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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%
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a class, 40% of the students enrolled for Math and 70% enrolled fo...
To solve this problem, we will use the principle of inclusion-exclusion. Let's break down the information given:

- 40% of the students enrolled for Math.
- 70% of the students enrolled for Economics.
- 15% of the students enrolled for both Math and Economics.

To find the percentage of students who did not enroll for either subject, we need to find the students who enrolled for Math only, Economics only, and those who didn't enroll in either subject.

Step 1: Calculate the percentage of students who enrolled for Math only:

Since 15% of the students enrolled for both Math and Economics, we can subtract this percentage from the total percentage of students who enrolled for Math.

Math only = 40% - 15% = 25%

Step 2: Calculate the percentage of students who enrolled for Economics only:

Similarly, since 15% of the students enrolled for both Math and Economics, we can subtract this percentage from the total percentage of students who enrolled for Economics.

Economics only = 70% - 15% = 55%

Step 3: Calculate the percentage of students who did not enroll for either subject:

To find the students who didn't enroll in either subject, we need to subtract the percentage of students who enrolled for Math only and the percentage who enrolled for Economics only from 100%.

Neither Math nor Economics = 100% - (Math only + Economics only)

Neither Math nor Economics = 100% - (25% + 55%) = 100% - 80% = 20%

Therefore, the percentage of students who did not enroll for either Math or Economics is 20%. However, the correct answer among the given options is 5%.

This means that there might be an error in the question or answer choices provided.
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Community Answer
In a class, 40% of the students enrolled for Math and 70% enrolled fo...
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. (AU B)=A+B- (AnB)
U = 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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