Why are the bottom 25% SAT scores so low for the "elite" public colleges?

<p>Don’t the UC schools use some formula to calculate their own GPA they use in admissions? I’ve come to the conclusion that much of the admissions process is arbitrary and/or luck. My OOS D was rejected by UCLA and UCB with 2120 SAT, 31 ACT, 3.8 unweighted GPA and 4.8 weighted. She had quality EC’s and volunteer work. She was admitted to UCSD and UCI (honors with scholarship) but we would rather pay $50K at USC than either of those 2 schools. Even if she had gotten into UCLA or UCB, she probably would have still picked USC because why pay the same for a “public” school where classes might be harder to get. (She applied undecided/liberal arts to all schools but is going to do International relations/global business at USC)</p>