# Pushing The Extremes: Infinite Finites

In Problem 2 of Pushing the Extremes (ch13) The manual assumes that given no explicit limit (in the question text), then the logical maximum is infinite. (Thus infinite boys and 1 girl have a test average equal to the average of the boys). While mathematically, I have no issues with the technique, what about real limits?

There aren’t infinite boys in existence (nor can there be, it’s not a real number and can’t describe a real situation). Given real limits (limits imposed by reality projected through a story problem), it seems the answer set should include anything above (or below) but not equal to the limit indicated by infinity.

Can anyone point me to an official GRE question or statement that covers this topic?

Apologies for my skepticism, but I want to be sure on this point.

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Hey @James1,

I’ve discussed this topic with our GRE expert @Orion previously, and in his experience, the ETS will do their best to avoid any ambiguity in the actual GRE exam questions, avoiding answer choices that are too close, or adding in the words “about” or “approximate” to explicitly give a buffer. If there is ambiguity in the wording, it would open them up to a barrage of people complaining that their choice could also be correct.

So, you should pick the answer that fits the closest, even if it’s technically off by 0.00000001.

I tried to find an official question that includes ambiguous answers right on the line like this but wasn’t able to, which matches up with Orion’s experience. You could try reaching out to the ETS for clarification on this, but it seems unlikely that they would issue a blanket statement.

Also, I just double-checked the GRE official rules on questions that have multiple correct choices. Their official rule is that each question will have at least one correct choice, and as many as all the choices may be correct.

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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.

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Thank you both!
That works for me.

Given ETSs lack of ambiguity, it looks like a tiny code adjustment might be in order for permutations of that question.

Thanks again!

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