Hopefully I can be succinct here, lets see.
If n is a multiple of 5, then n can be expressed as 5x where x is an integer.
If I substitute in the following eqn, I get 5x = p^2 * q
Now I know that, since x is an integer, that:
{1} (p^2 * q)/5 is also an integer.
If {1} is an integer and p and q are primes, the only way this can be an integer is if either p is 5 or q is 5. That leaves two things to consider, (1) p is 5 and q is some other prime number OR (2) p is some other prime and q is 5.
Now I'll look at each answer choice under each scenario side-by-side. The correct answer choice will be the one that is divisible by 25 under either circumstance (clue is "which answer choice MUST be divisible by 25).
Answer choice A, (1) 25; (2) q^2
Answer choice B, (1) p^2; (2) 25
Answer choice C, (1) 5q; (2) p5
Answer choice D, (1) 25q^2; (2) (p^2)25
Answer choice E, (1) 125q; (2) (p^3)5
As you can see, only Answer choice D offers both parts being divisible by 25.
Good luck, I have a feeling that I'll have to explain this one.
