Mathematics - Permutation & Combination Question with Solution | TestHub

The integers divisible by 3 are 33 in number.

The integers divisible by 5 are 20 in number.

The integers divisible by 7 are 14 in number.

The integers divisible by both 3 and 5 are 6 in number.

The integers divisible by both 3 and 7 are 4 in number.

The integers divisible by both 5 and 7 are 2 in number.

There are no integers divisible by all three. Hence, the sum of numbers divisible by 3 or 5 or 7 is:

$$\frac{33}{2}(3+99)+\frac{20}{2}(5+95)+\frac{14}{2}(7+98)-\frac{6}{2}(15+90)-\frac{4}{2}(21+81)-\frac{2}{2}(35+70)$$

$$=33(51)+950+735-315-210-105=2738$$