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# At a certain school, each of the 150 students takes between

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Intern
Joined: 07 Jul 2010
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At a certain school, each of the 150 students takes between [#permalink]

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25 Jul 2010, 11:37
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25% (medium)

Question Stats:

75% (01:36) correct 25% (01:44) wrong based on 161 sessions

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At a certain school, each of the 150 students takes between 1 and 3 classes. The 3 classes available are Math, Chemistry and English. 53 students study math, 88 study chemistry and 58 study English. If 6 students take all 3 classes, how many take exactly 2 classes?

A. 37
B. 43
C. 45
D. 60
[Reveal] Spoiler: OA

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Posts: 43323

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Re: Sets!!!!!Cab anybody help me solve thi susing venn diagram? [#permalink]

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25 Jul 2010, 11:57
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amlan009 wrote:
At a certain school, each of the 150 students takes between 1 and 3 classes. The 3 classes available are Math, Chemistry and English. 53 students study math, 88 study chemistry and 58 study english. If 6 students take all 3 classes, how many take exactly 2 classes?
1.)37 2.)43 3.)45 4.)60

Any help in demystifying the above problems with venn diagram shall be highly appreciated ?

Total = {Math} + {Chemistry} + {English} - {# of students who take exactly 2 classes} - 2*{# of students who take exactly 3 classes} + {# of students who take none of 3 classes}

$$150=53+88+58-x-2*6+0$$ --> $$x=37$$.

For more check: formulae-for-3-overlapping-sets-69014.html (there is my post in the end of the first page about the formulas of 3 overlapping sets with theory, diagrams and examples).

Hope it helps.
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Re: Sets!!!!!Cab anybody help me solve thi susing venn diagram? [#permalink]

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29 Jul 2010, 06:12
See this one too: how-to-draw-a-venn-diagram-for-problems-98036.html
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Re: At a certain school, each of the 150 students takes between [#permalink]

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11 Dec 2017, 10:28
amlan009 wrote:
At a certain school, each of the 150 students takes between 1 and 3 classes. The 3 classes available are Math, Chemistry and English. 53 students study math, 88 study chemistry and 58 study English. If 6 students take all 3 classes, how many take exactly 2 classes?

A. 37
B. 43
C. 45
D. 60

This is an overlapping sets question. We can use the following formula to determine how many students took exactly two classes:

Total students = # Math + # Chemistry + # English - # Exactly two classes - 2(# All three classes) + # None

150 = 53 + 88 + 58 - T - 2(6) + 0

150 = 199 - T - 12

150 = 187 - T

T = 37

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Re: At a certain school, each of the 150 students takes between   [#permalink] 11 Dec 2017, 10:28
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