Official Guide 12th Ed. DS #82

[aznmexicana]

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

(1) x is a multiple of 9
(2) y is a multiple of 25

[ShadowN]

The answer is B.


for xy to be a multiple of 105 (prime factorization of 5,3, 7), xy must have at least one 5, one 3 and one 7.

Only statement 2 tells us that y is a multiple of 5, the prime number we are looking for.

Saludos desde Mexico.

[Patrick_GMATFix]

Hi aznmexicana,

The key to this question, as to many DS questions, is accurate rephrasing. We know that xy is a multiple of 6*14, or of 2^2*3*7. We want to know whether xy is a multiple of 105, or of 3*5*7. Since we already know that xy is a multiple of 3*7, the rephrase is: "Is xy a multiple of 5?" Statement (2) gives us enough data to answer but statement (1) doesn't, so the answer is B

Attached is a more detailed solution and take-away strategies. If you cannot see the attachment, get it here

Good luck,
-Patrick

[aznmexicana]

thanks patrick!! that was really helpful!