Another way to think about this problem is to consider what we know about consecutive numbers and prime factors. For example, the questions stem gives us a hint that we are dealing with a series of three consecutive digits (i.e. the dividend was originally N and the dividend is now (n-1)(n+1), there...

The fastest way to solve mixture problems is to set up a weighted average equation and to then solve for the weights. For example, in the sulfuric acid example you are told that beaker A is 15% sulfuric acid and beaker B is 20% sulfuric acid. When these solutions are added together in a certain rati...