Question

Let $X$ and $Y$ be the sets of all positive divisors of $400$ and $1000$ respectively (including $1$ and the number), then $(X\cap Y)=$

• A. $4$
• B. $6$
• C. $8$
• D. $12$

Answer 1

Answer: (D)

$X$ and $Y$ be set of all divisors of $400$ and $1000$.
So $X=\{1,2,4,5,8,10,16,20,25,40,50,80,100,200,400\}$
$Y=\{1,2,4,5,8,10,20,25,40,50,100,125,200,....1000\}$
$X\cap Y=\{1,2,4,5,8,10,20,25,40,50,100,200\}$
$12$ elements are common in both the sets.
$\Rightarrow n(X\cap Y)=12$