Fact:   If you have high SAT score, high school transcript with excellent marks, solid recommendations and well written  application essay(s), most if not all schools will grant you admission.  

Fact:   Most schools such as - Williams College, Princeton University, etc. - that are ranked "very competitive" by Peterson's Guide will find a way for you to attend.  Your financial assistance will be mostly in the form of grant as you are an international student.

So, if you are a prospective student, keep these facts in mind as you navigate the application process and beware of those rascals who say s/he can provide you with scholarship whether you meet all, and I mean all, criteria.