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Students are in clubs as follows: Science-20, Drama-30, and

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by AAPL » Wed Aug 15, 2018 7:08 am

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Manhattan GMAT

Students are in clubs as follows: Science-20, Drama-30, and Band-12. No student is in all three clubs, but 8 are in both Science and Drama, 6 are in both Science and Band, and 4 are in Drama and Band. How many different students are in at least one of the three clubs?

A. 36
B. 38
C. 42
D. 44
E. 48

OA D.
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by GMATGuruNY » Wed Aug 15, 2018 8:24 am
AAPL wrote:Manhattan GMAT

Students are in clubs as follows: Science-20, Drama-30, and Band-12. No student is in all three clubs, but 8 are in both Science and Drama, 6 are in both Science and Band, and 4 are in Drama and Band. How many different students are in at least one of the three clubs?

A. 36
B. 38
C. 42
D. 44
E. 48
When we count the total in Science, the total in Drama, and the total in Band, any students in exactly two of the clubs are counted TWICE.
Thus, we must SUBTRACT these students so that they are not double counted:
Total = Science + Drama + Band - (exactly 2 clubs) = 20 + 30 + 12 - (8+6+4) = 44.

The correct answer is D.
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by Scott@TargetTestPrep » Fri Apr 19, 2019 9:14 am
AAPL wrote:Manhattan GMAT

Students are in clubs as follows: Science-20, Drama-30, and Band-12. No student is in all three clubs, but 8 are in both Science and Drama, 6 are in both Science and Band, and 4 are in Drama and Band. How many different students are in at least one of the three clubs?

A. 36
B. 38
C. 42
D. 44
E. 48

OA D.
We can use the following formula:

n(At least one set) = n(A) + n(B) + n(C) - n(A and B) - n(A and C) - n(B and C) + n(A and B and C)

n(At least one set) = 20 + 30 + 12 - 8 - 6 - 4 + 0

n(At least one set) = 44

Answer: D

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