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

Solution (By Examveda Team)

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