Question

A survey shows that 63% of the people watch news whereas 76% watch sports. If $x$% of people watch both sports and news, then

• A. $x=39$
• B. $x=63$
• C. $39\le x\le 63$
• D. $0\le x\le 39$

Answer 1

The correct option is C

$39\le x\le 63$

Let A be the set of percentage of those people who watch news and B be the set of percentage of those people who watch sports.
$n\left(A\right)=63,n\left(B\right)=76,andn(A\cap B)=x\because n(A\cup B)\le 100\Rightarrow n\left(A\right)+n\left(B\right)-n(A\cap B)\le 100\Rightarrow 63+76-x\le 100\Rightarrow x\ge 39Also,n(A\cap B)\le min\left\{n\right(A),n(B\left)\right\}\Rightarrow x\le 63\therefore 39\le x\le 63$