In the Lomonosov Moscow State Uni, in the math departments (Mechmat and VMK) there were 4 entrance exams, at the time of the article three of those graded at 3-5 points and one pass/fail. One could get 9-15 points total and the admission was in the order of the highest points, with the cut off being between 13 and 12 usually (the 12 pointers would compete in the high school's GPA and other extra credits). A failure in any of the exams (2 points) would eliminate one from the admission.

There was a shortcut: anybody with 9+ points for the first two (written and oral math) would be unconditionally admitted without even needing to take the two remaining exams (and risking a failure). There were other shortcuts not relevant here.

The written exam is 6 problems. You get a point for every one solved. Naturally the difficulty is increasing exponentially with the 5th and 6th being very hard (you only need to solve one of these to get the maximum 5 points, they are the same difficulty but one is usually an equation and another is a geometry problem). The first 4 problems are still easy for a good high school student, the 5th/6th requires extra preparation or going to a special math school. (some examples http://kvant.mccme.ru/1991/02/p65.htm )

The oral exam is two questions on a "ticket" and a problem. The list of questions is known beforehand and they are generic topics like "What are the properties of triangles?", the ticket is literally a piece of paper one pulls from a pile, face down. And each question and the problem give a point to add to 2. So you can only fail if you don't answer any question and don't solve the problem. Again, it's an easy 4 points with the two questions (out of total 50 or so) answered.

So what happens when somebody answered correctly the both ticket questions? He or she already has 4 points and the problem will decide between 4 and 5. If he or she has 5 for the written math (the written test is in front of the examiner) it does not matter, this person is already admitted with 9 points so the problem will be a simple one to save time. If the written score is 3, it will be a hard problem that this person is likely not going to solve (harder than the 4th problem in the written exam but not as hard as 5th or 6th) that will make the total math 7 points and limit that person's entrance exam score to 12 points, likely not letting them in because you really should not be in the math department if you could only solve 3 easy problems in the written exam.

The 4 points for the written math is the most peculiar, especially if one had good work done on the 5th problem even without solving it ultimately. If this person solves the problem in the oral math, it's the automatic admission. So a tricky problem comes out. You cannot give the same problem you give to the one with 3 points because it will be too easy. You cannot really give another 5th or 6th problem from the written math because it takes an hour to solve so they give a problem that is as hard as the 5th/6th but can be solved in minutes, giving a fair chance for an automatic admission. If the candidate fails it it's not the end, they continue with 8 points and still a fair chance for admission.

This is not related to Jews, as far as I know, I know people who were not Jewish and got these problems after getting 4 points for the written math. This is to set the uniform standard for the accelerated admission: five written exam problems and two theoretical questions.