Multiples - GMAT Prep

rosh26 wrote:Is integer n a multiple of 15?

I n is a multiple of 20

II n+6 is a multiple of 3

Answer is C

Can someone please explain?

Yes, there's no need to pick numbers here. The question asks 'Is n a multiple of 15'. It's a divisibility question, so it will normally be best to think about prime factorizations. We can translate the question:

Is n a multiple of 15 --> Is n a multiple of 3*5 --> Is n a multiple of both 3 and 5?

From 1: n is a multiple of 20 --> n is a multiple of 2^2*5. We don't care about the 2s for this question, but this does tell us that n is a multiple of 5. Not sufficient- we need to know if n is a multiple of 3 as well.

From 2: n+ 6 is a multiple of 3. Notice this just means that n is a multiple of 3 (if you add or subtract 6 from a multiple of 3, you'll get another multiple of 3). Not sufficient- we need to know if n is a multiple of 5.

From 1+2: we know n is a multiple of 3 and 5, which is what we wanted.

As a general note (and as a partial response to ildude's question in another thread, about working on DS questions), it is often very helpful on DS questions to translate the information given into more useful information. DS questions often do not present information in the most intuitive way. Here, for example, we had to translate the information into information about primes. In other questions, you might see equations like |x| = -x. That may look a bit confusing at first glance, but when you notice it just means that x is negative, it's a lot easier to think about.