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 Venn Diagram Problem. 35-40 seconds.

In a class, each student studies one or more of math, physics and chemistry. If  86 study physics, 72 study chemistry, 64 study math, 24 study math and physics, 25 study physics and chemistry, 26 study math and chemistry and 8 study all three, how many students are there altogether?