Hi swerve,
We're told that in a group of 20 people, 5 of them belong to the golf club, 7 to the swim club, and 9 to the tennis club, 2 of the people belong to ALL three clubs and 3 belong to EXACTLY two of the three clubs. We're asked for the number of people who belong to none of the three clubs. 3-Group Overlapping Sets questions are relatively rare on the Official GMAT (you likely will NOT see this version of Overlapping Sets on Test Day). However, there is a formula that you can use to solve it.
Total = (none of the groups) + (1st group) + (2nd group) + (3rd group) - (1st and 2nd) - (1st and 3rd) - (2nd and 3rd) - 2(all 3 groups).
In overlapping sets questions, any person who appears in more than one group has been counted more than once. When dealing with groups of people, you're not supposed to count any individual more than once, so the formula 'subtracts' all of the extra times that a person is counted. For example, someone who is in BOTH the 1st group and the 2nd group will be counted twice....that's why we SUBTRACT that person later on [in the (1st and 2nd) group].
Based on the information that we're given in the prompt, the equation would look like this...
20 = (none) + 5 + 7 + 9 - [3] - 2(2)
20 = (none) + 21 - 7
20 = (none) + 14
6 = (none)
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
