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## Number properties

This topic has 1 expert reply and 0 member replies

### Top Member

BTGmoderatorRO Moderator
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#### Number properties

Sat Sep 16, 2017 11:32 am
If p and q are positive integers, is every factor of p a factor of q?

(1) The product of the prime factors of p is a factor of q.
(2) p is a factor of q.

a. statement 1 and 2 are sufficient
b. Both are not sufficient
c. statement 1 is sufficient while statement 2 is not sufficient
d. statement 1 is not sufficient while statement 2 is sufficient
e. statement 1 is sufficient

OA is d
why is statement not sufficient and how do you arrive at this?

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
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Sun Sep 17, 2017 7:58 am
Roland2rule wrote:
If p and q are positive integers, is every factor of p a factor of q?

(1) The product of the prime factors of p is a factor of q.
(2) p is a factor of q.

OA is d
why is statement not sufficient and how do you arrive at this?

Statement 1: The product of the prime factors of p is a factor of q.

Case 1: Say p = 6 and q = 6

Prime factors of p are 2 and 3. The product of 2 and 3 = 6 is a factor of q and all the factors of p are factors of p. The answer is Yes.

Case 2: Say p = 12 and q = 6

Prime factors of p are 2 and 3. The product of 2 and 3 = 6 is a factor of q, but not all factors of p are factors of q (12 is not a factor of q). The answer is No. Insufficient.

Statement 2: p is a factor of q.

Since p is a factor of q , q/p = integer, thus every factor of p will be a factor of q. Sufficient.

Hope this helps!

-Jay
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