Your first shot at getting in comes when you’re four years old.

You have to live in Manhattan, speak English, and have $350 for an IQ test. If you’re invited back, a team of consultants will observe you in a classroom setting and make the final call.

You get a second chance several years later, assuming you’ve aced the state tests in fifth grade and know to apply for a high school seat in sixth grade. Then, your score on the school’s admissions test will decide your fate.

That’s how admissions works at Hunter College Campus schools, which serve students from kindergarten to 12th grade. Though the schools are operated by the city’s public university system, not its education department, they are public schools. And for about 1,600 students at a time, they provide what is considered one of the best public educations in New York City.

The schools look very little like the city its students live in, though, a fact that has been true for many years. And as New York City engages in a lively debate about the lack of diversity at eight elite city high schools — with Mayor Bill de Blasio calling the lack of black and Hispanic students there “a monumental injustice” — Hunter’s disparities in some cases are far starker.

At the specialized high schools, 10 percent of admissions offers went to black and Hispanic students last year, and nearly half of the students attending are poor. But just 7 percent of Hunter high school students are black and Hispanic, and only 9 percent come from low-income families. At Hunter’s elementary school, less than 3 percent of students come from low-income families.

Still, Hunter has flown under the radar. The schools have avoided the spotlight for a constellation of reasons, including their unique governance structure and the fact that their admissions numbers are not released annually by the city, something that has drawn special attention to demographics at the specialized schools.

“There’s no question that this is another crown jewel when it comes to public high school in New York City,” said Maurice Frumkin, a former city education department official who now runs an admissions consultancy. As for Hunter and CUNY, he said, “I think it’s a shame that they have not chimed in.”

Debra Wexler, a spokesperson for Hunter College, said the school has engaged in extensive outreach to find talented students from across the city. Hunter officials also note that multiracial students make up 18 percent of the high school, and that poverty is tough to track, since some families fail to turn in their free and reduced-priced lunch forms, the school’s standard means for collecting information about family income.

“The Hunter College Campus Schools are designed to serve intellectually gifted students,” Wexler said. “Those students exist in every community, and it’s our job to find them, so we have spent the past several years investing heavily in outreach and engagement strategies to encourage bright students from all backgrounds to apply.”

Officials at Hunter said their outreach is working and said they expect a more diverse kindergarten class next year.

But as officials and parents continue to examine equity, diversity, and segregation in the nation’s largest school district, observers wonder if Hunter has an obligation to more forcefully address the fairness of its admissions policies.

“Hunter is another one of these private schools masquerading as a public school,” said Lazar Treschan, a Hunter graduate who has studied New York City high school admissions and works at the Community Service Society. While it’s good to see that the school moving in the right direction, he said, “It has no business being a public school in New York City with those kind of disparities.”

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The Hunter College Campus Schools have been prestigious bastions of public education for gifted New York City students since the mid-1950s. The schools boast a string of notable alumni, including Supreme Court Justice Elena Kagan, “Hamilton” creator Lin Manuel-Miranda, and Cynthia Nixon, the “Sex and the City” star running for governor of New York. The high school also routinely sends about a quarter of its graduating class to Ivy League schools, MIT, or Stanford.

The schools also have a long history of grappling with a lack of racial and socioeconomic diversity, although the disparities are worse today than they have been in the past. In 1995, the incoming class of seventh graders was about 18 percent black and Hispanic, according to the New York Times. In 2017, 9 percent of seventh graders were black or Hispanic.

Fred McIntosh, the former director of admissions at Prep for Prep, which helps students of color get into private schools, took the Hunter entrance exam in the early 1980s. He said he didn’t know anyone who prepared seriously for the test, and thinks the lack of test prep and a program that admitted some poor students who just missed the cutoff score helped make his class more diverse than today’s student body.

(Hunter officials said they don’t know of such a program, which is mentioned in a report created by a school committee in the early 2000s, and they don’t have information about why it might have been phased out.)

“It was much more racially and ethnically diverse, but it was also very socioeconomically diverse,” said McIntosh, who is black. “That’s one of the things that I learned going to Hunter. I thought all of the kids were wealthy and that was not true.”

But at least as far back at 1997, faculty members have been devising ways to boost diversity at the school. In a report from that year, a committee on cultural diversity at Hunter College High School recommended a full review of the school’s admissions policies, investigating whether the school could eliminate the admissions testing fee, and developing an anti-discrimination statement.

Several years later, Glenn Kissack, then a math teacher at the school, participated in another review of admissions. After months of studying the small number of “feeder schools” that often produce Hunter students and looking into the expensive test prep available for the exam, the committee suggested potentially reserving more seats for poor students and selecting students based on more than just a single test score.

The committee submitted the report, and months went by with no word from the Hunter administration, Kissack said.

“We could have done something else with our time,” Kissack said. “It gathered dust and didn’t matter.”

