csatmedium
In a town, 45% population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazines A and B, 15% read magazines B and C, 25% read magazines A and C; and 10% read all the three magazines. What percentage do not read any magazine?
- A.10%
- B.15%
- C.20%
- D.25%
▶ Answer & Explanation
Correct answer: A. 10%
This problem can be solved using the principle of inclusion-exclusion for three sets. The formula for the union of three sets A, B, and C is P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C). Substituting the given percentages, we get P(A U B U C) = 45 + 55 + 40 - 30 - 15 - 25 + 10 = 140 - 70 + 10 = 80%. The percentage of the population that does not read any magazine is 100% - P(A U B U C) = 100% - 80% = 20%.
Source: UPSC csat 2015