Even the highest-achieving black and Hispanic students have trouble forging a path into the city’s eight specialized high schools that use the Specialized High School Admissions Test.

A new report finds that almost 55 percent of Asian students who scored in the top tier on their seventh grade math or English tests in the 2012-13 school year are now in specialized high schools. But only 16 percent of the city’s black and Hispanic students who scored Level 4 are enrolled in those schools.

The study, conducted by the Center for New York City Affairs, suggests that these high-performing black and Hispanic students either declined offers, failed the admissions test or did not take the test at all.

About 21 percent of these black and Hispanic high-scorers wound up in schools with significantly lower graduation and college admission rates — schools that their high-performing white and Asian peers do not attend.

Last week, the city announced initiatives to increase diversity at the eight specialized high schools. The measures include increasing the number of students who take the test and the number of students who accept offers.

Black and Hispanic students are underrepresented in both categories. Among those scoring Level 4 on a seventh grade math or English test, 96 percent of Asian students took the exam, while only 76 percent of black students and 80 percent of Hispanic students did. Seventy-three percent of black and Hispanic students offered a slot at a specialized school accepted it, compared to 86 percent of Asian students.