Question

The sum of integers from $1$ to $100$ that are divisible by $2$ or $5$ is

• A. $3150$
• B. $3550$
• C. $2550$
• D. $3050$

Answer 1

The correct option is D $3050$

The required sum
$=$ (sum of integers divisible by $2$)
$+$ (sum of integers divisible by $5$)
$-$ (sum of integers divisible by $10$)

$=(2+4+6+\cdots +100)+(5+10+15+\cdots +100)-(10+20+30+\cdots +100)=\frac{50}{2}(2+100)+\frac{20}{2}(5+100)-\frac{10}{2}(10+100)=50\times \left(51\right)+10\times \left(105\right)-10\times \left(55\right)=2550+10\times (105-55)=2550+500=3050$