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 Problem for TJ/AOS/Blair Test Prep (Difficult). Target Time 60 - 120 seconds.

There are four cylindrical containers A ( r = 8, h = 16, B (r = 4, h = 8), C and D. Containers C and D are identical to containers B and A respectively. Container A is completely filled with a "nonvolatile" liquid; containers B, C and D are empty.  Content of container A is poured to completely fill containers B and C.   Half of the remaining fluid in container A is poured into cylinder D. What is the height of fluid in container D?

Note. The target time assumes that you will do it step by step using formula taught in your prealgebra class. However, it is possible to solve it without using pencil and paper. See if you can do it? 

Science Trivia- If you read the problem carefully, you must be wondering why the word nonvolatile is put in quotation marks. If you can't think of a good answer, you can ask me by emailing to