Question

A survey shows that $63\%$ of the Americans like cheese where as $76\%$ like apples. If $x\%$ of the Americans like both cheese and apples, then the value of $x$ is

• A. $39\le x\le 63$
• B. $63$
• C. $39$
• D. $139\ge x$

Answer 1

Answer: (A)

Let total Americans be 100
$\therefore$ Let A Americans like cheese
$\therefore$ Let B Americans likes apple.
$\therefore n(A)=63,n(B)=76$
Then $n(A\cup B)=100$
$\begin{array}{l}\therefore n(A\cap B)=n(A)+n(B)-n(A\cup B)\\ \Rightarrow n=63+76-100\\ \Rightarrow n=39\end{array}$