How to Solve Any GRE Word Problem (Really)
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Word problems get a lot of hate from students. When you read the explanation for a tough GRE word problem, it’s easy to feel like the solution came out of nowhere. Maybe it makes sense now, but how were you supposed to figure it out on your own?
Fortunately, word problems really aren’t so bad—they’re just misunderstood. There’s a strategy for solving GRE word problems, just as there is for any other type of GRE Quant problem. Here’s a way to confidently solve any GRE word problem.
Where Do You Start?
The answer to this one is easy: you start by putting your pencil down and taking a deep breath. I mean that literally! I actually want you, when you spot a GRE word problem, to physically put down your pencil and breathe. Your brain needs oxygen for the challenge you’re about to give it. And a lot of mistakes come from writing too much, too quickly. Putting down the pencil will keep you from racing ahead when you should be slowing down.
All good? The next step is to read the problem. If you often have trouble getting the right equations down on your paper, don’t pick up your pencil until you’re done reading. That’s probably different from what you’re used to doing, and at first, you won’t know exactly what to focus on. However, a lot of mistakes on word problems come from writing down equations before you have all of the info. As you get better at solving word problems, you’ll have a better sense of what to write down while you read. For now, though, just focus on reading.
The Steps to Solving a GRE Word Problem
Did you read the entire problem? Then you’ve got a decision to make. If you understood what the problem was asking, and if you had a sense of what steps you’d take to solve it, go ahead and get to work. If not, either mark it and move on to the next problem, or choose a random guess.
If you feel okay about what you read, the next step is to determine what your variables are. Don’t write any equations until you know exactly what the unknown values in the problem are. If you know a quantity, it’s not a variable (for instance, if the problem says that Orion has six pieces of candy, you don’t need a variable to represent how much candy he has). But, if there’s a number that you don’t know, create a variable. For instance, maybe you only know that Orion and Janet have fifteen pieces of candy between them—you don’t know how much candy each person has individually, so you’ll need variables to represent those numbers. Jot your variables down on your paper before you start creating equations.
Ready to write some equations? Not just yet! Look back at the problem one more time. The trick to reading a GRE word problem is to see it as a series of relationships between values. Every piece of information in the problem will tell you how two or more values relate to each other. For example, here’s a sentence from a GRE word problem in the 5lb. Book of GRE Practice Problems:
An online merchant sells wine for $20 for an individual bottle or $220 for a case of 12.
This sentence tells you about a relationship between several unknown values: the number of bottles the merchant sold, the number of cases, and the merchant’s total income. Even though the total income isn’t mentioned in the sentence, you can still relate it to the two values that are mentioned.
Only start writing equations once you have a handle on the relationships that the problem describes. Each relationship will typically be a single equation. Don’t worry if you need to build up the equations one piece at a time. Also, don’t try to fit too much information into a single equation! That’s a good way to stumble while translating a GRE word problem into math.
Try It with an Actual GRE Word Problem
Here’s another word problem from the 5lb. Book of GRE Practice Problems. Let’s use the approach above.
Step 1: Don’t read the problem yet! Glance at it and note that it’s a word problem. Take a deep breath and put your pencil down.
Step 2: Now, read the problem—without writing on your paper.
Marcy bought one pair of jeans at 70% off, and one blouse at 40% off. If she paid $12 more for the blouse than for the jeans, and she spent a total of $84, what was the original price of the jeans?
(A) 76
(B) 96
(C) 100
(D) 120
(E) 124
Step 3: Identify your unknowns. We know the total amount that Marcy spent, so we won’t need a variable for that. However, there are four things we don’t know:
- The original price of the blouse: x
- The amount Marcy paid for the blouse: b
- The original price of the jeans: y
- The amount Marcy paid for the jeans: j
Step 4: Look for relationships. The problem describes four different relationships between your variables.
- The relationship between the price Marcy paid for the jeans and the original price. The price she paid was 30% of the original.
- The relationship between the price Marcy paid for the blouse and the original price. The price she paid was 60% of the original.
- Two different relationships between the two prices that Marcy actually paid: first, the price she paid for the blouse was $12 higher than the price she paid for the jeans. Second, the sum of the two prices she paid was $84.
Step 5: Turn those relationships into equations!
j = 0.3y
b = 0.6x
b = 12 + j
b + j = 84
Step 6: Solve the problem. The easiest place to start is by combining the third and fourth equations, to solve for the variables b and j. If b = 12+j, and b + j = 84, then j = 36.
You have an equation that relates j and y: j = 0.3y. So, you can use the following process to solve for y:
36 = 0.3y
y = 36/0.3 = 120
The answer to the problem is $120.
As you get more confident with GRE word problems, you’ll learn that you can abbreviate some of these steps. However, if you’re struggling with word problems, build a solid foundation using this process before you start skipping steps. The real key is to know what all of your variables are first, before you ever write down equations. If you try to combine those two steps into one, you might make a mistake and never notice it. ?
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Chelsey Cooley
is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.