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A certain school has three performing arts extracurricular activities:

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Re: A certain school has three performing arts extracurricular activities: [#permalink]
Agree with the above, answer should be 14. C.

So much information to take in.

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

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A certain school has three performing arts extracurricular activities: [#permalink]
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I also used a venn diagram, a bit differently than Akashmadaan though. Please look at the picture and I will explain here:

So, we will start by writing down the inromation we have about the numbers in each group and in two-groups.
In all three groups we have 8 people and 120 people in total.

W add 8 in the region shared by all. Then we are using the information we have about two-groups, and make sure to subtract 8 from each, as seen in the picture.

We now have all of the four areas of B complete (70 in total for B) and we are looking for the remaining three areas on the left (named x1, x2, x3).

To find these numbers we will use our knowledge that we have 120 people in total:
70 + x1 + x2 + x3 = 120
x1 + x2 + x3 = 50 [1]

x2+x3 = 45 - 20 = 25 [2]
*(the total # of people minus the 12+8 we already have)

We will now substiture [2] into [1]
x1 + x2 + x3 = 50
x1 + 25 = 50
x1 = 25

Then x2 = 73 - (25 + 29 + 8) = 11 and
x3 = 45 - (12 + 8 + 11) = 14.

x3 was the region we were looking for, so ANS C.
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Re: A certain school has three performing arts extracurricular activities: [#permalink]
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Refer diagram below

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Re: A certain school has three performing arts extracurricular activities: [#permalink]
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.

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Re: A certain school has three performing arts extracurricular activities: [#permalink]
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Re: A certain school has three performing arts extracurricular activities: [#permalink]
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