Here authors also filtered problems which have relatively "simple" solution (which is hard to find). The problems used to fail students included those with extremely hard (or non existent) solutions.
Andrei Sakharov once commented, that he reviewed those kind of math problems, and was perplexed by their complexity.
E.g. http://www.math.msu.su/admission/MATWRITE/w2001j~1.gif does not seem much easier than "jewish" problems; and my understanding is that math department of MSU attempts to admit brilliant people who deliberately prepare to solve problems of this kind.