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 Geometry Question for TJ/SHSAT/AOS/Blair Test Prep (Medium). Target Time 25-40 seconds.

In a far away galaxy, far beyond the reach of our most powerful rockets and weapons exist three planets -- Helios, Feros and Plumbos.   Assume the densities of the three planets are in the ratios of  1:40:60 and their diameters are 2, 4 and 8 million meters. Recall that Mass (commonly referred to as weight) = volume x density. What is the ratio of the volume of the largest plant to the volume of the smallest planet? What is the ratio of the mass of the largest planet to the mass of the smallest planet?