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In a certain class of 66 students, 30 students study Science, 40 students study Humanities and 40 students study Dance.

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by Gmat_mission » Thu Dec 17, 2020 1:03 pm

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B

C

D

E

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Difficulty—

In a certain class of 66 students, 30 students study Science, 40 students study Humanities and 40 students study Dance. If all the students studied at least one of the subjects, then what is the maximum possible number of students who study all the three subjects?

A.38
B.35
C.32
D.22
E.20

Answer: D

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Re: In a certain class of 66 students, 30 students study Science, 40 students study Humanities and 40 students study Dan

by Scott@TargetTestPrep » Wed Dec 23, 2020 4:10 pm
Gmat_mission wrote: ↑
Thu Dec 17, 2020 1:03 pm
 In a certain class of 66 students, 30 students study Science, 40 students study Humanities and 40 students study Dance. If all the students studied at least one of the subjects, then what is the maximum possible number of students who study all the three subjects?

A.38
B.35
C.32
D.22
E.20

Answer: D

Solution:

Since we are looking for the maximum possible number of students who study all 3 subjects, we should let the number of students who study exactly 2 subjects be 0. If we let x = the maximum possible number of students who study all 3 subjects, we can create the equation:

(30 - x) + (40 - x) + (40 - x) + x = 66

110 - 2x = 66

44 = 2x

22 = x

Answer: D

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