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.

Arithmetic Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 40-50 seconds.

Bob has some crackers. If he divides them in groups of 4, 3 are left over. If he divides them in groups of 7, 5 are left over.  How many crackers does bob have?

Note. Multiple answers are possible. Can you find all the answers below 200? Can you find a rule to find all the answers between any given range of positive integers?