The GMAT Sample Math question for the day is from the topic Set Theory.

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?

A. 5%
B. 15%
C. 0%
D. 25%
E. None of these

The correct choice is (A) and the correct answer is 5%.

Explanatory Answer
We know that (A U B) = A + B - (A n B), where (A U B) represents the set of people who have enrolled for at least one of the two subjects Math or Economics and (A n B) represents the set of people who have enrolled for both the subjects Math and Economics.

Note
(A U B) = A + B - (A n B) => (A U 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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