This GMAT Sample Math question is a problem solving question from Sets. Concept: Computing union of two overlapping sets and then finding its complement. An easy, GMAT sub 600 level, Set Theory sample question.
Question 4: 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?
Let A be the set of students who enrolled for Math.
Let B be the set of students who enrolled for Economics.
(A ∪ B) is the set of students who have enrolled for at least one of the two subjects.
And (A ∩ B) is the set of students who have enrolled for both Math and Economics.
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
In this question, all n(A), n(B), n(A ∪ B), and (A ∩ B) are expressed in percentage terms.
n(A ∪ 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.
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