Question

The sum of the integers lying between 1 and 100 and divisible by 3 or 5 or 7 is

• A. 2838
• B. 3468
• C. 2738
• D. 3368

Answer 1

The correct option is C 2738

The integers divisible by 3 are 33 in numbers.
The integers divisible by 5 are 20 in numbers.
The integers divisible by 7 are 14 in numbers.
The integers divisible by both 3 and 5 are 6 in numbers.
The integers divisible by both 3 and 7 are 4 in numbers.
The integers divisible by both 5 and 7 are 2 in numbers.
There are no integers divisible by all three.
Hence the sum of numbers divisible by
3 or 5 or 7 is
$=\frac{30}{2}(3+99)+\frac{20}{2}(5+95)+\frac{14}{2}(7+98)-\frac{6}{2}(15+90)-\frac{4}{2}(21+84)-1(35+70)$
$=33\left(51\right)+950+735-315-210-105=2738$