Is a positive integer n a multiple of 12

[hazelnut01]

Is a positive integer n a multiple of 12?

1) n is a multiple of 6
2) n is a multiple of 24

[Brent@GMATPrepNow]

Is positive integer n a multiple of 12?

1) n is a multiple of 6
2) n is a multiple of 24

Target question: Is positive integer n a multiple of 12?

Statement 1: n is a multiple of 6
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 12, in which case n IS a multiple of 12
Case b: n = 18, in which case n is NOT a multiple of 12
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n is a multiple of 24
This means we can write n = 24k (where k is an integer)
Since 24 = (12)(2), we can say that n = (12)(2)k
Since we can write n as 12 TIMES some integer, we can be certain that n IS a multiple of 12
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

[Jay@ManhattanReview]

Is a positive integer n a multiple of 12?

1) n is a multiple of 6
2) n is a multiple of 24

Hi ziyuenlau,

We have to check if a positive integer n is a multiple of 12.

let's teake each statement one by one.

S1: n is a multiple of 6

=> n = 6K; where K is an integer.

If K = 1, n = 6; n is not divisble by 12. The answer is NO.

However, if K = 2, n = 6*2 = 12; n is divisble by 12. The answer is YES. No unique answer. Insuffcient.

S1: n is a multiple of 24

=> n = 24K; where K is an integer.

Whatever be the value of K since 24 is divisible by 12, n is divisble by 12. A unique answer. Suffcient.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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[Scott@TargetTestPrep]

Is a positive integer n a multiple of 12?

1) n is a multiple of 6
2) n is a multiple of 24

We need to determine whether n/12 = integer.

Statement One Alone:

n is a multiple of 6.

If n = 6, then n/12 is not an integer; however if n = 12, then n/12 is an integer. Statement one is not sufficient to answer the question.

Statement Two Alone:

n is a multiple of 24.

Since n/24 = integer and 12 is a factor of 24, n/12 will always be an integer. Statement two alone is sufficient to answer the question.

Answer: B