LOUISVILLE — Gatekeepers for elite schools could fill their classes many times over with academic stars. But the primary job of most admissions chiefs is to market a university to prospective applicants and ensure the enrollment of a steady flow of qualified students.

So it was striking to hear Jenny Sawyer, executive director of admissions at the University of Louisville, talk openly this week about the advice she gives students on when not to enroll at this city’s public university. Sawyer said she worries about prospective students who would struggle to pay bills.

The total cost for Kentucky residents, counting tuition, fees, room and board and other expenses, is about $25,000 a year. That doesn’t include financial aid. Students from low-income families would typically pay in the range of $10,000 or less. Still, some must take on jobs and debt to make ends meet. That means they have far less time — or maybe no time — to take advantage of everything the campus offers in academics, social life, career exploration and extracurricular activities.

In some of these cases, Sawyer said she wonders: “Why pay to be at a four-year institution?” Sometimes she will advise prospective freshmen to enroll elsewhere — especially at a low-priced community college — if the initial burden is too high. “You should not be going here,” she will tell some cash-strapped students. “This is a bad financial decision.”

That doesn’t mean giving up on a university diploma. “There are many ways to become a University of Louisville graduate,” she said, “and they don’t all begin with starting here.”

Sawyer spoke with The Washington Post as she was waiting to greet Education Secretary Arne Duncan, who stopped in Louisville Thursday to tour the campus and speak with college-bound students. Duncan was on a seven-state back-to-school bus tour that wraps up Friday in Pittsburgh.

At Louisville, there are about 15,000 undergraduates. Sawyer said the school has rolling admissions and admits about 72 percent of its freshman applicants. Make no mistake: She is definitely a cheerleader for the university. “There is no better time to be a Louisville Cardinal!” the admission site says.

At the end of the meeting with Duncan, Sawyer gave one of the college-bound students a letter containing an offer of admission. Andrew Leyva, son of Cuban immigrants, said he wants to study business and become a lawyer. He was thrilled. She gave him a hug.

“The timing was perfect,” Sawyer said with a grin, just before she surprised the 17-year-old with a thick envelope.

But Sawyer also said she is clear on her mission. “Our intent is to graduate students,” she said. “Not to recruit students.”

That kind of straight talk sets Sawyer apart from others in her field.