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.

TJ Prep - A Medium Problem. 30-40 seconds.

ABCD is a square. P, Q, R, S are mid points of AB, BC, CD and DA respectively. Connecting P, Q, R, S gives square PQRS.  Connecting the mid points PQ, QR, RS and SP sequentially, creates the smallest square HIJK.

I. What is the ratio of the areas of squares HIJK and square ABCD? 

II. What is the ratio of the perimeters of squares ABCD and HIJK?