GMAT® Practice : Sets

Concept: Union of 2 overlapping sets

The GMAT math practice question is from set theory. Concept tested: Union and intersection of 2 sets. Task: Computing the cardinal number or number of elements in only set A.

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?

  1. 30
  2. 10
  3. 18
  4. 28
  5. 32

Explanatory Answer

Video explanation will be added soon

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, n(A \\cup) B) is the set of students who have enrolled for at least one of the two languages. As the students of the class have enrolled for at least one of the two languages, we will not find anyone outside A \\cup) B in this class.
So, n(A \\cup) B) = 40

n(A \\cup) B) = n(A) + n(B) - n(A \\cap) B)
i.e, 40 = n(A) + 22 - 12
Or n(A) = 30 which is the set of students who have enrolled for English. This number is the sum of those who have enrolled for only English and those who have enrolled for both the languages.

However, we have to find out the number of students who have enrolled for only English.
n(only English)= n(English) - n(A \\cap) B)
= 30 - 12 = 18.

Choice C is the correct answer.

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