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

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10 00:00

Difficulty:   25% (medium)

Question Stats: 74% (01:54) correct 26% (02:51) wrong based on 115 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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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

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

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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

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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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.

Best, gota900
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Re: In a certain class of 66 students, 30 students study Science, 40 stude  [#permalink]

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1
gota900 I believe you can also try to estimate, which is still quite risky though.
If you look at it logically, the answer can't exceed the value of 30, which is the smallest group (Science people)
Now, looking at the answers, 22 is the closest to 30, which could be a correct value.
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In a certain class of 66 students, 30 students study Science, 40 stude  [#permalink]

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thestanced wrote:
gota900 I believe you can also try to estimate, which is still quite risky though.
If you look at it logically, the answer can't exceed the value of 30, which is the smallest group (Science people)
Now, looking at the answers, 22 is the closest to 30, which could be a correct value.

Its not like you could drive a truck through the answer choices you know... I would be very precautious with estimating here. I guess we have to take the lengthy approach, even if its a pain in the keister...

Best, gota900
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Manager  B
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Re: In a certain class of 66 students, 30 students study Science, 40 stude  [#permalink]

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It is actually super easy once you think about it.
1) find the smallest set. That is 30 in this case
2) Choose the largest answer option below 30
3) Move on
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Re: In a certain class of 66 students, 30 students study Science, 40 stude  [#permalink]

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66=40+30+40-(Exactly 2) - (2*Exactly 3)

minimize Exactly 2 to maximize Exactly 3

66 = 66 + 44 - 0 - (2* Exactly 3)

Exactly 3 = 22 Re: In a certain class of 66 students, 30 students study Science, 40 stude   [#permalink] 21 Sep 2019, 06:57
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