Question

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

• A. 3050
• B. 3025
• C. 3060
• D. 3055

Answer 1

The correct option is A

3050

Numbers divisible by 2 are 2, 4, ........100.

$\Rightarrow$ 50 terms $\cdot \cdot \cdot \left(1\right)$

Numbers divisible by 5 are $5,10,\cdot \cdot \cdot ,100$

$\Rightarrow$ 20 terms $\cdot \cdot \cdot \left(2\right)$

Numbers divisible by 2 and 5 are $10,20,\cdot \cdot \cdot ,100$

$\Rightarrow$ 10 terms $\cdot \cdot \cdot \left(3\right)$

When we add (1) and (2), (3) gets added twice. So we will subtract it from the sum(1) + (2).

Sum of numbers in (1) is $\frac{50}{2}(2+100)$

$=102\times 25$

Sum of numbers in (2) is $\frac{20}{2}(5+100)$

$=105\times 10$

Sum of numbers in (3) is $\frac{10}{2}(10+100)$

$=110\times 5$

Required sum = (1) + (2) - (3) [from figure]

$=25\times 102+10\times 105-5\times 110$

$=3050$