Data Sufficiency

Is positive integer A greater than positive integer B?

(1) A has more factors than B does.

(2) Every prime factor of B is a factor of A.

Hi Anju Ma'am,

If suppose we change statement 2 to say that A and B have same prime factors, does this then change the answer to C?

Thanks.

Sonali.

Good question, Sonali - and it actually would still be E. Consider:

A = 3^4 * 2 = 162
B = 2^3 * 3 = 24
(YES)

or

A = 2^4 * 3 = 48 (with 10 factors)
B = 3^3 * 2 = 54 (with 8 factors)
(NO)


And the main reason I wanted to jump in here (sorry, Anju!) is that this question comes from the Veritas Prep question bank, so I have all the stats on it. Less than 20% of users (it's about 19.4%) get this one right as it's written at the top of this thread. People don't do a good job of picking numbers with the goal to prove insufficiency. People often pick similar numbers but don't have a clear goal in mind. Your goal should be to find numbers that give you the opposite answer.

In this case, it's pretty clear that you can get A to be bigger, so how do you try to create a situation in which it's smaller than B? You give it more factors, but you make as many of those factors as possible equal 2, the smallest prime number. Minimum/maximum thinking is really valuable on a lot of GMAT questions, and this is one of them. Your goal to try to get that last "no" is to minimize the value of A's factors and maximize the value of B's.

Thanks so much Brian,

It becomes clearer that we need to chose and prove the opposite in such questions.

One thing I will work on for sure!

Regards, Sonali.

Brian@VeritasPrep,

Yeah I know its from Veritas, and fortunately I did this question correct.