If HYPSM reject, say, 65% of students w/ perfect GPAs and SAT/ACT scores, that means 35% get in. That's good odds, no?

Applying to College
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I’ve also seen this quote but note that to qualify for the IMO, you have to be successful in a series of math tests that are harder than the SAT/ACT math section (so, it’s not surprising that their math 25-75% range is 790-800). So, scores matter quite a bit.

Also, MIT is the only school that I have come across that asks not only for the math and verbal (SAT) scores but each subsection (“Cross-Test Scores” and “Subscores”) as well.