WASHINGTON — NEW YORK CITY’S elite public high schools were always meant to provide a quintessentially American blend of academic excellence and democratic accessibility. Unlike the city’s expensive private schools, they would be free and open to all who were academically qualified, irrespective of pedigree.

“You pass the test, you get the highest score, you get into the school — no matter what your ethnicity, no matter what your economic background is,” Mayor Michael R. Bloomberg said in 2012. But this year, only 5 percent of seats at those eight schools were offered to black students and 7 percent to Latinos, in a city where the public schools are 70 percent black and Latino. At Stuyvesant High School, just 3 percent of offered seats this year went to black and Latino students.

When the number of black and Latino students admitted to a public school is a tiny fraction of their share of the general population, it raises red flags about the fairness of the admissions system.

New York City’s eight selective public high schools base admissions on a single two-and-a-half-hour assessment — the Specialized High Schools Admissions Test — a practice that is unusual among other large public school systems in the nation. The N.A.A.C.P. Legal Defense and Education Fund, along with other groups, has filed a federal civil rights complaint against this arrangement.