# Problem Solving Select Many GRE Sample Questions 9

## GRE Problem Solving Select Many Sample Questions

1. Question:

Which of the following numbers is divisible by 18? Indicate all correct choices.

• A. 12345678
• B. 87654321
• C. 13246587
• D. 87651234
• E. 54321876
Correct Answer: A, D and E

Explanation:

A number is divisible by 18 if it is even and it is divisible by 9.

1+2+3+4+5+6+7+8= 36

Since all the given numbers are formed from these digits, we just have to check for even numbers.

The even numbers are in options A, D and E, which are divisible by 18.

2. Question:

Which of the following is a perfect square? Indicate all such options.

• A. 36
• B. 47
• C. 900
• D. 100000
• E. 800

Explanation:

sqrt(36) = 6

47 is not a perfect square.

sqrt(900) = 30

100000 is not a perfect square.

800 is not a perfect square.

Options A and C are true.

3. Question:

Which of the following numbers can be multiplied with a prime number to give a perfect cube? Indicate all correct choices.

• A. 1944
• B. 72
• C. 196
• D. 243
• E. 1715

Explanation:

1944 = (2*2*2)*(3*3*3)*(3*3)

When multipled by 3, 1944 becomes a perfect cube.

72 = (2*2*2)*(3*3)

When multiplied by 3, 72 becomes a perfect cube.

196 = (2*2)*(7*7)

When multiplied by 14, 196 becomes a perfect cube. But 14 is not a prime number.

Hence option C is not true.

81 = (3*3*3)*3

When 81 is multiplied by 9, it becomes a perfect cube. But 9 is not a prime number.

Option D is not true.