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

Answer: Option C

Number which is divisible by 3
$$\begin{array}{rl}& \frac{700}{3}-\frac{950}{3}\\ & =233-316\\ & =\mathrm{83......}\left(\text{i}\right)\end{array}$$
⇒ Number which is divisible by 7
$$\begin{array}{rl}& \frac{700}{7}-\frac{950}{7}\\ & =100-135\\ & =35+1\\ & =\mathrm{36......}\left(\text{ii}\right)\end{array}$$
(∴ If 1^st number is totally divisible by 7 then we add +1 in final result)
⇒ Number which is divisible by 21 (LCM of 3 or 7)
$$\begin{array}{rl}& \frac{700}{21}-\frac{950}{21}\\ & =33-45\\ & =\mathrm{12......}\left(\text{iii}\right)\end{array}$$
∴ Number which is divisible by 3 or 7
(i) + (ii) - (iii)
(83 + 36) - 12 = 119 - 12 = 107
Total number from 700 to 950
n = (950 - 700) + 1 = 251
∴ Number which is neither divisible by 3 nor 7
⇒ 251 - 107 = 144