70% is lucky - most are higher. UVA, UNC, U Mich are “national” schools.
If you want to not be in the minority though, you need to go to an aggressive school - namely So Carolina or Alabama (if you have good stats, the most aggressive). Also, Florida State.
UVA and UNC both state they meet full need - but note they take the CSS in addition to the FAFSA and in most cases, your “need” as they calculate will not equal what you calculate.
If you’re looking at UVA - if you are that level of student, you might also look at the private schools that meet 100% of demonstrated need - but again, and I don’t know your specific situation, but the FAFSA does not equal need for these schools…the CSS does.
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