Question

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. $x=39$
• B. $x=63$
• C. $39\le x\le 63$
• D. None of these

Answer 1

Answer: (C)

$39\le x\le 63$

Let total Americans be $100$

$\therefore$ Let $A$ Americans like cheese

$\therefore$ Let $B$ Americans likes apple.

$\therefore n\left(A\right)=63,n\left(B\right)=76$

Then $n(A\cup B)=100$

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

$\Rightarrow n=63+76-100$

$\Rightarrow n=39$