Question

If $X$ and $Y$ are the sets of all positive divisors of $400$ and $1000$, respectively (including $1$ and the number). Then, $n(XintersectionY)$ is equal to:

• A. $4$
• B. $6$
• C. $8$
• D. $10$
• E. $12$

Answer 1

The correct option is E

$12$

Explanation for the correct option.

Since, $X$ and $Y$are the sets of all positive divisors of $400$ and $1000$, respectively. So, we will find the factors of $400$ and $1000$

Factors of $400=X=\left\{1,2,4,5,8,10,16,20,25,40,50,80,100,200,400\right\}$

Factors of $1000=Y=\left\{1,2,4,5,8,10,20,25,40,50,100,125,200,250,500,1000\right\}$

$X\cap Y=\left\{1,2,4,5,8,10,20,25,40,50,100,200\right\}$

$n\left(X\cap Y\right)=12$

Hence, option E is correct.