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

Question

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?

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?

scthakur · Answer

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%.

amitdgr · Answer

I am also getting 120 ... whats the OA ? and can you tell me the source of these questions you are posting ? Thanks

x2suresh · Answer

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

arjtryarjtry · Answer

how did you get 160?

x2suresh · Answer

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

icandy · Answer

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

incognito1 · Answer

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%)

leonidas · Answer

What is the source of this question?

ssandeepan · Answer

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

spriya · Answer

This is a good approach

KASSALMD · Answer

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.

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

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