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In a certain class of 66 students, 30 students study Science

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In a certain class of 66 students, 30 students study Science [#permalink]

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New post 16 Jan 2018, 08:50
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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
[Reveal] Spoiler: OA
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Re: In a certain class of 66 students, 30 students study Science [#permalink]

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New post 16 Jan 2018, 11:41
saswata4s wrote:
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


Total = A+B+C - Exactly(AB +BC +AC) - 2(ABC) since we need to maximize ABC exactly ( AB+BC+AC) should be 0.
Hence 66 = 30+40+40 - 2(ABC)
OR
ABC= (110-66)/2 i.e. 22.

Hence Ans is D
Re: In a certain class of 66 students, 30 students study Science   [#permalink] 16 Jan 2018, 11:41
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In a certain class of 66 students, 30 students study Science

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