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One-fifth of undergraduates did not apply for any financial aid during the 2011-12 academic year -- typically because they thought they could afford college without it or did not believe they would qualify, according to a report from the U.S. Education Department's National Center for Education Statistics.

That number was even higher at public two-year institutions, where 30 percent of students did not apply for financial aid. At public four-year institutions, 18 percent said they did not apply, according to the report.

The NCES report was based on data from the 2011-12 National Postsecondary Student Aid Study, a national survey that collects data on what grants, loans or other types of aid students apply for and receive.