JEE Main & Advanced Sample Paper JEE Main - Mock Test - 14

  • question_answer
    A survey shows that \[63%\]of the Americans like cheese whereas \[76%\] like apples. If \[x%\]of the Americans like both cheese and apples, then

    A) \[x=39\]              

    B)   \[x=63\]

    C) \[39\le x\le 63\]       

    D)               None of these

    Correct Answer: C

    Solution :

     Let C represents the set of Americans like cheese and A represents the set of Americans like apples.
    \[C\cap A\] represents the set of Americans like both cheese and apples.
    \[\therefore \,\,n(C)=63,\] \[n(A)=76,\]and \[n(C\cap A)=x\]
    We know that,
    \[n(C\cup A)=n(C)+n(A)-n(C\cap A)\]
    \[100=63+76-x\]
    \[\Rightarrow \,x=139-100=39\] and \[n(C\cap A)\le n(C)\]
    \[\Rightarrow \,x\le 63\]
    \[\therefore \,\,\,39\le x\le 63.\]


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