Question

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

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

Answer: (B)

5

Answer 2

$n\left(A -B\right)= 25 +x, n\left(B-A\right) =2x$ $n\left(A \cap B\right) =2x$ $n\left(A\right) =n\left(A -B\right) + n\left(A\cap B\right)$ $= 25+x+2x=25 +3x$ $n\left(B\right)=n \left(B-A\right)+n \left(A\cap B\right)=2x+2x=4x$ $n \left(A\right)=2n \left(B\right)\Rightarrow25+3x=2\left(4 x\right)$ $\Rightarrow 5x=25 \Rightarrow x=5$