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

Numbers between 1 to 200 which are divisible by 3 = 3,6,9,.........,198

This is an AP with first term $$a=3$$ and common difference $$d=3$$

Last term of AP = $$a+(n-1)d$$

=> $$3+(n-1)3=198$$

=> $$(n-1)3=198-3=195$$

=> $$(n-1)=\frac{195}{3}=65$$

=> $$n=65+1=66$$

Now, numbers which are divisible by L.C.M.(3,7) = 21 are : 21,42,63,......,189

Similarly, $$21+(n-1)21=189$$

=> $$(n-1)21=189-21=168$$

=> $$(n-1)=\frac{168}{21}=8$$

=> $$n=8+1=9$$

$$\therefore$$ Numbers between 1 to 200 which are divisible by 3 but not by 7 = $$66-9=57$$

=> Ans - (C)