MTAPGrade 6 Individual ORAL With Solutions

2009 METROBANK-MTAP-DEPED MATH CHALLENGE NATIONAL FINALS GRADE 6 INDIVIDUAL ORAL Part 1: 15 seconds (10 items) 1. If 45 x n = 805, what is the value of 45 x n + 7? Solution 45 x n + 7 = 805 + 7 = 812 Answer: 812 2. Gold purity ratings are proportional. If a 24-carat gold is 100% pure, what is the purity of an 18-carat gold? Solution 18 3 = = 75% 24 4

Answer: 75% 3. What number should be added to the numerator and denominator of fraction that is equivalent to

1 to get a 3

3 ? 4

Solution

1+5 6 3 = = 3+5 8 4

Answer: 5

4. All 7 sticks of equal lengths will be used to form a triangle. How many such triangles can be formed? Solution A triangle with sides 2 sticks, 2 sticks, and 3 sticks can be formed. Another triangle with sides 1 stick, 3sticks, and 3 sticks can also be formed. So there are 2 different triangles. Answer: 2 5. You are asked to cut a 20-cm long stick into 10 equal lengths. How long will it take you if each cut takes 3 seconds? Solution 9 cuts x 3 seconds = 27 Answer: 27 seconds 6. It takes one man one day to dig a 2m x 2m x 2m hole. How many days does it take 3 men working at the same rate to dig a 4m x 4m x 4m hole? Solution 8 m3 2m x 2m x 2m = per person day 8 m3 per person x 3 persons = 24 m3 in one day for 3 persons day

4m x 4m x 4m Answer:

÷ 24 m3 per day =

64 8 = days 24 3

8 2 or 2 3 3

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7. If x + y = 12, y + z = 20, and x = 5, what is z? Solution In x + y = 12, y = 7 since x = 5. In y + z = 20, z = 13 since y = 7. Answer: 13 8. If 50% of a number is 20, what is 80% of the number? Solution 50% of a number is 20, so the number is 40. 40 x 0.8 = 32 Answer: 32 9. If the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are all multiplied together, how many zeros are at the end of their product? Solution When 2 is multiplied by 5, there will be a zero at the end of their product. Also, when 10 is multiplied by any number there will be a zero at the end of their product. So there are 2 zeros at the end of the product of 1, 2, 3, 4, 5, 6, 7, 8, 9, and10. Answer: 2 10. What is 1010 divided by 1 billion? Solution 1010 has 10 zeros while 1 billion has 9 zeros, so1010 Answer: 10

÷ 1 billion = 10

Part 2: 30 seconds (5 items) 1. Aling Edna sells mangoes in bags of 5 kg and 10 kg. She has a total of 250 kg to sell in all. If she sells twice as many bags of one than the other and all the mangoes are sold, how many bags of 10 kg mangoes each are sold? Solution 10 x 5 kg + 20 x 10 kg = 50 + 200 = 250 kg Answer: 20 2. There are as many boys as there are girls. When 16 boys left, the number of remaining boys became half the number of girls. How many pupils were there at the start? Solution At the start, the number of boys equals the number of girls. When 16 boys left, the number of remaining boys became one half the number of boys at the start. So there were 32 boys at the start. And there were 64 pupils in all at the start. Answer: 64 3. What is the sum of 40% of

1 1 and 50% of ? 4 5

Solution 4 5 1 1 2 1 + = + = = 40 50 10 10 10 5

Answer:

1 or 0.2 5

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4. A 7 unit x 7 unit x 7 unit big cube is painted on all faces and then cut into unit cubes. How many of the unit cubes have no paint? Solution Removing all the unit cubes on the surface of the big cube will give a 5 unit x 5 unit x 5 unit cube. So there are 125 unit cubes that have no paint. Answer: 125 5. What is the area of the trapezoid below? (Note: A printed strip will be given to each contestant.)

One possible solution:

1 2 3

Figure 1

Figure 2

Figure 3

In Figure 1, the total area of the 2 triangles is 2 square units. In Figure 2, the total area of the 3 squares is 3 square units. In Figure 3, the total area of the 5 triangles is 2.5 square units. Area of the trapezoid = 7.5 square units. Answer: 7.5 square units Part 3: 60 seconds (5 items) 1. A pail that contains 40 nails of the same weight, weighs a total of 175g. When it contains 20 such nails, it weighs a total of 95g. What is the weight of each nail? Solution 175 - 95 = 80g 40 - 20 = 20 So, 20 nails weigh 80g. 80 ÷ 20 = 4g Answer: 4 g 2.

In a 40-item multiple choice type of test, scoring is done as: 1 point for correct answer 1 point for incorrect answer 4

0 for no answer Lina had items with correct, incorrect and no answers. She got a score of 32. How could she have gotten it?

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Solution Having 29 correct answers is not possible because this means that there will be 12 incorrect answers and the total number of items will be 41 which is already over 40 without accounting for the items with no answer. Having 32 correct answers is not possible because there will be no items with incorrect and no answer but it is given that Lina had incorrect answers, and no answers. Answer: 30 correct, 8 incorrect, and 2 no answer; or 31 correct, 4 incorrect, and 5 no answer 3.

Observe the following pattern: 1 3 5 7 9 11 13 15 17 19 In which row is the sum of the numbers equal to 343? Solution The sums of the numbers in the rows are 1, 8, 27, and 64 which are all perfect cubes, i. e. 13, 23, 33, and 43, respectively. Continuing the pattern, the sums are 125, 216, and 343, i.e. 53, 63, and 73. So it is the 7th row. Answer: 7th or 7

4. Two opposite sides of a square were increased by 6 cm. The other two opposite sides were decreased by 6 cm. By how much was the area changed? Solution Take any square with area greater than 6 cm say a 10 cm x 10 cm square. Its area is 100 square cm. Considering the conditions given in the problem, the resulting figure becomes 16 cm x 4 cm. So the area is 64 square cm. Therefore the area decreased by 36 square cm. Answer: [It decreased by 36 square cm.] 5. Different rectangular prisms will be formed out of 16 unit cubes. What are the dimensions of the prism with the least surface area? Solution The possible rectangular prisms would have dimensions: 1unit, 1unit, and 16 units; 1unit, 2 units, and 8 units; 1unit, 4 units, and 4 units; and 2 units, 2 units, and 4 units. The rectangular prism with the least surface area has dimensions 2 units, 2 units, and 4 units. Answer: 2 units, 2 units, 4 units

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