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

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shilpa20689
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College T has 1000 students. Of the 200 students majoring in [#permalink] New post   Updated on: 09 Oct 2012, 03:44
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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
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D

Originally posted by shilpa20689 on 08 Oct 2012, 13:20.
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
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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: College T has 1000 students. Of the 200 students majoring in [#permalink] New post   09 Oct 2012, 07:01
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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] New post   19 Oct 2020, 03:41
Total = Chemistry + Biology - Both + Neither

200 = 130 + 150 - Both + 30

200 = 310 - Both

Both = 110
Minimum of (130, 150) is 130.

So maximum student majoring in both subject will be 130.

So answer will be 110 to 130.
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Re: College T has 1000 students. Of the 200 students majoring in [#permalink] New post   19 Oct 2020, 16:43
saquibshaikh143 wrote:
Total = Chemistry + Biology - Both + Neither

200 = 130 + 150 - Both + 30

200 = 310 - Both

Both = 110
Minimum of (130, 150) is 130.

So maximum student majoring in both subject will be 130.

So answer will be 110 to 130.


Total Students are given as 1000 and not 200?
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Re: College T has 1000 students. Of the 200 students majoring in [#permalink] New post   20 Oct 2020, 03:58
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Given

    • College T has 1000 students.
    • 200 students majoring in one or more of the sciences.
    • Of the 200 students majoring in one or more of the sciences,130 are majoring in Chemistry and 150 are majoring in Biology.
    • At least 30 of the students are not majoring in either Chemistry or Biology.


To Find

    • The number of students majoring in both Chemistry and Biology could be any number from.


Approach and Working Out


    • 200 students majoring in one or more from Science.
    • 130 majoring in Chemistry and 150 majoring in Biology.
    • Students who are majoring in only chemistry or only biology or both can be at max 200 – 30 = 170.
      o At least that can be 150 (As 150 students are already in chemistry.
    • When it is 150 then all the 130 students in biology must also be in chemistry.
      o So the maximum limit is 130.
    • When it is 170 then 150 + 130 – both = 170
      o Both = 110
    • So the number varies from 110 to 130.

Correct Answer: Option D
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Re: College T has 1000 students. Of the 200 students majoring in [#permalink] New post   20 Oct 2020, 04:11
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shilpa20689 wrote:
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


Chemistry = 130 and Biology = 150.
Since 130+150 = 280 -- exceeding the total number of students by 80 -- at least 80 students must major in both subjects.
Eliminate A, B and C.

Since only 130 students major in chemistry, the number of students majoring in both subjects cannot exceed 130.
Eliminate E.

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D
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Re: College T has 1000 students. Of the 200 students majoring in [#permalink] New post   29 Sep 2023, 02:57
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Re: College T has 1000 students. Of the 200 students majoring in [#permalink]
29 Sep 2023, 02:57
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