Sometimes I will ask random questions such as "how many people fly in a plane every day in the world".
I'm not too concerned about the answer, but more if they can reason through the problem with sound logic.

The questions of this kind (how much would you charge to clean all windows in Seattle etc.) are the most tired questions in technical interviews. Dear interviewers, please use some imagination and come up with something original. What would be an example of "brilliant" answer to this question anyway?