Nearly one-fourth of the students who try to join the U.S. Army 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, according to a study released yesterday.

The report by The Education Trust bolsters a growing worry among military and education leaders that the pool of young people qualified for military service will grow too small.

"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 said.

"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.

The report 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. Questions are often basic, such as: "If 2 plus x equals 4, what is the value of x?"

The military exam results are also worrisome because the test is given to a limited pool of people: Pentagon data shows that 75 percent of those aged 17 to 24 don't even qualify to take the test because they are physically unfit, have a criminal record or didn't graduate from high school.

This is the first time that the army has released this test data publicly, said Amy Wilkins of The Education Trust, a Washington, D.C.-based children's advocacy group. The study examined the scores of nearly 350,000 high school graduates, ages 17 to 20, who took the ASVAB exam between 2004 and 2009.

Recruits must score at least a 31 out of 99 on the first stage of the three-hour test to get into the Army. The Marines, Air Force, Navy and Coast Guard recruits need higher scores.