On every GRE Math section, the test makers try to come up with a few extremely difficult problems that will leave even the cleverest students scratching their heads. The really evil part, though, is that even these problems can be solved in under a minute without a calculator – if you know what to do. This means that once you “figure out the trick,” these difficult problems become easy. So, while those test makers are busy cackling with sadistic glee, let’s see if we can’t beat them at their own game.

Consider the following problem:

If Aragorn can dispatch 5 orcs every 11 seconds and Legolas can dispatch 3 orcs every 9 seconds, then together, how many orcs they can dispatch in how many seconds?

A) 2 orcs every 5 seconds

B) 8 orcs every 20 seconds

C) 26 orcs every 33 seconds

D) half an orc every second

E) genocide

To solve this problem, all you need to realize is that the rates at which Aragorn and Legolas slaughter orcs can be represented as fractions and then combined to give their combined rate:

5 orcs every 11 seconds = 5/11

3 orcs every 9 seconds = 3/9 = 1/3

You will notice that we simplified 3/9 to 1/3. It’s always a good idea to simplify fractions whenever possible, as this will save time later. Next, we need to give the fractions like denominators so that we can add them together:

Thus, together they can kill 26 orcs every 33 seconds, and the answer is choice C. If you know what to do, it takes only about 30 seconds to solve this problem. So you see, with practice, even the hardest problems on the GRE become easy. Check back here each week for more extra hard problems and the tricks you need to solve them! Also, remember that you can find out all the tricks from experts like me with a Test Masters course or private tutoring. Until then, keep up the good work and happy studying!