zisis wrote:

3/8 of all students at Social High are in all three of the following clubs: Albanian, Bardic, and Checkmate. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Checkmate. If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?

(A) 1/8

(B) 1/4

(C) 3/8

(D) 1/2

(E) 5/8

We can let the total number of students = 8, and thus:

Since 3/8 of all students are in all 3 clubs, 3 students are in all 3 clubs

Since 1/2 of all students are in Albanian, 4 students are in Albanian

Since 5/8 of all students are in Bardic, 5 students are in Bardic

Since 3/4 of all students are in Checkmate, 6 students are in Checkmate.

From the given information, we know that 0 students are in none

Letting t = the number of students in exactly two clubs, we can now use the equation:

Total = A + B + C - (exactly two clubs) -2(all three clubs) + none

8 = 4 + 5 + 6 - t - 2(3) + 0

8 = 15 - t - 6

t = 1

So, 1/8 are in exactly two clubs.

Answer: A