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I'm on track to do a lot better than expected for my undergraduate degree (first class honours at one of OxBridge in the UK), and I already have an LSAT score of 177. I've seen posts from previous cycles where applicants with numbers similar to mine have been offered the Ruby/Hamilton, but as an international applicant I won't have a traditional GPA. Am I out of the running for named scholarships because I won't contribute to raising the average GPA of the school?

I've never seen internationals getting naming scholarships except Darrow (Umich).

For some data about the admissions and scholarship awards to international applicants, see the spreadsheet in the international applicants thread. One applicant was awarded a Dillard so far.