GMAT® Practice : Set Theory

Concept: Complement of union of 2 overlapping sets

This GMAT Sample Math question is a problem solving question from Sets. Concept:Computing union of two overlapping sets and then finding its complement

Question: In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enroll for either of the two subjects?

  1. 5%
  2. 15%
  3. 0%
  4. 25%
  5. None of these

Explanatory Answer

Video explanation will be added soon

n(A \\cup) B) = n(A) + n(B) - n(A \\cap) B), where (A \\cup) B) represents the set of people who have enrolled for at least one of the two subjects Math or Economics and (A \\cap) B) represents the set of people who have enrolled for both the subjects Math and Economics.

n(A \\cup) B) = 40 + 70 - 15 = 95%

That is 95% of the students have enrolled for at least one of the two subjects Math or Economics.

Therefore, the balance (100 - 95)% = 5% of the students have not enrolled for either of the two subjects.

Choice A is the correct answer.

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