TJ Prep Problems

TJ test prep practice problems  for our students and readers. The problems provide a very small sampling of what Optimal TJ Prep students work with.

A Mathematics Problem for TJ/AOS/Blair/SHSAT (Medium). Target Tie 30-75 seconds.

A model fruit stand has layers of rows of fruits, modeled by magnetic balls that are painted and textured like apples. Each layer of fruit (except the lowest)  has one less fruit than the layer below it. If the bottom row has 48 "fruits" and the top row has 8 "fruits", how many layers of "fruits" are there and how many "fruits" are required to make this arrangement?