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 Difficult Geometry Problem for TJ Test Prep. Target Time. 20 seconds to 2 minutes.

ABC is an equilatera triangle. AP = AQ = BU = BT = CS = CR = 1/3 of AB. .

I. Ratio of the area of the hexagon PQRSTU to the area of triangle ABC?

2. Ratio of the area of the hexagon to the sum of the areas of the equilateral triangles APQ, BUT and CRS?

Note. If you use the techniques taught in geometry class, you may take 2 to 4 minutes per part, however, if you have developed appropriate, geometry "common sense" or "geometric maturity", you can solve each part in 20-30 seconds.  I invite you to solve this two-part problem to check on geometric maturity.