Question

Let $n(A-B)=25+x,n(B-A)=2x$ and $n(A\cap B)=2x.$ If $n\left(A\right)=2\left(n\right(B\left)\right),$ then $x$ = ___.

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

The correct option is B

5

Given that $n(A-B)=25+x,n(B-A)=2x$ and $n(A\cap B)=2x.$

We know that $n\left(A\right)=n(A-B)+n(A\cap B).$$=25+x+2x=3x+25$

Similarly, $n\left(B\right)=n(B-A)+n(A\cap B)$
$=2x+2x$ = $4x.$

$n\left(A\right)=2\left(n\right(B\left)\right)\Rightarrow 3x+25$ = $2\times 4x$

$\Rightarrow 5x=25\Rightarrow x=5$