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SSC Quantitative Aptitude Number System and its Operations Question Bank Set Theory (I)

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

    A) 3200

    B) 3000

    C) 4200

    D) 3300

    Correct Answer: D

    Solution :

    [d] We have, \[n\,(A)=40%\]of \[10000=4000\] \[n\,(B)=20%\]of \[10000=2000\] \[n\,(C)=10%\]of \[10000=1000\] \[n\,(A\cap B)=5%\]of \[10000=500\] \[n\,(B\cap C)=3%\]of \[10000=300\] \[n\,(C\cap A)=4%\]of \[10000=400\] and       \[n\,(A\cap B\cap C)=2%\]of \[10000=200\] We want to find \[n\,(A\cap {{B}^{c}}\cap {{C}^{c}})=n\,[A\cap {{(B\cup C)}^{c}}]\] \[=n\,(A)-n\,[A\cap (B\cup C)]=n\,(A)-n\,[(A\cap B)\cup (A\cap C)]\] \[=n\,(A)-[n\,(A\cap B)+n\,(A\cap C)-\,n\,(A\cap B\cap C]\] \[=4000-[500+400-200]\] \[=4000-700\] \[=3300\]


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