Hi @James1. Orion here, to answer your question.

The GRE has a strange relationship with infinity – and this might be expected, as infinity is a strange quantity. Rather than avoid the concept entirely, ETS occasionally utilizes infinity *in the question* – but will *structure the answer choices* so that argument over certain fringe cases is moot. For instance, as you pointed out, the question of inclusivity at the limit indicated by infinity depends on whether we interpret this question as a “real world” problem or as a “pure math” problem embedded in language. This sounds like a lawsuit waiting to happen.

However, you’ll notice that this isn’t really an issue in practice, since 80 (the limit at infinity) isn’t among the answer choices. This was a deliberate choice on my part (the author of the question), as it aligns with the tendency of the actual test-makers to sidestep these issues altogether. This is also mirrored in the explanation in the manual which indicates that “the minimum class average is between answer choices A and B,” without explicitly indicating what the minimum class average *actually* *is* (as opposed to the minimum class average “in the case of” infinite boys, which was a thought experiment in the service of the solution). I’m careful *not* to say that the correct answers are between 80 and 83, inclusive. This is because, assuming a “real world” problem, the value of the limit at infinity is *not* technically the minimum class average (as you pointed out). This was a little bit of verbal smoke and mirrors to keep the explanation technically correct (for high scorers like you), while keeping the technique simple and accessible for all students (without compromising the practical applicability of the approach).

tl/dr: ETS won’t structure a quant problem so that the point hinges on the question of inclusivity at the limit of infinity. This means that we can safely use the technique described when appropriate.

Good question.