How many numbers are there from 700 to 950 (including both) which are neither divisible by 3 nor by 7?

Total numbers between 700 to 950 = $$950-700+1=251$$ ----------(i)

Numbers between 700 to 950 which are divisible by 3 = 702,705,708,.........,948

This is an AP with first term $$a=702$$ and common difference $$d=3$$

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

=> $$702+(n-1)3=948$$

=> $$(n-1)3=948-702=246$$

=> $$(n-1)=\frac{246}{3}=82$$

=> $$n=82+1=83$$ -------------(ii)

Similarly, numbers between 700 to 950 which are divisible by 7 = 700,707,714,.........,945

=> $$700+(n-1)3=945$$

=> $$(n-1)7=945-700=245$$

=> $$(n-1)=\frac{245}{7}=35$$

=> $$n=35+1=36$$ -------------(iii)

Now, numbers which are divisible by L.C.M.(3,7) = 21 are : 714,735,756,......,945

Similarly, $$n=12$$ ----------(iv)

$$\therefore$$ Numbers between 700 to 950 which are not divisible by 3 or 7 = $$251-83-36+12=144$$

=> Ans - (C)