Question

A survey shows that $73\%$ of the persons working in 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:

• A. $63$
• B. $54$
• C. $38$
• D. $36$

Answer 1

The correct option is D $36$

$C\to \text{Coffee}$ and $T\to \text{Tea}$
$n\left(C\right)=73\%,n\left(T\right)=65\%$
$n\left(\text{coffee}\right)=\frac{73}{100}$
$n\left(\text{tea}\right)=\frac{65}{100}$
$n(T\cap C)=\frac{x}{100}$
$n(C\cup T)=n\left(C\right)+n\left(T\right)-x\le 100$
$=73+65-x\le 100$
$\Rightarrow x\ge 38$
$\Rightarrow 73-x\ge 0\Rightarrow x\le 73$
$\Rightarrow 65-x\ge 0\Rightarrow x\le 65$
$\therefore 38\le x\le 65$
Therefore, $x\ne 36$