The other thing I realized is that racial quotas are unconstitutional as well. I know you were posting from memory and it's a minor detail of the hypothetical as it is but I just figured while we were talking about it...
Minority quotas for affirmative action were declared unconstitutional in the 1978 Regents of the University of California vs. Bakke. Bakke was a white engineer working for NASA trying to get into medical school. He was not admitted even though his scores were higher than several admitted students. The school had set a 16/100 quota for "disadvantaged" applicants. California Supreme Court ruled Bakke should be admitted. The school appealed to the Supreme Court which subsequently ruled the same way while declaring racial quotas unconstitutional. Schools can still use discretion to promote diversity but they can't actually set numbers for spots.