The way you've phrased your question kind of leads to a response that isn't super useful. Like Jon said, all schools care about stats. As they should - rankings are based on them. Things like GMAT scores, GPAs, incoming salaries, work experience, etc. all play a part.
So the answer you're looking for isn't the answer to your question as its stated. The reason a 760 isn't a huge deal at Harvard is because you have to consider the applicant / accepted pools. A lot of people applying to HBS have a 730+ score. So they don't use it as a yes/no gate. But like you said, it's super important and their steadily increasing GMAT average score is a testament to that. So, whenever you're looking at a stat like GMATs or GPAs, the lower in the rankings you go the more distance you'll put between your score (assuming it's higher) and the median. If you can fall outside of a standard deviation, it'll matter more.
Also, schools within tiers tend to act similarly. So schools within, say, the top 3, place a similar emphasis because they're seeing a similar applicant / accepted pool. Same with top 5, top 10, top 20, etc. Tiers matter.
The simple answer is #10 will care more about a higher GMAT score (all else equal) than #2. But that's relative and not necessarily always the case. Even if they do, that doesn't mean they care 2x or 5x as much. They could care MARGINALLY more.
That's why, when you look around these forums, admissions consultants are so focused on your WHOLE profile. Because the simple answer to your question doesn't really solve the puzzle.
Hope that helps!
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