I’ve spoken with several students recently who are struggling with translating wordy quant problems into the actual math necessary to set up and solve the problem. Some people make too many mistakes when doing this, and others find that, though generally accurate, they take more time than they can afford. In the next two articles (this is part 1!), we’re going to talk about how to translate efficiently and effectively.

We’re going to do this by example: I’ll provide short excerpts from actual problems, and then we’ll discuss how to know what to do, how to do the actual translation, and how to do everything efficiently. Note that I’m not necessarily going to provide the full text of problems “ and, therefore, we’re not going to solve fully. That’s not our goal today.

The Basics

Before we dive into more advanced issues, there are some basics we all need to know. We’re not going to spend a lot of time on the basics because all GRE books out there already explain this; I’ll give a quick introduction and, if you need more, seek out one of the standard books on this topic (in Manhattan Prep’s books, you’ll find this info in the Algebraic Translations chapter of the Word Problems Strategy Guide).

First, when the problem introduces certain people, objects or other things, we will likely need to assign variables. Cindy can become C and Bob can become B. Next, the words will give us some kind of relationship between variables.
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Have you started studying Number Properties yet? Most people find this topic on the more difficult side in general, particularly the area of divisibility and prime. We did learn all of these basic concepts years ago, when we were about 8 or 10 years old “ number properties refers to all of the building blocks we use later in school to do algebra, geometry, and more advanced math.

However, most of what we learned in school was at a much more basic level (we were only 10 after all!) and we also didn’t have to understand the number properties theory or answer questions that were anything like some of the bizarre-seeming questions we find on standardized tests.

Let’s try this problem first (© Manhattan Prep) from our GRE Number Properties Strategy Guide. Set your timer for 2 minutes.

The quantity 3³4⁴5⁵6⁶ “ 3⁶4⁵5⁴6³ will end in how many zeros?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 9

Got your answer? Great, let’s get started. You want to know what the correct answer is? Let me ask you a couple of questions first.

Are you confident about your answer? Did you end up having to guess? Did you give up without guessing? (If the last, make a guess right now. You can’t keep reading till you do. Well, obviously I can’t stop you, but I’m serious “ make a guess.)

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Occasionally, we’ll get an algebra problem in which a pre-defined formula is given for some phenomenon, and then we’re told to manipulate that formula in some way. People often find these quite tough because we typically didn’t see questions like this in school.

Let’s try this problem first (© Manhattan Prep) from our GRE Algebra Strategy Guide.

 Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GRE score. If Melvin’s GRE score is twice his monthly electric bill, and his life expectancy is 50, what is his shoe size?

(There are no multiple choice answers for this one. Also, yes, we’re being a little silly with this problem.

But don’t the big story problems feel like this sometimes? Just having a little fun while we learn : ) )

Many students will tell me, It doesn’t seem like we can solve this one at all. There are four variables and they only give us the value for one of them. How can we possibly figure out his shoe size?

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During class 2 of our program, we teach a lesson entitled Math Refresher. I thought it would be fun to share one of the problems with you and talk through two things: (1) the actual algebra (real math) we would need to solve the problem, and (2) the standardized testing skills that allow us to solve the problem much more easily.

First, try this problem (© Manhattan Prep). Note: there are no multiple choice answers: you have to come up with a number on your own!

Sarita and Bob together contribute to the cost of a $40 gift. If Bob contributes $12 more than Sarita does, how much does Bob contribute?

How did you do it? Did you write some equations? Try out some numbers? Find some other cool shortcut?

On this one, the best approach is a very neat shortcut that I’m going to show you “ but only after I show you the actual algebra. It’s important to know how to do the algebra, just in case you don’t know or can’t find any good shortcuts.
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This comic from XKCD is making a very nerdy joke:

The 70, upon opening a package, is “exploded” — into its prime factors.

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Come GRE test day, there isn’t much left to do in the way of studying. Cramming new material on the day of your exam is stressful and won’t give you much of a positive return on time invested. However, there are some things that you can do on test day to further your GRE success. One thing that I found very useful when I took my GRE was performing a math warm-up. Read more