A recent study from the National Bureau of Economic Research indicates that the quality of a high school can predict how well its students will perform in college.
According to a Gawker article, students from poor performing high schools are disadvantaged when attending good colleges alongside students from high performing high schools:
The study found that the quality of a student's high school is "a key predictor" of their grades in college, meaning that without a serious dose of remedial studies, kids from disadvantaged high schools are doomed to be at a disadvantage themselves in good colleges full of kids who attended better high schools.
The article goes on to argue that lower education must be improved before higher education:
From this we may draw the reasonable conclusion: If you want to fix higher education for disadvantaged students, first fix their high schools. And before that fix their middle schools and elementary schools. And before that, get that Universal Pre-K going.