Question

A survey shows that $63\%$ of the people in a city read newspaper $A$ whereas $76\%$ read newspaper $B$. If $x\%$ of the people read both the newspapers, then a possible value of $x$ can be:

$37$

$29$

$65$

$55$

• A. $37$
• B. $29$
• C. $65$
• D. $55$

Answer 1

The correct option is D

$55$

Finding the value of x:

Let the people read news $A$is $n\left(A\right)=63\%$

the people read news $B$is $n\left(B\right)=76\%$

the people read both the newspapers $n\left(A\cap B\right)=x$

We know that $max\left(n\left(A\right)\&n\left(B\right)\right)\le n\left(A\cup B\right)\le 100$

$\Rightarrow$$76\le 63+76-x\le 100$

$\Rightarrow$$-63\le -x\le -39$

$\Rightarrow$ $63\ge x\ge 39$

Hence, correct answer is option $\left(D\right)$.