Gifted programs generally offer an accelerated curriculum, as well as the opportunity to be around other high-performing children. The city did not provide a racial breakdown of students who qualified, but as in years past, the more affluent districts — 2 and 3 in Manhattan, in neighborhoods west and south of Prospect Park in Brooklyn, and in northeastern Queens — had the most students qualify. In District 2, 949 children qualified for a gifted program, far more than in any other district. In District 3, 505 children qualified. By contrast, in District 7, in the South Bronx, only six children qualified for gifted placements and none for the five most exclusive schools.

At one of those schools, the Anderson School on the Upper West Side, only parents whose children scored in the 99th percentile are invited to open houses. One parent, Kevin Wardally, has his sights set on Anderson for his son, Emerson, who scored in the 99th percentile, but with so many high scorers this year, Mr. Wardally is not sure Emerson will get in. Schools with more qualifying applicants than seats generally choose students by lottery.

“We definitely paid a lot of money to send him to a very good Catholic pre-K that has a very good reputation for helping get kids into excellent schools,” said Mr. Wardally, who lives in Harlem. “They never make you a guarantee, but I have to be honest, we made a little bit of an assumption that scoring as highly as he did, that we might have a pretty good shot. Well, we’re praying on it, because these are the kinds of choices that make a difference in young kids’ lives.”

Every year since 2008, when the city put the current testing program into effect and 2,230 students qualified for seats in gifted and talented kindergarten classes, the number of children scoring at or above the 90th percentile has steadily grown. The chancellor in 2008, Joel I. Klein, made the change to standardize the admissions process, replacing a system in which each district set its own standards for entry, a process that drew criticism from parents who said favoritism sometimes played a role.

But the new process has come under scrutiny for its complete reliance on the test — actually two exams, the Otis-Lennon School Ability Test, or Olsat, a reasoning exam, and the Bracken School Readiness Assessment, a knowledge test.

In January, the city awarded Pearson a three-year contract for roughly $5.5 million to replace the Bracken exam with the Naglieri Nonverbal Ability Test, which city education officials contend will better measure ability. The contract places restrictions on Pearson’s ability to sell its test materials to anyone outside the Education Department, to make it harder for test-preparation companies to get their hands on them.