Ok, so we know p^2*q is divisible by 5.

Suppose p = 3, and q = 5. That would equal 45. Disproves (A), (C), and (E).

Now suppose p = 5 and q = 3. That would equal 75. This disproves (B).

However, D has held true in both scenarios, so that's the answer.

This makes sense, in hindsight of course. To be divisible by 5, there must be a factor of five. Either q or p equals 5, since we are given that q and p are prime.

However, both do not have to equal 5, so therefore the only way to ensure that 25 is a factor of the resulting number is to square BOTH p and q, as 5x5 is 25.

POE is the best method for this.

Since the questions says "which of the following must be ...", it means that the answer options dont have a choice but to be true for any random legitimate value (i.e. no conditions on what values to choose).

try plugging in random values for p and q to satisfy the original equation, and keep eliminating incorrect ans. options.

i hope this helps - please let me know if further explanation required.

many thks
oa is D