Stardust Chris wrote:

Is 3 a factor of the positive integer m?

(1) 12 is a factor of 25m

(2) 12 is a factor of 15m

Target question: Is 3 a factor of the positive integer m?This is a good candidate for

rephrasing the target question.

-----ASIDE---------------------

A lot of integer property questions can be solved using prime factorization.

For questions involving divisibility, divisors, factors and multiples, we can say:

If N is a factor by k, then k is "hiding" within the prime factorization of NConsider these examples:

3 is a factor of 24, because 24 = (2)(2)(2)

(3), and we can clearly see the

3 hiding in the prime factorization.

Likewise,

5 is a factor of 70 because 70 = (2)

(5)(7)

And

8 is a factor of 112 because 112 = (2)

(2)(2)(2)(7)

And

15 is a factor of 630 because 630 = (2)(3)

(3)(5)(7)

-----BACK TO THE QUESTION!---------------------

The above concept allows us to REPHRASE the target question as...

REPHRASED target question: Is there a 3 hiding in the prime factorization of m? Statement 1: 12 is a factor of 25m 12 = (2)(2)(3)

In other words, statement 1 is telling us that there are two 2's and one 3 hiding in the prime factorization of 25m

25m = (5)(5)(m)

Since there are no 3's hiding in (5)(5), it must be the case that

there's a 3 hiding in the prime factorization of mSince we can answer the

REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: 12 is a factor of 15m 12 = (2)(2)(3)

In other words, statement 2 is telling us that there are two 2's and one 3 hiding in the prime factorization of 15m

15m = (

3)(5)(m)

As we can see, we already have a 3 hiding in the prime factorization of 15m, so we can't say for sure whether there's a 3 hiding in the prime factorization of m.

To more certain, consider these two counter-examples:

Case a: m = 4. This means 15m = (15)(4) = 60, and 12 IS a factor of 60. In this case,

3 is NOT a factor of mCase b: m = 12. This means 15m = (15)(12) = 180, and 12 IS a factor of 180. In this case,

3 IS a factor of mSince we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,

Brent

_________________

Brent Hanneson – GMATPrepNow.com

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