A survey shows that 73% of the persons working an office like coffee, whereas 65% like tea. If $x$denotes the percentage of them, who like both coffee and tea, then $x$ cannot be

Suppose that the number of employees in the office is 100

Given $n\left(A\right)=73,n\left(B\right)=65,n(A\cap B)=x$

We know that 

              $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

substitute the appropriate values in the above formula

we get 

       $\begin{array}{rcl}n(A\cup B)& =& n\left(A\right)+n\left(B\right)-n(A\cap B)\\ & =& 73+65-x\\ & =& 138-x\end{array}$

and $A\subseteq B,B\subseteq A\cup B\Rightarrow n\left(A\right)\le n(A\cup B),n\left(B\right)\le n(A\cup B)$

it implies that 

      $$\begin{gathered} 73\le 138-x\le 100 \\ \Rightarrow -65\le -x\le -38 \\ \Rightarrow 38\le n\le 65 \end{gathered}$$

Therefore ,$x$ can not be $\boxed{36}$