Our valedictorian had an ACT of 35 and didn't get accepted to any Ivies

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Personally, I doubt if the first two reasons make the difference very often. They are very subjective, and the colleges can’t really tell how to evaluate them, especially the recommendations. I think the third explanation is closer to the mark: there are really a lot of students with good grades and scores and extracurriculars that are mostly in the high school, or in the local community. While the most selective schools take some kids like this, there are just too many of them, when you consider that there are also quite a few students with the grades and scores and significant national achievements, or various hooks. There doesn’t have to be anything “wrong” with a student’s application in order for this to be the result. Plus, if you really want to go to an Ivy League school (or schools at that level of selectivity), don’t apply to just two of them.</p>