Special Relativity - Space-Time Interval

In an inertial reference frame S, two events occur on the x-axis separated in time by Δt and in space by Δx. In another inertial reference frame S’, moving in the x-direction relative to S, the two events could occur at the same time under which, if any, of the following conditions?

A. For any values of Δx and Δt.
B. Only if 
C. Only if 

D. Only if 
E. Under no condition

(GR0177 #34)

Solution:

The Invariant Space-Time Interval:  ΔS² = Δx² − (cΔt)² 

For the two events occur at the same time: ΔS²  0
Δx² − (cΔt)²  0
Δx²  (cΔt)²
(Δx/Δt)²  c²
|Δx/Δt|  c

Answer: C