MIAMI — Nearly one-fourth of the students who try to join the military fail its entrance exam, painting a grim picture of an education system that produces graduates who can’t answer basic math, science and reading questions.

The report by The Education Trust found that 23 percent of recent high school graduates don’t get the minimum score needed on the enlistment test to join any branch of the military. The study, released exclusively to The Associated Press today, comes on top of Pentagon data that shows 75 percent of those aged 17 to 24 don’t qualify for the military because they are physically unfit, have a criminal record or didn’t graduate high school.

“Too many of our high school students are not graduating ready to begin college or a career – and many are not eligible to serve in our armed forces,” U.S. Education Secretary Arne Duncan told the AP. “I am deeply troubled by the national security burden created by America’s underperforming education system.”

The effect of the low eligibility rate might not be noticeable now – the Department of Defense says it is meeting its recruitment goals – but that could change as the economy improves, said retired Navy Rear Admiral Jamie Barnett.

“If you can’t get the people that you need, there’s a potential for a decline in your readiness,” said Barnett, who is part of the group Mission: Readiness, a coalition of retired military leaders working to bring awareness to the high ineligibility rates.

Kenneth Jackson, 19, of Miami, enlisted in the Army after graduating from high school. He said passing the entrance exam is easy for those who paid attention in school, but blamed the education system for why more recruits aren’t able to pass the test.

“The classes need to be tougher because people aren’t learning enough,” Jackson said.

This is the first time ever that the U.S. Army has released this test data publicly, said Amy Wilkins with The Education Trust, a Washington, D.C.-based children’s advocacy group. She said the organization worked with the U.S. Army to get raw data on test takers from the past five years.

“It’s really about illuminating the issue of whether our high schools are preparing young people to serve the country,” said Wilkins, vice president of The Education Trust. “It’s important for national security.”

The Education Trust study shows wide disparities in scores among white and minority students. Nearly 40 percent of black students and 30 percent of Hispanics don’t pass, compared to 16 percent of whites.

Even those passing muster on the Armed Services Vocational Aptitude Battery, or ASVAB, usually aren’t getting scores high enough to snag the best jobs.

“A lot of times, schools have failed to step up and challenge these young people, thinking it didn’t really matter – they’ll straighten up when they get into the military,” said Kati Haycock, president of the Washington-based Education Trust. “The military doesn’t think that way.”

Christina Theokas, the author of the study, said the test was updated in 2004 to reflect the current needs of the Army, and the Army didn’t want to release data from before the realignment.

Recruits must score at least in the 31st percentile on the first stage of the three-hour test to get into the Army or the Marines. Air Force, Navy and Coast Guard recruits must have higher scores.

The average score for blacks is 38 and for Hispanics is 44, compared to whites’ average score of 55. The scores reflect the similar racial gaps on other standardized exams.

Further tests determine what kind of job the recruit can do with questions on mechanical maintenance, accounting, word comprehension, mathematics and science.

The Education Trust study examined the scores of nearly 350,000 high school graduates, ages 17 to 20, who took the ASVAB exam between 2004 and 2009. About half of the applicants went on to join the Army.

The study also found disparities across states, with Wyoming having the lowest passage rate, at 13 percent, and Hawaii having the highest, at 38.3 percent.

Retired military leaders say the report’s findings are cause for concern.

“The military is a lot more high-tech than in the past,” said retired Air Force Lt. Gen. Norman R. Seip. “I don’t care if you’re a soldier Marine carrying a backpack or someone sitting in a research laboratory, the things we expect out of our military members requires a very, very well educated force.”

A Department of Defense report notes the military must recruit about 15 percent of youth, but only one-third are eligible. More high school graduates are going to college than in earlier decades, and about one-fourth are obese, making them medically ineligible.

In 1980, by comparison, just 5 percent of youth were obese.

“Aptitude, educational attainment, and physical fitness are three factors that make the military a highly selective employer. Recent reports in these areas show that today’s youth are falling behind,” said Curt Gilroy, the director of Accession Policy in the Office of the Under Secretary of Defense for Personnel and Readiness.

Jackson is among those who had to lose weight to become eligible. At one point, he weighed more than 300 pounds. He was down to 250 pounds by the time he entered basic training.

Taking the entrance exam was the easy part.

“You’ve just got to be focused,” he said.