3121gmat wrote:

Hi, I'm struggling to understand the concept behind a particular perfect squares question. Could anybody help?

If 375y = x^2, and x and y are positive integers then which of the following must be an integer?

I. y/15

II. y/30

III. y^2/25

As I'm new to this forum, please do advise if I've used incorrect symbols or haven't laid everything out as per standard practice. Thanks in advance.

Welcome on board!

1. Looking 375y=x^2 tells us that y has to also be 375 in order for x to be a perfect square.

2. Breakdown 375 to its prime factor---- (5*5*5*3)=y

3. Now it's much easier to compare each statement.

I. y/15----> Yes (quotient=25)

II.y/30----> No (quotient=25/2)

III.y^2/25----> Yes (quotient=5625)