If n is a multiple of 5 and n = p²q

[shah-kartik]

If n is a multiple of 5 and n = p²q, where p and q are prime numbers, which of the following must be a multiple of 25?
1. p²
2. q²
3. pq
4. p²q²
5. p³q

My query:
This problem is from GMATPrep (old) Practice test 02
I have hit the dead-end with this question. Au secours!!

Thanks

[kyle_proctor]

Not 100% sure. Here is how I approached the problem.

Test two cases: N = 20 and N =50

Both cases are multples of five.


20 = 2^2 x 5 (P = 2 and Q = 5)

50 = 5^2 x 2 (P = 5 and Q = 2)


Test both cases in the answer choices. Only answer choice D yields a multiple of 25 for both cases. I am sure you will receive better direction but that's my thought-process. Simply prove the answer choices incorrect and you should arrive at the correct one. Curious to know if D is in fact correct. lol

[RonPurewal]

search the forum please, thanks.

np-prob-if-n-is-a-multiple-of-5-and-n-p-2-q-where-p-and-q-t4333.html