The math question for the 4gmat question bank today is from the topic set theory.

Question
In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?

A. 30
B. 10
C. 18
D. 28
E. 32

The correct choice is (C) and the correct answer is 18.

Explanatory Answer
Let A be the set of students who have enrolled for English and B be the set of students who have enrolled for German.

Then, (A U B) is the set of students who have enrolled at least one of the two subjects. As the students of the class have enrolled for at least one of the two subjects, A U B = 40

We know A U B = A + B - (A n B)
i.e, 40 = A + 22 - 12
or A = 30 which is the set of students who have enrolled for English and includes those who have enrolled for both the subjects.

However, we need to find out the number of students who have enrolled for only English = Students enrolled for English - Students enrolled for both German and English
= 30 - 12 = 18.

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