A new study by the Washington think tank New America finds that nearly 50 percent of public four-year colleges nationally are leaving the poorest students on the hook for more than $10,000 a year, a figure that has jumped by a third in just four years. But at private colleges, it’s close to 100 percent. Apart from the elites, most privates, despite all those hefty tuition hikes, have even fewer resources than public institutions and can’t come close to meeting students’ entire need.