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
The total number of students who study biology = .4(400) = 160.
Eliminate D and E, since the number who study ONLY biology cannot exceed 160.
The greatest remaining answer choice is 120, which is equal to 30% of the 400 students.
Plug (only B) = 30% and the other given percentages into a Venn diagram:
By letting SB = 10% -- so that the total who study biology = 40% -- we can see it's possible that only B = 30%.
The correct answer is
C.
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