Sample Question #2 (math)
Show that a set is convex if and only if its intersection with any line is convex. Show that a set is affine if and only if its intersection with any line is affine.
[Taken from chapter 2 of Boyd and Vandenberghe, Convex Optimization (click title to go to Amazon page)]
(Comment: concepts related to convex sets are important in optimization, and many quant jobs involve optimization research.)