) A container holds 8 times the amount of water in a cup that holds 2 deciliters of water. How many deciliters of water can be poured into the container? Solution: 8 x 2 dl Answer: 16 deciliters 45.) Each marble weighs 25 grams. The total weight of the marbles is 2 kilograms. How many marbles are there in the box? Solution: 2 kg = 2000 grams 2000 grams ÷ 25 grams = 80 Answer: 80 marbles 46.) An 8-meter ribbon costs Php 96.00. How much is the cost of 4.5 meters of ribbon? Solution: Php96.00 ÷8 m = Php12.00/ meter Php12.00 x 4.5 meters = Php54.00 Answer: Php 54.00 47.) Which fraction is the smallest? 3/5, 2/3, ¾, 4/7 Answer: 4/7
48.) Mark added 2 to a number then divided the sum by 3. He multiplied the quotient by 10 then subtracted 7 from the product and got a difference of 23. What was the number he started with? Solution: n+2÷3x10-7=23 (work backward) 7 = 2 -9 = 3 x 3 = 10 ÷ 30 Answer: 7 49.) A ribbon is 4 m and 60 cm long. Rissa cut it into shorter pieces each with a length of 50 cm. What is the length of the piece that was left? Solution: 4 meters and 60 cm = 400 cm + 60 cm = 460 cm = 460 cm ÷ 50 cm = 9 pcs remainder 10 cm Answer: 10 cm
50.) The area of the square ABCD below is 16 cm 2. If CE = 1 cm, what is the area of triangle ABE? Solution: 16 cm2 = 4cm x 4cm 4 cm measurement of a side 4 cm – 1 cm = 3cm Area of triangle = base x height 2 =4x3 2 =6 cm2 Answer: 6 cm2
