GMAT PREP Divisibilty Problem Help

[Niner710]

I wasn't sure about this question. Could someone explain the answer? Thanks.

If n is a multiple of 5 and n = (p^2)q, where p and q are prime numbers, which of the following must be a multiple of 25 ?

(A) p^2
(B) q^2
(C) pq
(D) (p^2)(q^2)
(E) (p^3)q

[linkinpark]

IMO D
n is multiple of 5 means n/5 is perfect number i.e. 0 remainder

so is [p^2 * q ] and p,q are primes so one of both is 5 whatever other number may be p*q will be multiple of 5
now from answer choice reject A and B because we don't know whether P or Q is 5

C will not give a number which is multiple of 25, and we want 5^2 to be present in the required number, only D has both P and Q square so condition is satisfied. again with E we don't know which number is 5

[papgust]

IMO D

Since n is a multiple of 5, either p or q has a 5 since both are prime.

But we are not sure which has a 5 (p or q). By squaring either p or q alone, we cannot say whether we are squaring a 5 or not. So eliminate A and B.

Choices that doesn't square p or q also do not make sure whether we are squaring a 5. So eliminate these choices.

To be safe enough to be sure that we are squaring a 5, we must square both p and q. Now we are sure that we have squared a 5 and say that it has a 25 for sure.

[viju9162]

nice reply papgust. I took long time to figure it out ...

Regards,
Viju

[tanviet]

I see number property is hard. I can solve this at home but on the test usually I can not do so.

so, any one can have solution for my problem.

[papgust]

Even i tend to do that. Normally, i'm able to think well when i'm simply practicing. But when i do that in a test, i tend to commit mistakes which i would never do while practice. Truly, stress gets to us while doing a test. We should actually learn to control stress. Just by doing tons of problems will never help us.