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:
Correct Option: , 4
Solution:
$\mathrm{C} \rightarrow$ person like coffee
$\mathrm{T} \rightarrow$ person like Tea
$\mathrm{n}(\mathrm{C})=73$
$\mathrm{n}(\mathrm{T})=65$
$n(C \cup T) \leq 100$
$n(C)+n(T)-n(C \cap T) \leq 100$
$73+65-x \leq 100$
$x \geq 38$
$73-x \geq 0 \Rightarrow x \leq 73$
$65-x \geq 0 \Rightarrow x \leq 65$
$38 \leq \mathrm{x} \leq 65$