Is the following rate law possible for the given reaction?
You should use steady state approximation which leads to the mentioned answer:

$$\frac{\mathrm{d}[\ce{CD}]}{\mathrm{d}t} = 0$$

$$
\begin{align}
\ce{C + D &amp;-&gt;[$k_1$] CD}\\
\ce{C + CD &amp;-&gt;[$k_2$] E}
\end{align}
$$

$$\ce{-&gt;[QSSA]}\quad k_1[\ce{C}][\ce{D}] = k_2[\ce{C}][\ce{CD}] \quad\to\quad k_1[\ce{D}] = k_2[\ce{CD}]$$

$$\frac{\mathrm{d}[\ce{E}]}{\mathrm{d}t} = k_2[\ce{C}][\ce{CD}] = k_1[\ce{C}][\ce{D}]$$