Each of the 59 members in a high school class is required to

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Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?
2
5
6
8
9

* I understand everything about this problem. I even got 12 as an answer but I didn't divide by 2. Can you please explain why the following is true and how I know when to do this:
o For each student who signs up for three clubs, there are two extra sign-ups. Therefore, there must be 6 students who sign up for three clubs:

12 duplicates / (2 duplicates/student) = 6 students

THANKS!

[StaceyKoprince]

See thread:
http://www.manhattangmat.com/forums/quantitative-question-32-on-cat-1-t506.html