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<p>Easier material does not necessarily make 800 math SAT (or 150 IQ, or some other result based on a battery of non-specialized questions) a less impressive measure than AIME qualification, since they target different populations. If half as many people qualify for AIME, but half of the perfect SAT results are from generalists with no special interest in math and who don’t participate in competitions, then the indication of ability is similar.</p>
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<p>Last year the AMC-12 qualifying score for AIME was 88.5, while “below 50” is around the 40-45th percentile and exceeded by some 60-70000 participants. Data is downloadable from the AMC website.</p>
<p>The bottom line is that 800 math SAT and one-time AIME qualification (without a notable AIME score) are of similar selectivity in the recent administration of the exams. In earlier years, before the expansion of the AIME and the added qualification paths, the AIME would have been significantly more selective.</p>