Hunter officials would not specifically address most of the recommendations in the reports, but said that the school has been engaged in many discussions over the years about improving diversity. Hunter has implemented many recommendations over the years, they said, including creating a Dean of Diversity position in 2002 and raising private funds for student outreach efforts.

The conflict came to a head in 2010 when the high school faculty selected Justin Hudson, one of the school’s few black students, to address his class at graduation. Hudson tackled the school’s demographics head-on in his speech.

“If you truly believe that the demographics of Hunter represent the distribution of intelligence in this city,” he said, according to an article in the New York Times, “then you must believe that the Upper West Side, Bayside, and Flushing are intrinsically more intelligent than the South Bronx, Bedford-Stuyvesant, and Washington Heights. And I refuse to accept that.”

Kevin Park was a junior at Hunter College high school in 2010, when he joined in the standing ovation for Hudson’s speech. He remembers that there were more students named “Kevin” in his grade than there were black students, and felt Hunter lacked faculty and classes that represented Asian students like himself.

After the speech, Park and some classmates created a skit about what it was like to be a black student at Hunter. It depicted assuming college acceptances came easier to black students and how being the only black student in a class can deter speaking up in class, he said.

“That sparked a discussion for a while,” Park said, “but it didn’t necessarily translate into concrete steps or policies.”

Even some of Hunter’s notable alumni have called out the school for its lack of diversity. MSNBC host Chris Hayes uses Hunter as an example of an admissions process that is rigged for the wealthy. Lin-Manuel Miranda recently tweeted a picture at his Hunter College High School reunion with a friend, and said the two of them were two of just five Latino kids in their elementary school grade.

Hunter College officials say that they are confident in their existing process, but are looking for ways to expand the pool of students who apply. At the elementary school level, they have hosted open houses and attended private or selective school admissions fairs, focusing on areas with a concentration of underrepresented students like Harlem or Washington Heights. As a result, Hunter’s kindergarten class is projected to be 22 percent Hispanic, 14 percent black, and 18 percent multiracial in the next school year, they said.

For the high school, they have worked to better notify students who qualify to take the Hunter entrance exam, including by mailing information to parents through the city’s education department. They have also done outreach at the Success Academy charter network, and have seen applications double from those schools.

“Those efforts are bearing fruit,” Wexler said.

The high school has also seen a slow uptick in the number of black and Hispanic students attending over the last decade, though the numbers remain relatively tiny — 7 percent of students in 2017-18.

About two-thirds of the city’s public-school students are black or Hispanic.

Officials at Hunter said they would like to do more outreach but that they are stymied by the fact that the education department will not share contact information for eligible middle schoolers. The city says it is constrained by federal privacy law, but sends an invitation to take the test to all eligible students.

Officials at the mayor’s office did not specifically address Hunter’s admissions policies, but said the mayor is looking to expand diversity initiatives beyond specialized high schools. They also said he believes schools should reflect the diversity of the city.

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One of the reasons Hunter stands apart — even from other elite New York City schools that select students based on ability — is that its sorting process can essentially guarantee a four-year-old a spot at one of the city’s most sought-after high schools.

That was the experience of Andy McCord’s daughter, who took and passed Hunter’s elementary school tests more than a decade ago at the age of three.

It’s hard to say exactly what the testers found since the exam took place away from parents, said McCord, who is now the chair of programming and recruitment at the Exam Schools Partnership Initiative, which tutors underrepresented students vying for seats at the city’s selective high schools. (The exam still takes place separate from parents.)

McCord remembers his daughter telling him that the psychologist had showed her a picture of a person walking a fish on a leash, and she was able to say it should be a dog. In the next phase of the test, where she was observed by a team of adults, his daughter remembers playing with another kid.

Based on those experiences, she got into Hunter elementary school, stayed through high school, and is now a student at Harvard. (Students who finish sixth grade at the school earn a seat in the high school, though some families will be asked beforehand to find a different place for their child, officials said.)

Hunter no longer tests children at age three; instead the process is for four-year-olds. But the basic idea — that based on an IQ test and an observation at a very young age, the school can identify gifted children — is something Hunter stands by. Officials said the Stanford-Binet V exam it uses is the oldest and most widely used measure of aptitude in the country and noted that they consult with experts to ensure their admissions standards are appropriate.

Others, however, say testing such young children can miss their academic potential, capturing wealth and privilege instead.

“There’s just a really strong argument to be made that when you’re testing four-year-olds, at that age, an awful lot of what you’re measuring seems to be about the social advantage that students have had up to that point as opposed to innate potential,” said Halley Potter, a fellow at The Century Foundation whose work focuses on school integration.

And tacking on a $350 price tag is almost certain to exclude more families.

“Even in the best case scenario, it’s hard to imagine the admissions process, as it exists now, actually finding and serving gifted low-income students,” Potter said.

