How many numbers are there from 500 to 650 (including both) which are neither divisible by 3 nor 7?

Answer: Option C

Total number from 500 to 650 = 650 - 500 + 1 = 151
Total number from 500 to 650 which are divisible by 3
$$=\frac{650}{3}-\frac{500}{3}=216-166=50$$
Total number for 500 to 650 which are divisible by 7
$$=\frac{650}{7}-\frac{500}{7}=92-71=21$$
Total number from 500 to 650 which are divisible by 21
$$=\frac{650}{21}-\frac{500}{21}=30-23=7$$
Number neither divisible by 3 nor 7
= 151 - 50 - 21 + 7
= 151 - 71 + 7
= 80 + 7
= 87