Is pq divisible by 168? Number Properties p105 Q5

[b.shmorhun]

Is pq divisible by 168?
(1) p is divisible by 14
(2) q is divisible by 12

The Answer in the Book is C. However, why isn't it E?

LCM of 12 and 14 = 2x2x3x7 = 84

84 is not evenly divisible by 168. So aren't both statements insufficient?

[jnelson0612]

Is pq divisible by 168?
(1) p is divisible by 14
(2) q is divisible by 12

The Answer in the Book is C. However, why isn't it E?

LCM of 12 and 14 = 2x2x3x7 = 84

84 is not evenly divisible by 168. So aren't both statements insufficient?

Be careful! This is a tricky question.

Notice that if p is divisible by 14, p must be a multiple of 14. Thus, p could be 14, 28, 42, etc. The smallest possible value for p is 14.

Using the same logic, q is a multiple of 12. Possible values are 12, 24, 36, and so forth. The smallest possible value of q is 12.

Thus, if we know that p must be *at least* 14, and q *at least* 12, pq must be at least 168. C!

Please let us know if you need more help.

[b.shmorhun]

Thanks Jamie! (sorry for taking such a long time!)

A follow up to this. 0 is also a multiple of 14 and 12. Is being a multiple of a number different from being divisible by it in this case?

[RonPurewal]

Hi,
This is the wrong folder for this thread. (Jamie shouldn't have answered the question in the first place; she should have told you to post the problem in the correct folder!)

This folder is only for math questions from the GMAT PREP software from mba.com.

If the question originates in our books, then please post it in the "MGMAT non-CAT" folder. If it's a random question that's ... random, then post it in the "General Math Questions" folder.

Thanks.