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Is M a multiple of 6

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Is M a multiple of 6

by GMAT_AS » Sat Jun 06, 2015 4:42 am
Is m a multiple of 6?

Statement 1 : More than 2 of the first 5 positive integer multiples of m are multiples of 3

Statement 2 : Fewer than 2 of the first 5 positive integer multiples of m are multiples of 12

Answer choices A,B,C,D,E being in the regular order.

Please advise on the solution!
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by DavidG@VeritasPrep » Sat Jun 06, 2015 5:04 am
Is m a multiple of 6?

Statement 1 : More than 2 of the first 5 positive integer multiples of m are multiples of 3

Statement 2 : Fewer than 2 of the first 5 positive integer multiples of m are multiples of 12

I'd pick some simple numbers here.

For statement 1 -

CASE 1: m = 3, NO, m is not a multiple of 6.
CASE 2: m = 6, YES m is a multiple of 6.

Not Sufficient

For statement 2:
ANY multiple of 6 will have at least two multiples of 12 among its first five multiples.

If m = 6, first five multiples (multiples of 12 in bold) 6, 12, 18, 24, 30 --> doesn't satisfy condition
If m = 12, first five multiples (12, 24, 36, 48, 60) ---> doesn't satisfy condition
If m = 18, first five multiples (18, 36, 54, 72, 90) --> doesn't satisfy condition

So statement 2 is telling us, definitively, that m will NOT be a multiple of 6. Because the answer is always NO, this is sufficient.

Answer is B
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by GMATGuruNY » Sat Jun 06, 2015 5:09 am
GMAT_AS wrote:Is m a multiple of 6?

Statement 1 : More than 2 of the first 5 positive integer multiples of m are multiples of 3

Statement 2 : Fewer than 2 of the first 5 positive integer multiples of m are multiples of 12
Statement 1:
Case 1: m=3
Here, the first 5 positive multiples of m are 3, 6, 9, 12 and 15, with the result that all five values are divisible by 3.
In this case, m is NOT a multiple of 6, so the answer to the question stem is NO.

Case 2: m=6
Here, the first 5 positive multiples of m are 6, 12, 18, 24 and 30, with the result that all five values are divisible by 3.
In this case, m IS a multiple of 6, so the answer to the question stem is YES.

Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statement 2:
Case 1 also satisfies statement 2.
In Case 2, the answer to the question stem is NO.

Case 2 does NOT satisfy statement 2.
Test increasing multiples of 6.

Case 3: m=12
Here, the first 5 positive multiples of m are 12, 24, 36, 48, and 60, with the result that all five values are divisible by 12.
Thus, Case 3 does not satisfy statement 2.

Case 4: m=18
Here, the first 5 positive multiples of m are 18, 36, 54, 72, and 90, with the result that two values -- 36 and 72 -- are divisible by 12.
Thus, Case 4 does not satisfy statement 2.

Cases 2, 3, and 4 imply that no multiple of 6 will satisfy statement 2.
Since m cannot be a multiple of 6, the answer to the question stem is NO.
SUFFICIENT.

The correct answer is B.
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