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GRE - Quantitative Reasoning - Sets

Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in the school are in the band but are not in the science club, what percent of the students who are in the science club are not i

Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in the school are in the band but are not in the science club, what percent of the students who are in the science club are not in the band?

A : 5%
B : 20 
C : 25
D : 60
E : 75% 

Let Set S consist of students in science and Set B consist of students in band

n(S) = 20

n(B) = 30

n(B) - n(S∩B) = 25

30 - n(S∩B) = 25

n(S∩B) = 5

n(S) - n(S∩B) = 20 - 5 = 15%

% of science students not in club = 15/20 * 100 = 75%