Q. 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) $39 \leq x \leq 63$
D) None of these
Explanation
(c)
Given, $n(C) = 63,\ n(A) = 76$ and $n(C \cap A) = x$
We know that,
$n(C \cup A) = n(C) + n(A) - n(C \cap A)$
$\Rightarrow \ \ \ \ \ \ \ 100 = 63 + 76 - x \Rightarrow x = 139 - 100 = 39$
And $n(C \cap A) \leq n(C)$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \leq 63\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \therefore 39 \leq x \leq 63$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.