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.