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%

Answer 1

The correct option is A

5%

We know that (A $\cup$ B) = A + B - (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 n B) represents the set of people who have enrolled for both the subjects Math and Economics.

Note: -
(A $\cup$ B) = A + B - (A $\cap$ B) $\Rightarrow$ (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 remaining 5% did not enroll for either of the two subjects.


Approach 2- Using S-X Technique
S = 40% + 70% = 110%, X = ? and II = 15%
S - X = II, $\Rightarrow$ 110% - X = 15% $\Rightarrow$ X = 95%. Therefore, the remaining 5% did not enrol for either of the two subjects.