AMC 8 1986 Problem 14

If $200\leq a \leq 400$ and $600\leq b\leq 1200$, then the largest value of the quotient $\frac{b}{a}$ is $\text{(A)}\ \frac{3}{2} \text{(B)}\ 3 \text{(C)}\ 6 \text{(D)}\ 300 \text{(E)}\ 600$