# 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

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. 