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)
_________________

You've got what it takes, but it will take everything you've got