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# If k is a multiple of 3 and k = (m^2)n, where m and n are

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Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]
megafan wrote:
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

must be a multiple of 9
m and n are prime...lets have 2 and 3
now either of then can be a 3...
a) m can be 2 and n = 3...out
b) n can be 2 and m = 3...out
c) m = 2 and n=3 ...out
d) n can be 2 and m = 3...out
e) m = 2/3 or n = 3/2 both satisfies .......must be a multiple of 9
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Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]
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megafan wrote:
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

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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Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]
Either m or n is 3,
so "E" is correct
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Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]
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
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If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]
Top Contributor
If k is a multiple of 3 and $$k = (m^2)n$$ then $$(m^2)n$$ will also be a multiple of 3

Since both m and n are prime numbers, so either m is 3 or n is 3 or both are 3
In any case, m*n will be a multiple of 3
=> $$(mn)^2$$ will be a multiple of $$3^2$$ or 9

So, $$Answer will be E$$
Hope it helps!
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Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]
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Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]
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