jp.jprasanna wrote:Thank you all for your explanations... very useful. However I did the double set matrix got the below..

-----------------Male--------No Male-------------Total

Drama --------15------------?-------------------- 16

*

*

Music----------10------------?---------------------20

*

*

Total-----------25------------?--------------------36

So considering the answer is E what is wrong with the above matrix? Could you please help.. very disappointed with myself! :-(

I was going to select E because C is too obvious to be correct in GMAT.

Here's the problem . . . when you use a double-set matrix you are assuming that every member fits into ONLY one of the four descriptive boxes you lay out. For example, maybe a problem says that a country club offers golf and tennis as activities. You would lay out your two sides as "golf"/"no golf" and "tennis"/"no tennis". Thus, your four descriptive boxes would be 1)golf/tennis, 2)tennis/no golf, 3)golf/no tennis, 4)no tennis/no golf. Notice that every member of the club would fit in ONLY one of those boxes. There is zero overlap among the four boxes. That is the beauty of the double-set matrix; it helps you strictly define who does what.

In this case your four boxes are Drama-Male, Drama-Female, Music-Male, Music-Female.

Notice that some of the males COULD be in both drama and music, but by setting up the table this way you are assuming that there is NO overlap. We can't make that assumption based on this problem, since it doesn't tell us that there is no overlap.

I hope that this clears things up!