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College T has 1000 students. Of the 200 students majoring in

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College T has 1000 students. Of the 200 students majoring in [#permalink] New post 08 Oct 2012, 13:20
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College T has 1000 students. Of the 200 students majoring in one or more of the sciences,130 are majoring in Chemistry and 150 are majoring in Biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?

A. 20 to 50
B. 40 to 70
C. 50 to 130
D. 110 to 130
E. 110 to 150
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Oct 2012, 03:44, edited 2 times in total.
Renamed the topic, edited the question and moved to PS forum.
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Re: urgent solution [#permalink] New post 08 Oct 2012, 13:28
Why is this urgent?

I edited your post to make it coherent..Please review the posting guidelines here: rules-for-posting-please-read-this-before-posting-133935.html

Anyway, here is the solution:

Total = Chemistry + Biology - Both + Neither

200 = 130 + 150 - Both + N

We know that N (Neither) must be at least 30, so set N=30 and solve:

200 = 130 + 150 - Both + 30

200 = 310 - Both

Both = 110

Even if you're not sure whether 110 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range, which means only answers D or E could be correct.

Both can not be greater than 130, because even if every chemistry major was also a biology major, there are only 130 chemistry majors total. D the solution.
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Re: urgent solution [#permalink] New post 08 Oct 2012, 23:08
hamm0 wrote:
Why is this urgent?


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Re: College T has 1000 students. Of the 200 students majoring in [#permalink] New post 09 Oct 2012, 07:01
D: 110-130
A - students who major in chemistry, B - students who major in biology.

P(A+B) = P(A) + P(B) - P(A*B)

Since P(A+B) <= 200-30 = 170, then

P(A) + P(B) - P(A*B) <= 170, P(A*B) >= P(A)+P(B) - 170 = 130+150-170 = 110, 110 - possible 30 students major in neither bio or chem, 20 major only in chem, 110 in both chem and bio, 40 - in bio only

P(A*B) <= min(P(A), P(B)) = 130 - possible when all students who major in chemistry also major in biology
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Re: College T has 1000 students. Of the 200 students majoring in   [#permalink] 09 Oct 2012, 07:01
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