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Do factors like out of state/instate, private/public make a difference?
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Absolutely!!
Public OOS schools rarely give much/any need based aid. SOME give merit scholarships if your test scores are high for that school (well into upper quartile) and have a good GPA, too.
NY publics seem to mostly only give aid to modest income people. Your parents likely earn way too much to qualify. However, some SUNYs do give merit for high stats.
Privates can vary depending on how large their endowment is. Many have small endowments and can’t give a ton of aid. Some give a good bit of aid, but families still have to pay a good bit, too. Some have large endowments and are generous (like the Ivies and some others), but you need tippy top stats to hopefully get into those schools…and families still have to pay a bit, unless low income.