KöMaL 2007 C921

The average of Steve's mathematics marks was between 4 and 5 before the last maths test of the first semester was given back to the class. (Marks in Hungarian schools are 1 to 5, 5 means excellent and 1 means fail. Teachers sometimes give half marks such as 3 and a half, too, to indicate that it is between a 3 and a 4, but final marks are whole numbers.) The teacher said to Steve, ``16 of you took this test. I also gave half marks. The range of your marks is 2, the mode is 4.5, and the median is 4. The average of the marks is the worst possible average that a group of 16 may have with these conditions. If you can tell me whether you may or may not have got a 5 on this test, then you will get a 5 for the first semester.'' Steve did get his 5. What was his answer to the question?