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Among 400 students, 56% study sociology, 44% study

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Among 400 students, 56% study sociology, 44% study [#permalink]

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New post 12 Sep 2008, 00:05
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?

A. 30
B. 90
C. 120
D. 172
E. 188

im getting 120 as the bio students, but the question says 40% whihc is 160.
what is the mistake?
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Re: venn confusion [#permalink]

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New post 12 Sep 2008, 00:37
In your diagram, if intersection of biology and mathematics as well as of biology and sociology is 0 then maximum % of biology will be what is given in the question itself and that is 40%.

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Re: venn confusion [#permalink]

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New post 12 Sep 2008, 04:07
I am also getting 120 ... whats the OA ? and can you tell me the source of these questions you are posting ?

Thanks :)
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Re: venn confusion [#permalink]

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New post 12 Sep 2008, 21:21
Without solving.. this problem I chose Answer in 10 sec.. :lol: that is 120..
I will this logic when I don't have time.. (Educated Guess)

Question talking about 400 students.. Given info is in percentage.. so generally everyone .. pick 100 as number of students..then solve equation.
So answer would be some number say "M%' but answer would be 4M.

only 30 and 120 are in that ratio (1:4) ..

After solving I got the same answer.

100 = A+B+C - (x+y+z)-2(T)

100= 160-(30+y+z)-2(T)
y= 60-30-z-2T

y is maximum when z and t are zeros.

Y=30%

y =120
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Re: venn confusion [#permalink]

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New post 13 Sep 2008, 04:55
x2suresh wrote:
Without solving.. this problem I chose Answer in 10 sec.. :lol: that is 120..
I will this logic when I don't have time.. (Educated Guess)

Question talking about 400 students.. Given info is in percentage.. so generally everyone .. pick 100 as number of students..then solve equation.
So answer would be some number say "M%' but answer would be 4M.

only 30 and 120 are in that ratio (1:4) ..

After solving I got the same answer.

100 = A+B+C - (x+y+z)-2(T)

100= 160-(30+y+z)-2(T)
y= 60-30-z-2T

y is maximum when z and t are zeros.

Y=30%

y =120


how did you get 160?

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Re: venn confusion [#permalink]

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New post 13 Sep 2008, 12:02
arjtryarjtry wrote:
x2suresh wrote:
Without solving.. this problem I chose Answer in 10 sec.. :lol: that is 120..
I will this logic when I don't have time.. (Educated Guess)

Question talking about 400 students.. Given info is in percentage.. so generally everyone .. pick 100 as number of students..then solve equation.
So answer would be some number say "M%' but answer would be 4M.

only 30 and 120 are in that ratio (1:4) ..

After solving I got the same answer.

100 = A+B+C - (x+y+z)-2(T)

100= 160-(30+y+z)-2(T)
y= 60-30-z-2T

y is maximum when z and t are zeros.

Y=30%

y =120


how did you get 160?



For get about my solution... I was dumb yesterday... Long day.. I answered while I was in half sleep.. even I didn't read the questions properly.


assume we have 100 students.

No of students who study Sociology or Mathematics
=S+M-both(S and M) = 56+44-30=70

to get the max students who study Biology= 100-70=30%

total number=400*0.3=120
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Re: venn confusion [#permalink]

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New post 13 Sep 2008, 13:30
arjtryarjtry wrote:
Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?

A. 30
B. 90
C. 120
D. 172
E. 188

im getting 120 as the bio students, but the question says 40% whihc is 160.
what is the mistake?



who study biology but do not study either mathematics or sociology. Does this mean there is no one who studies all three??

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Re: venn confusion [#permalink]

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New post 13 Sep 2008, 16:08
arjtryarjtry wrote:
Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?

A. 30
B. 90
C. 120
D. 172
E. 188

im getting 120 as the bio students, but the question says 40% whihc is 160.
what is the mistake?


160 should be the correct answer. If the students taking Biology do not take any other course (possible with the given percentages), then we have 40% of students as the solution.

EDIT: Just realized my mistake. 120 should be the answer. 56 + 44 - 30 = 70%. That leaves 30% who do not take either mathematics or sociology. My earlier mistake was taking an entire overlap between Mathematics and Sociology students (as in every sociology student was also taking mathematics, which which case the overlap was 0% not 30%)
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Last edited by incognito1 on 13 Sep 2008, 17:47, edited 1 time in total.

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Re: venn confusion [#permalink]

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New post 13 Sep 2008, 17:03
What is the source of this question?
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Re: venn confusion [#permalink]

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New post 13 Sep 2008, 17:22
It should be C. 120

Total student taking math and socio= (56 + 44 -30 )%= 70 %

So, maximum bio students ( no need to consider socio or math students.. as not other conditions are given)= 30 % of 400 = 120

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Re: venn confusion [#permalink]

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New post 14 Sep 2008, 00:25
ssandeepan wrote:
It should be C. 120

Total student taking math and socio= (56 + 44 -30 )%= 70 %

So, maximum bio students ( no need to consider socio or math students.. as not other conditions are given)= 30 % of 400 = 120

This is a good approach
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Re: venn confusion [#permalink]

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New post 19 Sep 2008, 07:42
How do you still explain the fact that the question says 40% of 400 for Bio. which comes to 160 students? The answer should definitely be 120 and the only way to account for that is to assume that some students( actually 40) study all three subjects. If you read the question carefully, it is no where discounting the fact that there could be students studying all 3 subjects.

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Re: venn confusion   [#permalink] 19 Sep 2008, 07:42
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