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

Answer: Option C

Number from 1 to 200 which is divisible by 3
3, 6, . . . . . . . . ., 198
$$\begin{array}{rl}& =\frac{198-3}{3}+1\\ & =66\end{array}$$
Total number which divisible by 3 & 7
$$\begin{array}{rl}& =\frac{189-21}{21}+1\\ & =\frac{168}{21}+1\\ & =9\end{array}$$
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