# GRE Problem Solving Select Many SAMPLE QUESTIONS-2

## GRE Problem Solving Select Many Sample Questions

1. Question:

By which number can 6728 be divided so that the resulting number is a perfect square? Indicate all correct options.

A. 2

B. 4

C. 8

D. 29

E. 58

Correct Answer: A and C

Explanation:

6728= 2*2*2*29*29

6728/2=2*2*29*29 which is a perfect square

6728/4=2*29*29 which is not a perfect square

6728/8=29*29 which is a perfect square

6728/29=2*2*2*29 which is not a perfect square

6728/58=2*2*29 which is not a perfect square

Options A and C are true.

2. Question:

Find the value of 64^(1/5)*512^(1/5). Indicate all correct options.

A. 16

B. 8

C. 4

D. 2^(2/3)

E. 2^3

[x^2 = x*x]

Correct Answer: B and E

Explanation:

64^(1/5)*512^(1/5)

= (64*512)^(1/5)

= (8^2*8^3)^(1/5)

= [8^(2+3)]^(1/5)

= 8^(5/5)

= 8 = 2^3

Options B and E are true.

3. Question:

If a^2+b^2=45 and ab=18, then which of the following is equal to 1/a+1/b? Indicate all correct options.

A. 1/4

B. 2/3

C. 1/2

D. -1/2

E. -1/4

[b^2=b*b]

Correct Answer: C and D

Explanation:

1/a+1/b = (a+b)/ab

= sqrt[(a+b)^2]/ab

= sqrt(a^2+b^2+2ab)/ab

= sqrt(45+2*18)/18

= sqrt(81)/18

= +9/18,-9/18

= +1/2, -1/2

Options C and D are true.