Add and multiply

Let the two number be $a$ and $b$ . Then, we have:

$\begin{aligned} a+b & = 7 \implies b = 7-a \\ \implies ab & = a(7-a) \\ & = 7a - a^2 \\ & = - \left(a^2 - 7a + \frac {49}4\right) + \frac {49}4 \\ & = \frac {49}4 - \color{#3D99F6} \left(x- \frac 72 \right)^2 & \small \color{#3D99F6} \text{Note that }\left(x- \frac 72 \right)^2 \ge 0 \\ \implies ab & \le \frac {49}4 \end{aligned}$

Therefore, the answer is " None of the others ".

Using AM-GM inequality :x + y ≥ 2√xy , 7≥ 2√xy, 49/4 ≥ xy, so max.(xy) = 49/4