Admitted with $$$/scholarship

I think it's practically impossible to generalize scholarship decisions across schools and types of scholarships, especially since so many scholarships have very specific requirements (e.g. female Asian who works for Bain but worked at Teach for America who will major in marketing and pursue a job at Goya post-graduation).

Clearly an exaggeration, but most schools list out most of their scholarships on their websites. You can check there to see if you match the backgrounds they're looking for. I imagine that in all cases it helps to have a higher GMAT score but I doubt under 720 will hamper you, particularly in the ones focused on a very specific background.