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A number of students from the same high school graduating class are en

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Bunuel
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A number of students from the same high school graduating class are en [#permalink] New post   20 Mar 2018, 00:58
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A number of students from the same high school graduating class are enrolled at the same regional university in the fall semester. Of these students, 52 are enrolled in a mathematics course, 52 are enrolled in a psychology course, and 64 are enrolled in an English course. None of the students are enrolled in both mathematics and psychology. If 12 of the students are enrolled in both mathematics and English and 22 are enrolled in both psychology and English, how many of the students are in at least one of these three courses?

(A) 104
(B) 134
(C) 142
(D) 146
(E) 158
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Bunuel
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Re: A number of students from the same high school graduating class are en [#permalink] New post   20 Mar 2018, 00:59
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Bunuel wrote:
A number of students from the same high school graduating class are enrolled at the same regional university in the fall semester. Of these students, 52 are enrolled in a mathematics course, 52 are enrolled in a psychology course, and 64 are enrolled in an English course. None of the students are enrolled in both mathematics and psychology. If 12 of the students are enrolled in both mathematics and English and 22 are enrolled in both psychology and English, how many of the students are in at least one of these three courses?

(A) 104
(B) 134
(C) 142
(D) 146
(E) 158


19. Overlapping Sets



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A number of students from the same high school graduating class are en [#permalink] New post   20 Mar 2018, 02:07
Bunuel wrote:
A number of students from the same high school graduating class are enrolled at the same regional university in the fall semester. Of these students, 52 are enrolled in a mathematics course, 52 are enrolled in a psychology course, and 64 are enrolled in an English course. None of the students are enrolled in both mathematics and psychology. If 12 of the students are enrolled in both mathematics and English and 22 are enrolled in both psychology and English, how many of the students are in at least one of these three courses?

(A) 104
(B) 134
(C) 142
(D) 146
(E) 158


Given data:
P(M) = P(Ps) = 52
P(E) = 64
P(M U Ps) = 0
P(M U E) = 12
P(E U Ps) = 22

The maximum possible value of P(M U E U Ps) = 0 because we have
0 students who take both Mathematics and Psychology

P(Only M) = P(M) - {(P(M U E) + P(M U Ps)} = 52 - 12 = 40
P(Only E) = P(E) - {(P(M U E) + P(E U Ps)} = 64 - 34 = 30
P(Only Ps) = P(Ps) - {(P(E U Ps) + P(M U Ps)} = 52 - 22 = 30

Therefore, the total number of students who are in at least one course = \(40 + 30 + 30 +12 + 22\) = 134(Option B)
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Re: A number of students from the same high school graduating class are en [#permalink] New post   20 Mar 2018, 02:30
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Bunuel wrote:
A number of students from the same high school graduating class are enrolled at the same regional university in the fall semester. Of these students, 52 are enrolled in a mathematics course, 52 are enrolled in a psychology course, and 64 are enrolled in an English course. None of the students are enrolled in both mathematics and psychology. If 12 of the students are enrolled in both mathematics and English and 22 are enrolled in both psychology and English, how many of the students are in at least one of these three courses?

(A) 104
(B) 134
(C) 142
(D) 146
(E) 158


I like to solve 3-overlapping sets problems with a diagram as it helps me visualize the data better.

Please find the image with solution.

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Re: A number of students from the same high school graduating class are en [#permalink] New post   21 Mar 2018, 16:14
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Bunuel wrote:
A number of students from the same high school graduating class are enrolled at the same regional university in the fall semester. Of these students, 52 are enrolled in a mathematics course, 52 are enrolled in a psychology course, and 64 are enrolled in an English course. None of the students are enrolled in both mathematics and psychology. If 12 of the students are enrolled in both mathematics and English and 22 are enrolled in both psychology and English, how many of the students are in at least one of these three courses?

(A) 104
(B) 134
(C) 142
(D) 146
(E) 158


We can use the following equation:

#(at least one course) = #(M) + #(P) + #(E) - #(M & P) - #(M & E) - #(P & E) + #(M & P & E)

Since there are no students enrolled in both Mathematics and Psychology, #(M & P) = 0 and #(M & P & E)
= 0 and we have:

#(at least one course) = 52 + 52 + 64 - 0 - 12 - 22 + 0

#(at least one course) = 134

Answer: B
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Re: A number of students from the same high school graduating class are en [#permalink] New post   22 Mar 2018, 10:44
I found B as answer.

considering number of student who enrolled for all 3 subject is zero and number of students enrolled for Mathematics & Psychology is zero (Given)
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Re: A number of students from the same high school graduating class are en [#permalink]
22 Mar 2018, 10:44
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