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# If p and q are positive integers, is pq a multiple of 36?

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Math Expert
Joined: 02 Sep 2009
Posts: 58415
If p and q are positive integers, is pq a multiple of 36?  [#permalink]

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28 Mar 2018, 23:57
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Difficulty:

35% (medium)

Question Stats:

76% (01:13) correct 24% (01:51) wrong based on 28 sessions

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If p and q are positive integers, is pq a multiple of 36?

(1) p = 6x , where x is a prime number.
(2) q = 15y, where y is a positive integer.

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Re: If p and q are positive integers, is pq a multiple of 36?  [#permalink]

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29 Mar 2018, 01:45
Bunuel wrote:
If p and q are positive integers, is pq a multiple of 36?

(1) p = 6x , where x is a prime number.
(2) q = 15y, where y is a positive integer.

Prime factorization of 36 gives us:
$$36 = 6*6 = 2^2*3^2$$

(1) : p = 6x .. Insuff we do not know anything about q!

(2) : q = 15y ..Insuff don't know anything about p

(1) + (2) : $$pq = 2*3^2*5*x*y$$ Insuff as we need another factor of 2 from x or y and that cannot be guaranteed.

Hence Option (E) is our answer.

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Re: If p and q are positive integers, is pq a multiple of 36?   [#permalink] 29 Mar 2018, 01:45
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