If a positive integer q is divisible by both 3 and 11, then q must als

This hinges on the wording of the question. The question asks what q *must* be divisible by. It certainly is *possible* that q=66, say, and that q is divisible by 66, but it's also possible that q = 33, in which case q is not divisible by 66. So q does not *need* to be divisible by 66 here, which is why we can rule out III. I'd add that it's also *possible* for q to be divisible by 14 (it might be that q = 3*11*14 = 462, for example) but q certainly does not need to be divisible by 14. However, if q is divisible by 3 and 11, then q will always be divisible by the LCM of 3 and 11, which is 33, so q must be divisible by 33.

Well fancy that, thanks a lot IanStewart! I get it!=D

Hi All,

We're told that Q is a positive integer that is divisible by BOTH 3 and 11. We're asked which of the following MUST also divisible evenly into Q. This question can be approached in a couple of different ways, including by TESTing VALUES.

With these types of prompts, it often helps to choose the SMALLEST value that fits everything that you're told. Here, the smallest positive value of Q that is divisible by 3 and 11 is 33.

IF.... Q=33...

I. 14
14 does NOT divide evenly into 33.
Eliminate Answers A and D

II. 33
33 DOES divide evenly into 33, so we'll keep this option for now.

III. 66
66 does NOT divide evenly into 33.
Eliminate Answers C and E.

There's only one answer remaining...

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Since q is divisible by both 3 and 11, it’s also divisible by the LCM of 3 and 11 (and all the factors of this LCM). Since the LCM of 3 and 11 is 3 x 11 = 33, q is divisible by 33. (Note: q is not divisible by 14 and 66 since they are not factors of 33.)

Answer: B