Question

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

• A. 3000
• B. 3050
• C. 4050
• D. None of these

Answer 1

Answer: (B)

3050

Answer 2

The sum of integers from 1 to 100 that are divisible by 2 or 5 = sum of series divisible by 2 + sum of series divisible by 5 – sum of series divisible by 2 and 5.

$- ( 10 + 20 + 30 + \ldots \ldots \ldots + 100 )$

$= \frac { 50 } { 2 } \{ 2 \times 2 + ( 50 - 1 ) 2 \} + \frac { 20 } { 2 } \{ 2 \times 5 + ( 20 - 1 ) 5 \}$

$- \frac { 10 } { 2 } \{ 10 \times 2 + ( 10 - 1 ) 10 \}$ $= 2550 + 1050 - 550 = 3050$.