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:

• A. 65
• B. 37
• C. 29
• D. 55

Answer 1

Answer: (D)

Finding the value of $x$ : Let the people read news $A$ is $n(A)=63\%$ the people read news $B$ is $n(B)=76\%$ the people read both the newspapers $n(A\cap B)=x$ We know that $\max (n(A)\&n(B))\le n(A\cup B)\le 100$ $\Rightarrow 76\le 63+76-x\le 100$
$\Rightarrow -63\le -x\le -39$
$\Rightarrow 63\ge x\ge 39$