Recall that two events could occur at the same time in an inertial reference frame if and only if the invariant interval between them is spacelike i.e.
$\begin{align*}\left(\Delta x\right)^2 + \left(\Delta y\right)^2 + \left(\Delta z\right)^2 - c^2 \left(\Delta t \right)^2 >...$
In our case $\Delta y = \Delta z = 0$ , so this inequality reduces to
$\begin{align*}\left(\Delta x\right)^2 - c^2 \left(\Delta t \right)^2 > 0 \Rightarrow \frac{\left|\Delta x \right|}{\left|\...$
Therefore, answer (C) is correct.

Solution to 2001 Problem 34