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# If n is positive integer, is 6 a factor of n?

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Math Revolution GMAT Instructor
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If n is positive integer, is 6 a factor of n?  [#permalink]

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24 Oct 2017, 06:52
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Difficulty:

25% (medium)

Question Stats:

82% (01:00) correct 18% (01:00) wrong based on 66 sessions

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[GMAT math practice question]

If n is positive integer, is 6 a factor of n?

1) 6 is a factor of n^2
2) 6 is a factor of 2n

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Re: If n is positive integer, is 6 a factor of n?  [#permalink]

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24 Oct 2017, 06:59
1. Since n is an integer, this is sufficient
2. n=3, 2n=6. 6 is a factor of 2n but noṭ of n. If n=6, then 6 is a factor of n. Noṭ sufficient.

A

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Re: If n is positive integer, is 6 a factor of n?  [#permalink]

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24 Oct 2017, 07:00
The answer should be A... n^2 is a multiple of 6 and n is a positive integer... then n has to be a factor of 6... the second statement is not sufficient as 2n may or may not be a multiple of 6...

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Re: If n is positive integer, is 6 a factor of n?  [#permalink]

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24 Oct 2017, 07:17
1
Some similar questions

https://gmatclub.com/forum/is-a-positiv ... fl=similar

https://gmatclub.com/forum/for-positive ... fl=similar
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Re: If n is positive integer, is 6 a factor of n?  [#permalink]

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25 Oct 2017, 23:44
=>

Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Since we have 1 variable and 0 equation, D is most likely to be the answer. According to CMT4(B), if D is chosen as an answer too easily for key area questions, we should check the answer A or B. This question is about integers, which is one of the key question areas.

Condition 1)
n^2 = 2*3*k for an integer.
Since 2 and 3 are prime factors of n^2, 2 and 3 are prime factor of n.
Thus, 2*3 = 6 is a factor of n.
This is sufficient.

Condition 2)
We have two cases as follows.
n = 3 does not have 6 as a factor.
n = 12 has 6 as a factor.
This is not sufficient.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Thus, D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

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Re: If n is positive integer, is 6 a factor of n? &nbs [#permalink] 25 Oct 2017, 23:44
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