How many number are there between 1 to 200 which are divisible by 3 but not by 7?

Solution(By Examveda Team)

Number from 1 to 200 which is divisible by 3
3, 6, . . . . . . . . ., 198
$$\eqalign{ & = \frac{{198 - 3}}{3} + 1 \cr & = 66 \cr} $$
Total number which divisible by 3 & 7
$$\eqalign{ & = \frac{{189 - 21}}{{21}} + 1 \cr & = \frac{{168}}{{21}} + 1 \cr & = 9 \cr} $$
Total number which is divisible by 3 but not 7
= 66 - 9 = 57

Alternate solution
Total number which is divisible by 3 & 7 both from 1 to 200
LCM (3 & 7) $$ \to \frac{1}{{21}} - \frac{{200}}{{21}} = 0 - 9 = 9$$
Total number which is divisible by only 3, from 1 to 200
$$\frac{1}{3} - \frac{{200}}{3} = 0 - 66 = 66$$
∴ Total number which is divisible by 3 but not 7
= 66 - 9 = 57