Hi All,
The concept in these types of questions is based on the 'worst case scenario' - to guarantee that something will happen, you have to focus on the 'extreme/longest' way that it could happen.
Here, we have 8 black socks, 6 gray socks and 4 orange socks. The question asks for the MINIMUM number of socks that would be need to be randomly removed from the drawer to guarantee that a matching pair of socks would drawn. Since the original poster didn't include the 5 answer choices, we're forced to deal with this prompt in a certain way (instead of using the answers to our advantage).
So let's start with 2 socks - is it possible that you could draw 2 socks and NOT get a matching pair? Certainly - there are several examples. If we pull one black sock and one gray sock, then we do NOT have a matching pair. Thus, 2 socks is NOT enough to guarantee a matching pair.
Next, let's try 3 socks - is it possible that you could draw 3 socks and NOT get a matching pair? Absolutely - if we pull one black sock, one gray sock and one orange sock, then we do NOT have a matching pair. Thus, 3 socks is NOT enough to guarantee a matching pair.
Next, let's try 4 socks - is it possible that you could draw 4 socks and NOT get a matching pair? NO, and here's why - if we pull one black sock, one gray sock and one orange sock....we would still have to draw one more sock - and that 4th sock would match one of the 3 colors that we had already pulled. So we WOULD have a matching pair and 4 socks IS enough to guarantee a matching pair.
GMAT assassins aren't born, they're made,
Rich
