Where did you find this question? You're right, the given answer doesn't make sense. Furthermore, a real GMAT question would have said "which of the following MUST be an integer?" All 3 of the answer choices could potentially be integers, but only the first one must be.

If n^3 = 450y, then n^3 = (2)(3^2)(5^2)y

Since we know that in any cube, all of the prime factors must be in groups of 3, then we know that y must contain at least the extra factors to get us to (2^3)(3^3)(5^3). 450 on contains one 2, two 3's, and two 5's. So, y must contain at least (2^2)(3)(5) to get three of each factor. y might also contain other prime factors in groups of 3 - it might contain 7^3, or an extra 3^3, etc - but we don't know. All that we know it that it must contain at least (2^2)(3)(5) to make n^3 a cube.

If y contains (2^2)(3)(5), then it will be divisible by those things. So, statement I must be an integer. However, we can't prove that y is definitely divisible by 3^2 (unless it's also divisible by 3^4 - the extra 1, plus another set of 3). Statement II is actually wrong.

Beware of studying from sources that contain incorrect information!