Bunuel wrote:
Of the 27 participants in a talent show, 13 are singers, 14 are musicians, and 9 are dancers. If 4 people are both singers and dancers, 3 are both singers and musicians and 1 person is all three, how many people are both dancers and musicians?
A. 0
B. 1
C. 2
D. 3
E. 4
If S=singers, M=musicians and D=dancers, we have:
D∩S=4, S∩M=3 and S∩M∩D=1
We are looking for D∩M=1+x (because S∩M∩D=1)
Dx is the part of circle D without the intersections with the other circles
Mx is the part of circle M without the intersections with the other circles
Thus, we have 3 equations with 3 unknowns:
Mx+Dx+13+x=27
Mx+3+x=14 (Because m=14)
Dx+4+x=9 (Because d=9)
Which gives x=2 and D∩M=1+x=3
Answer (D)
PS: I couldn't upload a file because I have less than 5 posts, but if you make a Venn diagram, you'll see what I am talking about.