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# For positive integer n, is 12 a factor of n?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6823
GMAT 1: 760 Q51 V42
GPA: 3.82
For positive integer n, is 12 a factor of n?  [#permalink]

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11 May 2017, 00:24
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Difficulty:

25% (medium)

Question Stats:

76% (01:07) correct 24% (01:13) wrong based on 108 sessions

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For positive integer n, is 12 a factor of n?

1) n is a factor of 48
2) n is a multiple of 24

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Re: For positive integer n, is 12 a factor of n?  [#permalink]

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11 May 2017, 00:38
MathRevolution wrote:
For positive integer n, is 12 a factor of n?

1) n is a factor of 48
2) n is a multiple of 24

(1) n is a factor of 48.

If n=1 then 12 is not a factor of n.
If n=12 then 12 is a factor of n.

Insufficient.

(2) 24 is divisible by 12. Hence, n is divisible by 24 also divisible by 12. Sufficient.

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Re: For positive integer n, is 12 a factor of n?  [#permalink]

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14 May 2017, 17:31
==> In the original condition, there is 1 variable. In order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), n=2 no, n=12 yes, hence it is not sufficient.
For con 2), n=24t(t=any positive integer), hence it is always yes and sufficient.

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Re: For positive integer n, is 12 a factor of n? &nbs [#permalink] 14 May 2017, 17:31
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