About 125 students who took the ACT college-admission test at a Los Angeles school are in limbo after their answer sheets were lost in transit, leaving them and their parents upset as testing officials scramble to locate the missing material.

It isn’t the first time ACT answer sheets have been lost—several other known incidents occurred in the past few years due to packages being lost or damaged during transport. But ACT spokesman Ed Colby said that it is “extremely rare” for the answer sheets to go missing. He said the company...