Question

In a survey, it is found that $63\%$ Americans like cheese and $76\%$ like apple. If $x\%$ Americans like both, then

• A. $39\le x\le 63$
• B. $37\le x\le 63$
• C. $24\le x\le 37$
• D. $24\le x\le 63$

Answer 1

The correct option is A $39\le x\le 63$

$n\left(A\right)=63=$ The Americans who like cheese
$n\left(B\right)=76=$ The Americans who like apple
Let $n(A\cap B)=x$
$\because n(A\cup B)\le 100$
$n\left(A\right)+n\left(B\right)-n(A\cap B)\le 100$
$\Rightarrow x\ge 39$
$n(A\cap B)\le min\left\{n\right(A),n(B\left)\right\}\Rightarrow x\le 63$