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Bunuel
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A number of students from the same high school graduating class are en 20 Mar 2018, 00:58
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15% (low)

Question Stats:

89% (02:18) correct 11% (04:04) wrong based on 98 sessions

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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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B
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A number of students from the same high school graduating class are en 20 Mar 2018, 00:59
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Bunuel
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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19. Overlapping Sets



For more:
ALL YOU NEED FOR QUANT ! ! !
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A number of students from the same high school graduating class are en 20 Mar 2018, 02:07
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Bunuel
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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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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A number of students from the same high school graduating class are en 20 Mar 2018, 02:30
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Bunuel
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
Show more

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.

Best,
Gladi
Attachments

3-overlapping-sets.jpg
3-overlapping-sets.jpg [ 3.34 MiB | Viewed 3717 times ]

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A number of students from the same high school graduating class are en 21 Mar 2018, 16:14
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Bunuel
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
Show more

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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A number of students from the same high school graduating class are en 22 Mar 2018, 10:44
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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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