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. $39 \leq x \leq 63$
• B. $63$
• C. $39$
• D. $139 \geq x$

Answer 1

Answer: (C)

$39$

Answer 2

Let total number of persons = 100
Let A = \\{x : x like cheese\\}
B = \\{x:x like apples \\}
\therefore A \, \cap B= \\{x: x likes both cheese and apples \\}
Given $n(A) = 63, n(B) = 76$
$n(A \,\cap\,B)=x$.
We know that
$n(A\,\cup\,B)=n(A)+n(B)-n(A\,\cap\,B)$
$\therefore 100 =63+76-x$
$\Rightarrow x = 139 - 100 = 39$.