3 Overlapping Set Question

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havok: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Tue Jun 30, 2009 4:51 pm; Thanked: 24 times; Followed by:7 members; GMAT Score:750

3 Overlapping Set Question

by havok » Sat Apr 16, 2011 1:32 pm

This table lists enrollment in an afterschool program by activity. There are 30 total students enrolled in the entire program. Students may participate in one, two, or three activities. 21 students only participate in one activity. How many students participate in all three activities?

Basketball: 19
Math: 12
Wrestling: 11

There is a shortcut that I am trying to apply but I can't seem to make it work on this question.
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

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Source: Beat The GMAT — Problem Solving | Sat Apr 16, 2011 1:32 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Apr 16, 2011 2:21 pm

havok wrote:This table lists enrollment in an afterschool program by activity. There are 30 total students enrolled in the entire program. Students may participate in one, two, or three activities. 21 students only participate in one activity. How many students participate in all three activities?

Basketball: 19
Math: 12
Wrestling: 11

There is a shortcut that I am trying to apply but I can't seem to make it work on this question.
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

For this question, it helps to sketch and label the various regions:

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