I’ve been on a story problem kick lately. People have a love / hate relationship with these. On the one hand, it’s a story! It should be easier than “pure” math! We should be able to figure it out!

On the other hand, we have to figure out what they’re talking about, and then we have to translate the words into math, and then we have to come up with an approach. That’s where story problems start to go off the rails.

You know what I mean, right? Those ones where you think it’ll be fine, and then you’re a minute or two in and you realize that everything you’ve written down so far doesn’t make sense, but you’re sure that you can set it up, so you try again, and you get an answer but it’s not in the answer choices, and now you’ve crossed the 3-minute mark…argh!

So let’s talk about how to make story problems REAL. They’re no longer going to be abstract math problems. You’re riding Train X as it approaches Train Y. You’re the store manager figuring out how many hours to give Sue so that she’ll still make the same amount of money now that her hourly wage has gone up.

Note: I’ve used GMAT problems in this article because the makers of the GRE don’t allow us to re-publish their problems. I’d rather work from actual problems written by standardized test-writers, just to show you how well this technique does work on real problems. I’ve chosen two problems that could just as easily be seen on the GRE.

Try this GMATPrep® problem:

* ” Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

“(A) 2

“(B) 3

“(C) 4

“(D) 6

“(E) 8”

Yuck. A work problem.

Except… here’s the cool thing. The vast majority of rate and work problems have awesome shortcuts. This is so true that, nowadays, if I look at a rate or work problem and the only solution idea I have is that old, annoying RTD (or RTW) chart… I’m probably going to skip the problem entirely. It’s not worth my time or mental energy.

This problem is no exception—in fact, this one is an amazing example of a complicated problem with a 20-second solution. Seriously—20 seconds!

You own a factory now (lucky you!). Your factory has 6 machines in it. At the beginning of the first day, you turn on all 6 machines and they start pumping out their widgets. After 12 continuous days of this, the machines have produced all of the widgets you need, so you turn them off again.

Let’s say that, on day 1, you turned them all on, but then you turned them off at the end of that day. What proportion of the job did your machines finish that day? They did 1/12 of the job.

Now, here’s a key turning point. Most people will then try to figure out how much work one machine does on one day. (Many people will make the mistake of thinking that one machine does 1/12 of the job in one day.) But don’t go in that direction in the first place! If you were really the factory owner, you wouldn’t start writing equations at this point. You’d figure out what you need by testing some scenarios. Read more