But they get to use $200 a month in their work-study earnings as spending money to get a haircut, for instance, or go out for pizza with classmates so they don’t feel excluded.

Image Tony Jack receiving his Amherst College diploma on Sunday. Credit... Charles Quigg/Amherst College Public Affairs

Mr. Jack, who is black and had never been on a plane until he flew to Amherst for his first visit, arrived as an A student, and with a steely focus.

His mother, Marilyn, 53, had guided her son from Head Start to a gifted program in elementary school to a magnet middle school and, in his final year of high school, to the private Gulliver Preparatory School on a full scholarship. But she never had to push Tony, she said. “He was on a mission from Day 1,” she said.

Mr. Jack’s high grades and test scores — a respectable 1200 on the SAT — won him a full scholarship to the University of Florida. But the median score for his Amherst class was 1422, and he would have been excluded had the admissions office not considered his socioeconomic class, and the obstacles he had overcome.

“Tony Jack with his pure intelligence — had he been raised in Greenwich, he would have been a 1500 kid,” said Tom Parker, the dean of admission. “He would have been tutored by Kaplan or Princeton Review. He would have had The New Yorker magazine on the coffee table.”

“Tony Jack is not an anomaly,” he added.

Mr. Jack, Amherst officials say, would likely not have benefited under traditional affirmative action programs. In their groundbreaking 1998 study of 28 selective universities, William Bowen, the former president of Princeton, and Derek Bok, now the interim president of Harvard, found that 86 percent of blacks who enrolled were middle or upper middle class. (Amherst was not included in that study.) The white students were even wealthier.

“Universities have prided themselves on making strides in racial diversity, but for the most part they have avoided the larger issue of class inequality,” said Richard D. Kahlenberg, a senior fellow at the Century Foundation.