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 Medium Geometry Problem for TJ/AOS/Blair Prep. Target Time. 25-55 seconds.

In the figure below two triangles are shown. In triangle ABC, a new triangle is formed by connecting midpoints of sides AB, BC and CA resulting in formation of 4 smaller triangles. Find the ratio of the blue region to the white region. In triangle PQR,  the process used in triangle ABC is repeated successively three times. What is the ratio of the area of the green region to the white region in triangle PQR.