Problem Solving

Hi All,

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 = (Those in 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].

In this prompt, we're given the Total, a number for each of the 3 individual groups, the number of people in two of the groups and the number of people who appear in all 3 groups. The equation would look like this (note: the [ ] includes all three of the 2-group groups)...

20 = (None) + 5 + 7 + 9 - [3] - 2(2)

20 = (None) + 21 - 7

20 = (None) + 14

6 = (None)

The number of people who are in none of the three groups is 6.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

AAPL wrote:Veritas Prep

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. If 2 of the people belong to all three clubs and 3 belong to exactly two of the three clubs, then how many of 20 people belong to neither of the three clubs?

A. 1
B. 2
C. 4
D. 6
E. 11

OA D.

We can create the following equation:

Total = # who belong to golf + # who belong to tennis + # who belong to swim - (# who belong to exactly 2 clubs) - 2(# who belong to all 3 clubs) + # who belong to none

20 = 5 + 9 + 7 - 3 - 2(2) + N

20 = 14 + N

6 = N

Answer: D