The entrance math exam in MSU is not pass/fail but graded. There are two math exams (at least in the "math department", I imagine she meant either Mech-Mat or VMK), written and oral. Written exam consists of 6 problems with the passing mark 3 and maximum 5 (you only need to solve 5 correctly, 5th and 6th problems are the hardest and usually allow a choice between an algebra and a geometry problem, giving the time limit it's hard to solve both). Oral test is administered by drawing a random "ticket" with two general questions from the school program (e.g. "What are properties of a triangle?") and the problems the person conducting the test can choose based on the answers and the result of the written test. Answering two "ticket" questions correctly gives you the passing grade (3) already. So there is no way anybody could be failed by any number of the problems given during the oral test if they managed to answer the "ticket". At the worst case one could be dropped to 3 at the oral test, giving total of 8 for the both math tests and that's a pretty good mark. Total test score of 13 (you need to get 5 for the third marked test, written Physics and pass unmarked written Russian) is guaranteed admission. 12 - is a good chance of admission and, depending on the year, even 11 can get you in.

However there is a shortcut - under some conditions (either being a subject of one of Soviet "AA" incentives or being a winner of a math Olympiad), 4 or 5 for the first test (written math) gives automatic admission. 9 for the both math tests is also automatic and unconditional admission.

So the way the hard questions in the oral test come up is usually when you get 4 for the written test. If you could not solve 5th or 6th problem in the written test you are at the average level and giving you 5 (and automatically admitting you) in the oral test would defeat the whole purpose of the shortcut rule to secure admission for the exceptional students. So you have to get 4 or, really, 3 and such a question is to ensure that.

I don't know about anti-semitism, maybe there was some yet I have seen plenty of Jews both among students and faculty so, evidentially, they have not been entirely kept out. Yet I have seen a lot of people (of all origins) complaining about entrance exam being "too hard" and them being persecuted for various reasons. The reality is that pretty much every year from 70s to late 90s there had been several candidates for each student place so some people had to fail the test.