The existence of such students — eager, yet at high risk for failure — exposes a split in education policy. On one hand, believers in the standards movement frown on social promotion and emphasize measurable performance in high school.

At the same time, because a college degree is widely considered essential to later success, some educators say even students who could not complete high school should be allowed to attend college.

Nowhere is this contradiction more evident than in California. This year, 47,000 high school seniors, about 10 percent of the class, have not passed the exit examinations required to graduate from high school. They can still enroll in many colleges, although they are no longer eligible for state tuition grants.

State Senator Deborah Ortiz, Democrat of Sacramento, has proposed legislation to change that.

"As long as the opportunity to go to college exists for students without a diploma," Ms. Ortiz said, "qualifying students from poor or low-income families should remain entitled to college financial aid."

Many community colleges and two-year commercial colleges take these students, as do some less selective four-year colleges. At Interboro Institute, a large commercial college in Manhattan, 94 percent of the students last year did not have a high school diploma. Yet most received federal and state financial aid, up to $9,000 a student for the neediest.

At the College of New Rochelle, a four-year Catholic women's college whose main campus is in Westchester County, N.Y., students without high school degrees account for one-third of the students entering its School of New Resources, for those 21 or older, which has 4,500 students.

At Interboro, the state recently found cheating by employees on the exam students have to pass to qualify for state and financial aid. The college, part of EVCI Career Colleges Holding, said the problems were not pervasive.