$$n \in[100,700]$$

$$n(A)=$$ Total $$-$$ (multiple of $$3$$ + multiple of 4) + (multiple of 12)

Total $$=601$$

Multiple of $$3=102,105, \ldots, 699$$

$$\begin{aligned} & n=699=102+(n-1) 3 \\ & \Rightarrow n=200 \end{aligned}$$

Multiple of $$4=100,104 \ldots ., 700$$

$$\begin{aligned} & n=700=100+(n-1) 4 \\ & \frac{600}{4}+1=n \\ & \Rightarrow n=151 \end{aligned}$$

Multiple of $$12=108,120 \ldots .696$$

$$\begin{aligned} & n=696=108+(n-1) 12 \\ & n=50 \\ & \therefore n(A)=601-(200+151)+50 \\ & =300 \end{aligned}$$