Ivy League colleges once again disappointed tens of thousands of teenagers as they accepted a lower percentage than ever -- even as they encouraged more to apply.

Harvard University said it accepted a record-low 5.3 percent of hopefuls after attracting 37,307 applicants as it heightened recruiting with a new social-media campaign. The previous year, the figure was 5.9 percent. The admission rates for the seven other Ivies, which told students their verdicts Tuesday, ranged from 6.1 percent at Columbia to 14.9 percent at Cornell.

Stanford, on the West coast and far from the eastern Ivies, surpassed them all for a second year. It reported Friday that it had admitted 5 percent.

The competition for top slots shows no sign of abating as students seek prestige as well as financial-aid packages that tend to be more generous at these wealthy schools. High school guidance counselors pointed to the near-absurdity of the low numbers, considering the quality of many applicants.

“At what point do we reach zero?” said Carol Wasden, director of college counseling at the private Hockaday School in Dallas. “It’s difficult for even terrific students. You have to take a ‘no’ with a little bit of a shrug.”

Heightening the frenzy, colleges reach out to students with a barrage of glossy brochures and e-mails. This year, at least a dozen -- including University of Pennsylvania and Dartmouth College, which each said they admitted about 10 percent of applicants -- extended their application deadlines, encouraging even more students to apply.

Dartmouth Rebound

Dartmouth saw a rebound in applications from last year’s admissions cycle, when they dropped 14 percent after the school received media attention for drinking and sexual-assault allegations. Since then, the school has announced efforts to improve its campus culture. Applications for this fall’s class rose 6 percent, to 20,504.

Colleges say their outreach reflects efforts to assemble the strongest classes possible and reach out to underrepresented students. Still, because of these marketing efforts, seniors should eye the low acceptance rates with some skepticism, said Michael Motto, who worked as assistant director of undergraduate admissions for two years at Yale, which admitted 6.5 percent.

“There is an inflation factor in terms of those numbers,” said Motto, now a private admissions counselor in New York. “But it is important for students to realize these are very selective places who do see the best and brightest students applying from across the world.”

Perfect, But ...

Consider Aly Berger, a senior at Hockaday. A top student, she earned perfect scores on five Advanced Placement exams and is taking four more Advanced Placement courses this year. Yet Harvard, Yale and Duke University, in Durham, North Carolina, which isn’t in the Ivy League, rejected her. Duke accepted only 11.3 percent of applicants. She got into Dartmouth, the honors program at the University of Virginia, Georgetown University and the London School of Economics.

“So much of these admit rates becomes colleges boosting their numbers by getting people who aren’t competitive to apply,” said Berger, 18, who volunteers every Sunday at a shelter for victims of domestic violence and human trafficking. “I’ve gotten into many good schools. It hasn’t really bothered me.”