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 Counting Problem for TJ/AOS/Blair/HSPT Test Prep (Medium-Hard). Target Time. 35-95 seconds.

The figure below shows points X, Y and Z on rectangular grid drawn in green. Starting on X, how may paths are to reach Y under the restriction that you can go right  and/or up. How many ways are there to go from X to Z under the same restrictions. If the restriction is changed so that you can move up and/or to the left, how many ways or there to go from X to Y?