If k is a multiple of 3 and \(k = (m^2)n\), where m and n are prime numbers, which of the following must be a multiple of 9?

(A) \(m^2\)
(B) \(n^2\)
(C) \(mn\)
(D) \(mn^2\)
(E) \((mn)^2\)

Source: Gmat Hacks 1800
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Since 'm' and 'n' are primes, In order for k to be a multiple of 3 either 'n' or 'm' must be 3. Also, In order to be a multiple of 9 the product must have two 3's as factors.
A) No. 'm' could be 3 or 'n' could be 3 we don't know which one
B) No. Same logic as above.
C) No. 'm' and 'n' could both be 3 in which case it would work. But they could also be '5' and '7' or some other pair of primes.
D) No. n^2 could be 3^2 or it could be 5^2 (or some other prime number)
E) Correct Answer. Since 3 must be one of the numbers, squaring the product must yield 9 as a factor.

This question is almost exact copy of the following GMAT Prep question: if-is-n-is-multiple-of-5-and-n-p-2-q-where-p-and-q-are-prim-92383.html
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A) No since n could be 9
B) No since m=3
C) No since m could be 2 and n=3
D) No since M could 3 and n=2
E) Yes since either M or N have to be 3 (or factor) so they will become a factor of 9