QUESTION

CSAT

Easy

Maths

Prelims 2015

In a town, 45% of the 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 three magazines. What percentage do not read any magazine?

Select an option to attempt

Explanation

Given Data:

  • 45% read magazine A
  • 55% read magazine B
  • 40% read magazine C
  • 30% read both magazines A and B
  • 15% read both magazines B and C
  • 25% read both magazines A and C
  • 10% read all three magazines A, B, and C

Using the Inclusion-Exclusion Principle: Formula: P(ABC)=P(A)+P(B)+P(C)P(AB)P(BC)P(AC)+P(ABC)P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(B \cap C) - P(A \cap C) + P(A \cap B \cap C)

Substituting the given values: P(ABC)=45%+55%+40%30%15%25%+10%P(A \cup B \cup C) = 45\% + 55\% + 40\% - 30\% - 15\% - 25\% + 10\%

Calculations: 45%+55%+40%=140%45\% + 55\% + 40\% = 140\% 30%+15%+25%=70%30\% + 15\% + 25\% = 70\% 140%70%=70%140\% - 70\% = 70\% 70%+10%=80%70\% + 10\% = 80\%

Thus, 80% of the population reads at least one magazine.

Conclusion: The percentage of the population that does not read any magazine is: 100%80%=20%100\% - 80\% = 20\%

Correct answer: C. 20%

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