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The table above shows the number of students in three clubs

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The table above shows the number of students in three clubs

by swerve » Tue Dec 11, 2018 10:08 am

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The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. How many different students are in the three clubs?

A. 68
B. 69
C. 74
D. 79
E. 84

The OA is C.

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by GMATGuruNY » Tue Dec 11, 2018 10:40 am
swerve wrote:Image

The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. How many different students are in the three clubs?

A. 68
B. 69
C. 74
D. 79
E. 84
The values in the chart DOUBLE-COUNT any student who belongs to 2 of the 3 clubs.
The totals for chess and drama -- 40 and 30 -- double-count the 10 students who belong to both chess AND drama.
The totals for chess and math -- 40 and 25 -- double-count the 5 students who belong to both chess AND math.
The totals for drama and math -- 30 and 25 -- double-count the 6 students who belong to both drama AND math.
Since the students in red have been double-counted, they must be SUBTRACTED from the total.

Resulting equation:
Number of students = (total in chess) + (total in drama) + (total in math) - (red students who have been double-counted).

Thus:
Number of students = 40 + 30 + 25 - (10+5+6) = 74.

The correct answer is C.
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by [email protected] » Tue Dec 11, 2018 2:32 pm
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 = (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, the table above shows the number of students in three clubs at McAuliffe School, NO student is in all three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. We're asked for the number of DIFFERENT students in the three clubs. We can plug all of the given numbers into the formula....

Total = 40 + 30 + 25 - (1st and 2nd) - (1st and 3rd) - (2nd and 3rd)- 2(All 3 Clubs)

Total = 95 - (10) - (5) - (6) - 2(0)

Total = 95 - 21

Total = 74

Final Answer: C

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by Scott@TargetTestPrep » Fri Mar 15, 2019 5:33 pm
swerve wrote:Image

The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. How many different students are in the three clubs?

A. 68
B. 69
C. 74
D. 79
E. 84

The OA is C.

Source: GMAT Paper Tests
We can create the equation:

Total = #chess + #drama + #math - #chess and drama - #chess and math - #drama and math + #all three

Total = 40 + 30 + 25 - 10 - 5 - 6 + 0

Total = 74

Answer: C

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