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JEE Main & Advanced Mathematics Sets Question Bank Self Evaluation Test - Sets

  • question_answer
    In a town of 10000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% buy A and B, 3% buy B and C and 4% buy A and C. if 2% families buy all of three newspapers, then the number of families which buy A only, is

    A) 4400

    B)                    3300

    C) 2000    

    D)                    500

    Correct Answer: B

    Solution :

    [b]\[n(A)=40\] % of \[10000=4000,\text{ }n\left( B \right)\text{ }=\text{ }2000,\] \[n(C)=1000,m(A\cap B)=500,n(B\cap C)=300,\] \[n(C\cap A)=400,n(A\cap B\cap C)=200\] \[\therefore n(A\cap \overline{B}\cap \overline{C})=n\left\{ A\cap (B\cup C)' \right\}\] \[=n(A)-n\{A\cap (B\cup C)\}\] \[=n(A)-n(A\cap B)-n(A\cap C)+n(A\cap B\cap C)\] \[=4000-500-400+200=3300.\]


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