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 value of x can be
 

 Let A denote the set of Americans who like cheese and let B denote the set of Americans who like apples. 

Let population of America be 100. 

$\begin{array}{l}\text{ Then }n\left(A\right)=63,n\left(B\right)=76\\ \text{ Now, }n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)\\ =63+76-n(A\cap B)\\ \Rightarrow n(A\cap B)=139-n(A\cup B)\\ \text{ But }n(A\cup B)\le 100\end{array}$

$\begin{array}{l}\therefore 139-n(A\cup B)\ge 139-100=39\\ \therefore n(A\cap B)\ge 39\text{ i.e., }39\le n(A\cap B)\\ \text{ Again, }A\cap B\subseteq A,A\cap B\subseteq B\\ \therefore n(A\cap B)\le n\left(A\right)=63\text{ and }n(A\cap B)\le n\left(B\right)=76\\ \therefore n(A\cap B)\le 63\\ \text{ Then, }39\le n(A\cap B)\le n\left(B\right)\Rightarrow 39\le x\le 63\end{array}$