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

The correct option is A

$x=39$

Finding the number of Americans who like both cheese and apples:

Given,

Let, the given the Americans like cheese $n\left(C\right)=63$

Americans like apple $n\left(A\right)=76$

Americans like both cheese and apples$n\left(C\cap A\right)=x$

Americans like both cheese or apples $n\left(C\cup A\right)=100$

$\Rightarrow$$100=63+76-x$ $\mathbf{;}\mathit{n}\mathbf{(}\mathbf{A}\mathbf{\cup }\mathbf{B}\mathbf{)}\mathbf{=}\mathit{n}\mathbf{\left(}\mathbf{A}\mathbf{\right)}\mathbf{+}\mathit{n}\mathbf{\left(}\mathbf{B}\mathbf{\right)}\mathbf{-}\mathit{n}\mathbf{(}\mathbf{A}\mathbf{\cap }\mathbf{B}\mathbf{)}$

$\Rightarrow$ $x=39$

Therefore, correct answer is option $\left(A\right)$.