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Meh, this dips into a bit of history, but 'O well. There is this thing called, "affirmative action" or "positive discrimination." Signed into act by JFK. Thus more presidents elaborated on it, etc. (In this case take the Grutter v. Bollinger case.) The United States Supreme Court ruled that the University of Michigan Law School had to have class diversity or something like that. So basically, @ParthKohli since you're from a different race, you have a better change of getting into a college than a US student. Yay, positive discrimination! (I may have that wrong though, I'm running on just coffee... So... Might want to check with @Preetha or someone higher up.)
same credential, that scenario is highly unlikely
Financial aid is generally not an issue at the larger schools. For those with a documented need, they have lots of aid packages. In fact, people have gone to top schools for free because they needed aid and worked hard to get it. By free, I mean they never took out a loan or paid for a book or tuition out of their own money. As for applications in general, supposedly the determining factor in many cases is the personal statement. I have talked with some people at USC, another school that turns down tons of people, and according to them, they have had people with a high GPA, lots of volunteer hours, and more get turned away because of a simply average personal statement. Wish I had more than one ride on a train with the guy, because it would be great to know more. For a special program that requires recommendations, it is how strong and positive are those recommendations. Had a prof that went over this. Sure, anybody can write a letter of recommendation. However, how strong is it going to be if say your favorite math professor recommends you for a psychology program? As for positive, just ask up front if someone can make a strong, positive letter for you. Many letters are equivocal rather than positive, and that is a death sentence to your chances.
Actually, if you are an international student, you have very little chances for getting financial aid. If you are a truly exceptional student, you may get the merit scholarships offered by many schools. You have to be in the top 1% of their applicants. Admissions are based on quotas in a sense. So you will fall into the International bucket and a US student will fall into - US/Florida or Georgia Bucket. You will be evaluated against other international applicants - not the US applicants. Many schools have a cut off of how many international applicants they take. So some private schools want to cap that at 11% for example. And most international students if not all are usually paying full tuition. Admission is usually aid blind - which means they will consider you whether you want aid or not. So what do you need to do? You need stellar grades, fabulous recommendations, and a strong record of non academic leadership. Art, sports, community service, something like that. And of course fabulous TOEFL and SAT scores. If you can pay the tuition, then hey, Welcome to the US son!