Hard to say. I've never seen any firm rule on this apply. It seems to be a guessing game. For instance - Even for someone with a "medium level" understanding it is still uncertain what they know. It often depends on how they learned it and what question is being asked.
The quesion of the relativistic mass for light is a good example. If a student has a text which defines inertial (aka relativistic) mass, m, as
[tex]m = \frac{m}{\sqrt{1-v^2/c^2}}[/tex]
then they might think that the relativistic mass for light is undefined. They might think that its zero too. However if the students text defines inertial mass in the correct way, i.e. as m = p/v, then its obvious that anything with a finite momentum and finite speed has a finite m. This fact is not a well known fact but this is the most rigorous and the most precise way to define inertial mass and its the definition upon which all derivations of m are based. Its an unfortunate fact that basic physics texts don't explain this. However texts which are devoted to relativity often elxplain this.
Hence my suggestion to define precisely what one means by "mass" when speaking about whether or not light has mass or not.