The multiple-choice test that determines admission to the city’s specialized high schools, the Specialized High School Admissions Test, is at the center of a legal complaint as well as a vast and lucrative business of test-prep tutoring.

Each fall, about 30,000 kids take the test in the hope of landing one of the 6,000 available spots. Out of nearly 28,000 students who applied for the 2012-13 school year, only 5 percent of black students received offers and 6.7 percent of Latinos while 30.6 percent of white and 35 percent of Asians received offers.

Asian students currently account for 60 percent of the students attending the highly competitive schools.

In response to complaints about lopsided demographics, the city has opened up two more free tutoring centers and made other changes to increase the number of black and Latino ninth graders entering the eight specialized schools. But education officials have said they will not replace the single-test admissions policy. As a result, test-prep and tutoring programs have flourished in the neighborhoods where families are intent on getting into these particular schools.

“Last year almost 1,000 students were offered admission to Stuyvesant, only 19 of those offers were to African American students,” said Damon Hewitt, director of the education practice at the NAACP Legal Defense and Educational Fund. “I don’t believe there are only 19 brilliant African-American students rising from 8th to 9th grade.”

Last year, Hewitt’s group filed a complaint with the U.S. Department of Education about the SHSAT because Black and Latino enrollment at the schools had fallen over the last decade.

“It’s the test prep that helps them get in,” Hewitt said. “Not what they’re learning in school. Because the test isn’t even proven to be related or aligned to the curriculum the kids are supposed to be learning in middle school.”

Hewitt noted that the most selective colleges would never rely on just one exam, and the city’s gifted and talented programs use two exams, one of which was changed to a test that isn’t considered easy to prep for.

The city stood by its policies in a recent SchoolBook interview. Dorita Gibson, deputy chancellor for equity and access, said a single test is still the fairest measurement.

“I think some kids do get test prep because their parents are savvy and they understand what it takes to take the test, not unlike the SAT’s,” she said. “That’s why we try to get children involved and parents involved that don’t know about the test.”

Gibson said the city has expanded its free DREAM tutoring program to 20 locations, from 18 last year. It centralized the process and offers the classes in middle schools, which are considered more familiar to kids. The program now has 2,600 seats.

The Bloomberg administration also added five more specialized high schools, in addition to Stuyvesant, Brooklyn Technical and Bronx Science.

Brooklyn parent Stanley Ng disagreed with those who said the schools weren’t diverse enough. “I would say we have economic diversity in the schools today,” he said in a recent interview.

Brooklyn parent Stanley Ng, with daughters Nicole (center), who attends Brooklyn Tech, and Christie, who graduated from Stuyvesant.

Six years ago, Ng filed his own lawsuit to increase access to the specialized schools. He is a member of the Citywide Council on High Schools and was previously a member of the Community Education Council for District 20, which has a large concentration of Asian students. When his own children were planning to take the specialized high schools test, enrollment in the free tutoring program in District 20 was limited to blacks and Latinos. Ng’s suit forced the city to make income the main priority in every district.

He said that’s contributed to changes at the schools but there is still diversity.

“Brooklyn Tech in 2006 was 29 percent Title 1 at that time, ” he said, referring to the federal program for students who qualify for free lunch. “As of last year, it was 51 percent Title 1. Stuyvesant in 2006 was 18 percent Title 1. Today, it’s 30 percent Title 1. The low income kids are getting in.”

The 10 zip codes that send the most students to specialized high schools.

But why are so many of the kids Asian? It’s an awkward question. Ng and other Asian-Americans said immigrants bring with them a hunger for education, plus a long tradition of preparing for national exams. In Sunset Park, the Chinese community has opened lots of test prep centers. The neighborhood is now one of the top feeders to the specialized schools.

Savvy families choose to live in areas such as District 20 because of the good schools. The district has two selective middle schools that are among the top 10 feeders to the specialized high schools, including the Christa McAualiffe School/IS 187.

Principal Justin Berman said about 75 percent of his eighth graders got into specialized high schools each year. He believed a broad curriculum was the best way to educate students; there are nine band classes and elective classes in meditation and sewing. But, during a recent visit, several eighth graders said they still take classes to prepare for the SHSAT.

“Taking a prep course was kind of like clarifying exactly what was going to be on it,” said 13-year-old Rebekah Rainford.

“You can’t take a test without knowing what’s going to be on it or having a visualization of what’s going to be on it,” added her friend, Brianna Ku.

While Berman acknowledged many of his students enroll in outside classes, he said some of his families focused too much on the tests — and it took a toll.

“We do battle with the idea that sometimes a 96 is OK,” he said. “We need to have the parents sometimes sort of back off a little bit and say, maybe this weekend go to a ballgame. Go to a movie.”

Berman has been showing the film “Race to Nowhere” to families so they understand the risks of pushing too hard.

Meanwhile, students who aspire to get the best public education available and have limited resources have few options. On a recent visit to a free tutoring program in Brooklyn’s Pershing Junior High School, students accepted into the DREAM program said they were thrilled to be picked by lottery for the program.

The city program is open to sixth and seventh graders eligible for free lunch, have good attendance and score well on their state math and English tests.

“When they told me I was like yes, I finally get to go,” said 12-year-old Lenny Jacome, about when he learned last fall that he was accepted. He goes to Sunset Park Prep middle school and said he’d love to get into to Stuyvesant High School or Brooklyn Technical High School.

“I just don’t want to be another person going to a high school with all your friends,” he said. “It would be nice, but still, you don’t get the education that you want.”

His classmate, 12-year-old Shanjida Kamal, who goes to Junior High School 223-The Montauk, said she also felt very lucky.

“I know that if I wanted to get into specialized high schools I’d have to go to Kaplan or Princeton or something, and I knew that would cost my family a lot,” she said.

Christine Streich and Richard Yeh contributed reporting to this piece as well as the first part in the series.