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In a certain class of 66 students, 30 students study Science, 40 stude

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In a certain class of 66 students, 30 students study Science, 40 stude  [#permalink]

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New post 15 Dec 2018, 09:11
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (01:15) correct 33% (02:52) wrong based on 30 sessions

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GMATbuster's Weekly Quant Quiz#13 Ques #3


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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

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Re: In a certain class of 66 students, 30 students study Science, 40 stude  [#permalink]

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New post 16 Dec 2018, 01:12
science = a+b+d+e = 30
humanities = b+e+c+f = 40
dance = d+e+f+g = 40

(a+b+d+e) + (b+e+c+f) + (d+e+f+g )= 30 + 40 + 40 = 110
(a+b+c+d+e+f+g) + (b+e+d+e+f) = 110
66+(b+d+f+2e) = 110
Now to maximize e, we need to minimize b+d+f
Taking b,e,f, each = 0
2e = 110-66 = 44
e = 22
So, Maximum value of e = 22

Answer D

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Re: In a certain class of 66 students, 30 students study Science, 40 stude  [#permalink]

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New post 20 Dec 2018, 02:31
shashankism wrote:
science = a+b+d+e = 30
humanities = b+e+c+f = 40
dance = d+e+f+g = 40

(a+b+d+e) + (b+e+c+f) + (d+e+f+g )= 30 + 40 + 40 = 110
(a+b+c+d+e+f+g) + (b+e+d+e+f) = 110
66+(b+d+f+2e) = 110
Now to maximize e, we need to minimize b+d+f
Taking b,e,f, each = 0
2e = 110-66 = 44
e = 22
So, Maximum value of e = 22

Answer D


Could you please explain (a+b+c+d+e+f+g) = 66
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Re: In a certain class of 66 students, 30 students study Science, 40 stude  [#permalink]

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New post 20 Dec 2018, 03:32
Bunuel maybe you can bring some light into this. The OA is 22. the total number is 66. maximum # for 3 overlaps therefore 22. 22 is one third of 66. Is there a shortcut (logical or otherwise) to approach such topics? I doubt that only the lengthy and time-consuming approach with drawing up equations is the best way here.

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Re: In a certain class of 66 students, 30 students study Science, 40 stude &nbs [#permalink] 20 Dec 2018, 03:32
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