Question

How many positive integers less than $1001$ are divisible by either $2$ or $5$ or both?

• A. $400$
• B. $500$
• C. $540$
• D. $600$
• E. $700$

Answer 1

The correct option is D $600$

there are thousand positive numbers less than $1001$.( $1$ to $1000$)

There are $\frac{1000}{2}=500$ numbers which are divisible by $2$

There are $\frac{1000}{5}=200$ numbers which are divisible by $5$

But there are some numbers which are divided by both $2$ and $5$. They are repeated twice, so we have to remove once.

There are $\frac{1000}{10}=100$ numbers which are divided by both $2$ and $5$.

Therefore the number of positive integers divisible by either $2$ or $5$ or both is $500+200-100=600$.