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. 38
• C. 54
• D. 36

Answer 1

Answer: (D)

$C\to$ person like coffee
$T\to$ person like Tea

$n(C)=73$
$n(T)=65$
$n(C\cup T)\le 100$
$n(C)+n(T)-n(C\cap T)\le 100$
$73+65-x\le 100$
$x\ge 38$
$73-x\ge 0\Rightarrow x\le 73$
$65-x\ge 0\Rightarrow x\le 65$
$38\le x\le 65$