At my school, I once worked with an administrator who helped with the admissions process (every application is read by a minimum of two people, at least back then), and she had her hands on a lot of data, including a big set of accepted students. We looked through them and noted a couple of things: a disproportionate number were first born (like me) or only children, and
no admits she looked at were from broken families. She also got a feel for that based on people asking about going to the university in her department, she hears a
lot of stories, arranges and gives lots of tours, etc. Hmmm, now that I think about it I cannot remember a single student I knew who came from a broken home.
Basically, it appears that once parents divorce, at least one parent is not willing to pay what the College Board/the school expects, and that's game over.