The basic way to solve this is to look at the factors of 375:
Since we need pairs of everything for this to be a perfect square, we know that y must include, at a minimum, one 5 and one 3. There may be other terms, but these are a minimum. We'll call the other terms a*a (since they must also be in pairs)
Looking at statement III:
y^2 contains two 3's and four 5's at a minimum.
This gives us
3*3*5*5*a*a / 25.
We know that the 25 cancels with two of the 5's, leaving us with an integer value in the numerator and nothing in the denominator. Thus, the answer is an integer.