In the past, we’ve talked about making story problems real. In other words, when the test gives you a story problem, don’t start making tables and writing equations and figuring out the algebraic solution. Rather, do what you would do in the real world if someone asked you this question: a back-of-the-envelope calculation (involving some math, sure, but not multiple equations with variables).
If you haven’t yet read the article linked in the last paragraph, go do that first. Learn how to use this method, then come back here and test your new skills on the problem below.
This is a GMATPrep® problem from the free exams. Give yourself about 2 minutes. Go!
* “Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?
“(1) Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.
“(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.”
You work in a factory. Your boss just came up to you and asked you this question. What do you do?
In the real world, you’d never whip out a piece of paper and start writing equations. Instead, you’d do something like this:
I need to figure out the difference between how long it takes X alone and how long it takes Y alone.
Okay, statement (1) gives me some info. Hmm, so if machine X takes 1 hour to do the job by itself, then the two machines together would take two-thirds…let’s see, that’s 40 minutes…
Wait, that number is annoying. Let’s say machine X takes 3 hours to do the job alone, so the two machines take 2 hours to do it together.
What next? Oh, right, how long does Y take? If they can do it together in 2 hours, and X takes 3 hours to do the job by itself, then X is doing 2/3 of the job in just 2 hours. So Y has to do the other 1/3 of the job in 2 hours. Continue Reading…