Bunuel wrote:
A certain school has three performing arts extracurricular activities: Band, Chorus, or Drama. Students must participate in at least one, and may participate in two or even in all three. There are 120 students in the school. There are 70 students in Band, 73 in the Chorus, and 45 in the Drama. Furthermore, 37 students are in both the Band and Chorus, 20 are in both the Band and the Drama, and 8 students are in all three groups. Twenty-five students are just in the chorus, not in anything else. How many students participate in only the drama?
A. 11
B. 12
C. 14
D. 17
E. 21
Kudos for a correct solution.
MAGOOSH OFFICIAL SOLUTION:Here, we have three categories, so we need three circles. Every student must take at least one of these three performing arts extracurricular activities, so there will be no one outside the three circles.
The sum of all seven = 120 (we never use this number in this question)
The totals for the band (70), the chorus (73), and the drama (45) each involve the sum of four discrete regions. We will have to find other information before we can employ them.
“8 students are in all three groups”
N = 8.
“37 students are in both the Band and Chorus”
37 = K + N = K + 8 —> K = 29
“20 are in both the Band and the Drama”
20 = M + N = M + 8 —> M = 12
“twenty-five students are just in the chorus, not in anything else”
L = 25
We now have identified three of the regions in the Chorus circle, so we can solve for P.
chorus = 73 = K + L + N + P
73 = 29 + 25 + 8 + P
P = 11
Now, we have identified three of the regions in the Drama circle, so we can solve for Q.
drama = 45 = M + N + P + Q
45 = 12 + 8 + 11 + Q
Q = 14
This is precisely what the question was asking: how many students are only in drama? There are 14 students who take only drama.
Answer = C
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