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Kayla Rosenblum sat upright and poised as she breezed through the shapes and numbers, a leopard-patterned finger puppet resting next to her for moral support.

But then came something she had never seen before: a visual analogy showing a picture of a whole cake next to a slice of cake. What picture went with a loaf of bread in the same way?

Kayla, who will be 4 in December, held her tiny pointer finger still as she inspected the four choices. “Too hard,” she peeped.

Test preparation has long been a big business catering to students taking SATs and admissions exams for law, medical and other graduate schools. But the new clientele is quite a bit younger: 3- and 4-year-olds whose parents hope that a little assistance — costing upward of $1,000 for several sessions — will help them win coveted spots in the city’s gifted and talented public kindergarten classes.

Motivated by a recession putting private schools out of reach and concern about the state of regular public education, parents — some wealthy, some not — are signing up at companies like Bright Kids NYC. Bright Kids, which opened this spring in the financial district, has some 200 students receiving tutoring, most of them for the gifted exams, for up to $145 a session and 80 children on a waiting list for a weekend “boot camp” program.

These types of businesses have popped up around the country, but took off in New York City when it made the Otis-Lennon School Ability Test, or Olsat, a reasoning exam, and the Bracken School Readiness Assessment, a knowledge test, the universal tests for gifted admissions beginning in 2008.

Kayla’s session at Bright Kids was an initial assessment; her mother, Jena Rosenblum, had not decided whether to put her through a full course of tutoring. She was considering it at the suggestion of Kayla’s preschool teacher. “Even though we live in the West Village and there are great public schools, obviously, any opportunity to step it up a notch in caliber, we would like to try,” Ms. Rosenblum said.

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Melisa Kehlmann said her main concern was that her 4-year-old son, Adrian, would be shut out of the well-regarded but overcrowded schools in her Manhattan neighborhood.

“It’s quite pricey, but compared to private school, which averages about $20,000 for kindergarten, the price is right,” she said of the tutoring. “I just want the opportunity to have a choice.”

Private schools warn that they will look negatively on children they suspect of being prepped for the tests they use to select students, like the Educational Records Bureau exam, or E.R.B., even though parents and admissions officers say it quietly takes place. (Bright Kids, for example, also offers E.R.B. tutoring.)

“It’s unethical,” said Dr. Elisabeth Krents, director of admissions at the Dalton School on the Upper East Side. “It completely negates the reason for giving the test, which is to provide a snapshot of their aptitudes, and it doesn’t correlate with their future success in school.”

No similar message, however, has come from the public schools. In fact, the city distributes 16 Olsat practice questions to “level the playing field,” said Anna Commitante, the head of gifted and talented programs for the city’s Department of Education.

As for parents doing more — like hiring a tutor — Ms. Commitante said she finds “anything else a little too stressful for young kids” but that “we can’t dictate what parents choose to do.”

There is no state registry or licensing for these services, but an Internet search turns up numerous companies with names like Another Young Scholar, Junior Test Prep and Thinking to Learn. Harley Evans, the owner of Manhattan Edge Educational Programs, raised prices this year to $90 a session from $65, but still has his maximum load of 70 children. Daniel C. Levine, the founder of Exclusive Education, based in Manhattan, said that a few years ago, 2 percent of his clientele were children under 6. Now it is about 10 percent.

“It’s the same phenomenon as with the SATs: a gradual rise in test prep, until it becomes the norm,” said Emily Glickman, a Manhattan educational consultant. “Given that the demand for high-stakes schools outstrips supply, that’s what’s happening.”

Some of the thousands of students registered to take the gifted tests in January are also preparing at home. Bright Kids is selling a few hundred $90 workbooks per month, said Bige Doruk, the company’s founder. Dr. Robin MacFarlane, who developed the Kindergarten Test Study System, said she was on track to sell more than a thousand of the $60 Olsat prep kits this year, though she advises parents against intensive cramming.

Tutoring preschoolers is not quite the same as drilling high school students for the SAT. At Bright Kids, Kayla was initially stumped by the visual analogy, but once the learning specialist, Meredith Resnick, explained that she was looking at a whole-to-part relationship, she easily found the right answer: a slice of bread. “You can see that when I scaffolded her, she knew it,” Ms. Resnick said.

Children often have to be trained to listen to questions from strangers and to sit still for about an hour, the time it takes to complete the two tests.

“If their mind isn’t keyed into listening, the whole question can fly over their heads,” said one tutor, a retired teacher in gifted programs.

She spoke on condition of anonymity because she has administered the test for the city and wants to do so again.

“Some kids can do well without preparation, but children who are familiar have an edge,” the tutor said. From an equity perspective, she said, “it’s ridiculous.”

Ms. Commitante said the city had not noticed any bias due to test preparation. For this year’s kindergarten class, 3,231 students scored in at least the 90th percentile, the minimum to qualify for a gifted program, a 45 percent increase from the year before.

But that rise was attributable to “a variety of factors,” including increased participation, she said: 14,822 took the tests, an increase of 19 percent. The percentage scoring 90 percent or higher rose to 22 percent from 18 percent.

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“I would hope that parents make decisions around this program because they feel that this is an educational option that their child really needs, as opposed to, ‘I have to get my child into this program because that’s the only place where they are going to get a good education,’ ” she said. “I just don’t think that’s true — we have a lot of really good schools.”