If $200\leq a \leq 400$ and $600\leq b\leq 1200$, then the largest value of the quotient $\frac{b}{a}$ is
$\text{(A)}\ \frac{3}{2} \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 300 \qquad \text{(E)}\ 600$
$\frac{b}{a}$ will be largest if $b$ is the largest it can be, and $a$ is the smallest it can be.
Since $b$ can be no larger than $1200$, $b = 1200$. Since $a$ can be no less than $200$, $a = 200$. $\frac{1200}{200} = 6$
$6$ is $\boxed{\text{C}}$