Grade 7 MTAP 2015 Questions with Solutions Part 4

This is the fourth part of the Metrobank-MTAP Math Challenge Questions for Grade 7. In this post, we discuss the solutions to number 21-30. You can also read the solutions to 1-10, 11-20, and 21 – 30.

31.) If $n$ is a prime number not equal to 2, which of the following can be a prime:

$n + 3$, $2^n - 1$, $n^2 + 1$.

Solution

All prime numbers not equal to 2 are odd. If $n$ is odd, then $n + 3$ and $n^2 + 1$ are both even, while $2^n - 1$ is odd. Therefore, only $2^n - 1$ can be a prime.

Answer: $2^n - 1$

32.) What must be added to the product of $2x - 1$ and $4x +5$ to obtain $4x^2 + 8x + 1$Continue reading “Grade 7 MTAP 2015 Questions with Solutions Part 4”

Grade 7 MTAP 2015 Questions with Solutions Part 3

This is the third part of the Metrobank-MTAP Math Challenge Questions for Grade 7. In this post, we discuss the solutions to number 21-30. You can also read the solutions to 1-10 and 11-20.

21.) The average of five numbers is 14. The average of the three of the numbers is 12. What is the average of the other two numbers?

Solution

The average of five numbers is 14 means that their sum is 70. The average of the three of those numbers is 12 means that their sum is 36. Now, 70 – 36 = 34 is the sum of the remaining two numbers. Their average is 34/2 = 17.

22.) A sandwich costs p pesos. A cookie costs Php9 pesos less than a sandwich. How much more expensive are 8 cookies than 5 sandwiches?  Continue reading “Grade 7 MTAP 2015 Questions with Solutions Part 3”

Grade 7 MTAP 2015 Questions with Solutions Part 2

This is the second part of the full solution series for the MTAP 2015 Questions with solutions. You may also want to read the solutions for problems 1 – 10 and download the questions.

11.) Danny had some stickers. He gave 1/3 of the stickers plus 1 sticker to his brother. Then, he gave 1/3 of the remaining stickers plus 4 stickers to his sister. Finally, he gave ½ of what remained plus 3 stickers to best friend. He found that he had 4 stickers left. How many stickers did Danny have at first?

Solution
If we let $x$ = number of stickers
$\frac{1}{3}x + 1$ = number of stickers given to his brothers. If we subtract the stickers given to his brother, we have  Continue reading “Grade 7 MTAP 2015 Questions with Solutions Part 2”

Grade 7 MTAP 2015 Questions with Solutions Part 1

Below are actual MTAP Questions that has been released. I have created a detailed solution for each question. In this post, we answer 1-10. You can also read the solutions of problems 2-20.  The file can be downloaded here.

1.) Simplify: $2(3)^2 - 3(2)^3 + (1 - 4)^3$

Solution
$2(3)^2 - 3(2)^3 + (1-4)^3$
$= 2(9)- 3(8) + (-3)^3$
$= 18 - 24 + (-27)$
$= -33$

Answer: $-33$

2.)  By how much is 3 – 1/3 greater than 2 and 1/2?

Solution

$3 - \frac{1}{3} = 2 \frac{2}{3}$
$2 - \frac{1}{2} = 1 \frac{1}{2}$

Subtracting the two results, we have  Continue reading “Grade 7 MTAP 2015 Questions with Solutions Part 1”

Grade 6 MTAP Reviewer – Set 9

This is the 9th set of the MTAP Reviewer for Grade 6.

1. Yana bought 20 blouses for Php300 each. He sold 10 blouses at a 20% profit and the remaining at a 10% profit. How much was her profit after selling all the t-shirts?
2. What is the sum of 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9?

3. Amy baked a cake and gave ½ to her children. He gave 1/3 of the remaining cake to her neighbors. What fraction of the cake was left?

4. Karen started studying at 7:45pm last night. She said that she studied for 2 hours and 30 minutes with a 15-minute snack break. What time did she finish studying?

5. The volume of a cube is 125 cubic centimeter. What is its surface area?

6. The sum of two numbers is 51. One is twice the other. What are the numbers?  Continue reading “Grade 6 MTAP Reviewer – Set 9”