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

Let the total numbers be 100 given that  $n\left(A\right)=63,n\left(B\right)=76$
$n(A\cap B)=x$  we know that
$n(A\cap B)\le$  minimum of  $n\left(A\right),n\left(B\right)$
$\therefore n(A\cap B)=x\le 63$  we know that 
 $n(A\cup B)\le 100\Rightarrow x\ge 39\Rightarrow 39\le x\le 63$