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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 30 Jul 2008, 11:00
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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

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Re: venn diagram [#permalink]

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New post 30 Jul 2008, 11:21
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


I got C. will explain if it is correct.
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Re: venn diagram [#permalink]

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New post 30 Jul 2008, 11:23
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


I'm feeling sleepy and i DO NOT recommend solving question this way..... but lets try

first two options are trap options ... becuase problem is in % but we have to answer number of students.... lets look at these "trap" options ..... 90 is too much .... can not ... in all probabbilities ...30 is the trap option .... so if you make venn diagram with %... most probably you'll endup with 30 ..... exactly why its the first option....

but we are smart 8-) .... we know its a trap but test writer has already solved the % and gave it to us in a platter ...

number of studenst will be 400 * 30% = 120 ... option C

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Re: venn diagram [#permalink]

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New post 30 Jul 2008, 11:45
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


Fastest way.. is.
40% study biology (400 *0.40) .. max 160
eliminate D and E

If we see the question all % are .. whole numbers (56%, 44% .. etc)..
when we solve it will lead whole % ... say may be 30% 22%... not 21.5%..
So, option A (30), B(90) divided by 4 --> leads to fraction number 7.5% 22.5%..
A, B -- 30, 90
eliminate A and B.

C is left.


I solved it using vendiagram too...

It leads to 30% --> 400 *.30 --> 120
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Re: venn diagram [#permalink]

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New post 03 Aug 2008, 09:20
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


Tedious calculations and ended up with C is there any easy way out
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Re: venn diagram [#permalink]

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New post 03 Aug 2008, 09:22
x2suresh wrote:
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


Fastest way.. is.
40% study biology (400 *0.40) .. max 160
eliminate D and E

If we see the question all % are .. whole numbers (56%, 44% .. etc)..
when we solve it will lead whole % ... say may be 30% 22%... not 21.5%..
So, option A (30), B(90) divided by 4 --> leads to fraction number 7.5% 22.5%..
A, B -- 30, 90
eliminate A and B.

C is left.


I solved it using vendiagram too...

It leads to 30% --> 400 *.30 --> 120

This is a smart way but often risky :wink:
_________________

cheers
Its Now Or Never

Kudos [?]: 392 [0], given: 0

Re: venn diagram   [#permalink] 03 Aug 2008, 09:22
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Among 400 students, 56% study sociology, 44% study

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