Question

The sum of all natural numbers less than $500$ which are not divisible by $7$ is

• A. $17,892$
• B. $124,750$
• C. $106,858$
• D. $107,358$

Answer 1

The correct option is D $107,358$

Natural no.'s less than $500$ not divisible by $7$

Total $=\left[\frac{500}{7}\right]=71$

Greatest integer function

Sum $=(1+2+3+...\dots .500)-(7+14+\mathrm{21...}\dots .497)$

Sum $=\frac{500\left(501\right)}{2}-7(1+2+......71)$

Sum $=250\left(501\right)-\frac{7\times 71\left(72\right)}{2}$

Sum $=125250-17892$

Sum $=107358$

D is correct.