Question

A and B are joined sets.If $n(A-B)=25+x,$ $n(B-A)=2x,$ $n(A\cap B)=2x$ and $n\left(A\right)=2\left[n\right(B)$], then $x=$ ____.

• A. 5

Answer 1

The correct option is A 5

$n(A-B)=25+x,n(B-A)=2x$

$n(A\cap B)=2x$

$n\left(A\right)=n(A-B)+n(A\cap B)$

$=25+x+2x=25+3x$

$n\left(B\right)=n(B-A)+n(A\cap B)$

$=2x+2x=4x$

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

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