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

A
3050
B
3150
C
3250
D
3350

Solution:

Required sum

$\begin{array}{l} = (2 + 4 + \dots + 100) + (5 + 10 + \dots + 100) - \\ (10 + 20 + \dots + 100) \\ = \frac{50}{2} (2 + 100) + \frac{20}{2} (5 + 100) - \frac{10}{2} (10 + 100) \\ = (50) (51) + (10) (105) - 550 \\ = 2550 + 1050 - 550 = 3050 \end{array}$

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