Gags - Each prime factor of a cubed integer must also be cubed. So if a, b, and c are the prime factors of n, a^3, b^3, and c^3 must be factors of n^3.
We see that n^3 is equal to 450*y. Doing the prime factorization of 450 gives us 2*3*3*5*5. So we have 2, 3^2, and 5^2. Because 450*y is equal to a cube, y needs to complete the cube by filling in the missing factors. So y must include 2^2, 3, and 5.
Now look at the answer choices. A has exactly those factors in the denominator, which means that they must completely cancel out and leave only the numerator, i.e. an integer. B has an extra 3 in the denominator, and C has an extra 5 in the denominator. We cannot be sure that these will cancel out, so we cannot be sure that B or C will be an integer.
I hope that helped.