Hunter has begun outreach to some Head Start programs, which provide federally funded pre-K, and waives fees for families there. Officials at Hunter also said they would work with other families who couldn’t pay. But they said they didn’t know how many Head Start students had been admitted, and didn’t track how many students had gotten the fee reduced. The price, they said, reflects the psychologist’s time.

For some parents, however, those explanations provide little solace — especially when their child isn’t admitted. One mother, who asked to remain anonymous, said that she “scrimped and saved” to afford the psychologist’s test several years ago after her husband was laid off. When the test day came, a stranger took her daughter into a room. A few days later, she was told her daughter had not passed.

Feeling like she had lost hundreds of dollars, and not knowing why, was difficult to take, she said. “You have no idea what was said because you weren’t in the room with the psychologist. It was just total agony.”

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PHOTO: Monica Disare
Jennifer and Jayden Tolliver stand outside of a Barnes & Noble on the Upper West Side. Jayden just missed the cutoff to get into Hunter this year.

There’s another way into Hunter, though, for students who don’t win seats before losing baby teeth.

Students from across the city who score well on their fifth-grade state tests can sit for an entrance exam in sixth grade, which includes an essay. That looks a lot like the one-test admissions method currently under fire at the city’s eight specialized high schools.

The mayor and schools chancellor have both criticized the Specialized High School Admissions Test as a blunt instrument that excludes gifted students from all over the city. Their criticism has broken open a debate about how to select students for seats at coveted city schools. Members of the Asian community in particular have defended the test as an objective marker of talent and hard work that gives immigrant families a shot to send students to top schools.

Some make similar arguments about the Hunter entrance exam. Standing in the courtyard at New Explorations into Science, Technology and Math, a gifted elementary school in Manhattan, Cecilia Feliciano said her son just passed Hunter’s test and will be attending the school next year for seventh grade.

Feliciano, who lives in Queens, said she is an immigrant from the Philippines who couldn’t afford test prep, so she downloaded materials and worked with her son to study for the exam. The test allowed her son to compete on an equal footing with more affluent students from around the city, she said.

“It means a lot to me to have have an equalizer, but you have to work hard,” Feliciano said. “It takes a lot of work, passion, love.”

But like with the SHSAT, preparation for the Hunter exam is costly for many families. A test prep class for the Hunter exam in Manhattan can cost $3,000. Some private tutors who specialize in the Hunter exam charge up to $350 per hour.

And unlike the SHSAT, which students take in eighth grade, students take the Hunter exam in sixth — well before many students are thinking about high school. That catches many students, like Ethan Moses, now a freshman at Manhattan Village Academy, off guard.

Moses said he heard about the test a couple weeks before it was administered. He figured he would apply the skills he learned at Success Academy, but he didn’t recall any of his classmates making the cut, he said. (Success officials said they do not track how many students are admitted to Hunter.)

“The mail came in out of nowhere and said we were taking the test,” Moses said. “None of us were really prepared.”

Alternatively, even if students know about the test, qualify for it, and can prepare for it, the crux of the problem could be the entrance exam itself, critics say.

The entrance exam is not created by a national testing company, but by teachers at Hunter College High School.

“It’s a home-created test,” said Kissack, the retired math teacher who worked on test questions himself, which means “we have no idea how valid it is.”

Hunter officials defend the test by saying that the school’s results speak for themselves: The school has graduated a number of notable alumni and the test has been consistently able to identify students who excel in Hunter’s rigorous academic environment, they said. They also said the test has been able to consistently find students who are able to excel in Hunter’s challenging environment.

But Daniel Koretz, a professor at Harvard who has studied standardized testing, says pointing to successful alumni is not a good way to figure out if a test truly measures whether students are gifted. It’s incumbent on schools to figure out if the school is missing good candidates — not just whether the candidates who are selected succeed, he said.

“Are they denying admissions to kids who are lower [test scorers] who would also be equally successful?” Koretz said. “The answer to that question is almost certainly yes,” which means administrators need to be able to justify why their test should be used to select students.

The answer to that question could have mattered a lot to Jayden Tolliver, who is black, on the math team at his middle school in Harlem, and a self-proclaimed “book nerd.”

His fifth-grade state test results qualified him for the Hunter test, and he spent last fall and winter preparing for it through the Exam Schools Partnership Initiative. (Sometimes, his mom said, she could hear him doing math problems in his sleep.)

Hunter told Tolliver that he scored well enough on the multiple choice portion of the test, but his essay wasn’t strong enough to earn a seat at the school.

On a recent afternoon, Tolliver wandered through a Barnes & Noble on the Upper West Side looking for something to read. He’s disappointed that he didn’t make it into Hunter, but said he’s ready to start thinking about finding another high school to take his love of math.

“I was just born liking this stuff,” he said.