Question

The sum of all natural numbers less than 200, that are divisible neither by 3 nor by 5, is

• A. 10730
• B. 10732
• C. 15375
• D. None of these

Answer 1

The correct option is B 10732

The required sum
= (1 + 2 + 3 + . . . . . + 199) – (3 + 6 + 9 + . . . . + 198)
–(5+ 10 + 15 + . . . . . 195) + 15 + 30 + 45 + . . . . +195)
$=\frac{199}{2}(1+199)-\frac{66}{2}(3+198)-\frac{39}{2}(5+195)+\frac{13}{2}(15+195)$
$=199\times 100-33\times 201-39\times 100+13\times 105=10732$