GMAT Word Problems: Introduction and Strategies.

You may love GMAT word problems or you may hate them, but you can’t get around them if you want to ace the GMAT Quant section. However, no matter what your feelings are about this problem type, Magoosh’s experts have put together everything you need to know (and practice!) in order to master GMAT word problems before you encounter them on test day.

Table of Contents

• What to Expect from GMAT Word Problems
• Strategy Guide: What’s the Trick to Mastering GMAT Word Problems?
• A Final Word on GMAT Word Problems

What to Expect from GMAT Word Problems

Think of GMAT word problems as questions that ask you to turn real-world situations into math problems. Of course, this can be a lot more complicated than it sounds. After all, it’s one thing to understand algebra in the abstract and quite another to think about where the rubber meets the road.

Here’s one way to think about it: The reason human beings created algebra was to solve problems about real-world situations, and the GMAT loves asking you to apply mathematical concepts to realistic, everyday scenarios, a.k.a. word problems! If you find word problems challenging, you are not alone! Even folks who are skilled at algebra in the abstract will often find word problems very difficult to navigate.

Why is it so important to develop skills for this, at times, downright annoying type of math question? Well, GMAT word problems show up on the Quantitative Reasoning section a whole lot! Now, you may be feeling a bit of pressure here, but hang in there!

If you’re worried about how to master word problems on the GMAT, keep reading for our GMAT Word Problems strategy guide.

Strategy Guide: What’s the Trick to Mastering GMAT Word Problems?

First, the disappointing news: There’s no one strategy that will work to immediately solve every word problem, every time (where would the fun be in that?). The good news: By using and combining a variety of strategies, you will have tools at the ready to ace even the most complex GMAT word problems!

With that in mind, here are the four key strategies you’ll need.

1. Translate from Words to Math

Suppose we have the following sentence in a word problem: “Three-fifths of x is 14 less than twice y squared.” How do we change words to math? Here’s a quick guide:

1. The verb “is/are” is the equivalent of an equal sign; the equal sign in an equation is, in terms of “mathematical grammar,” the equivalent of a verb in a sentence. Every sentence has a verb and every equation has an equal sign.
2. The word “of” means multiply (often used with fractions and percents). Ex. “26% of x” means (0.26x)
3. The words “more than” or “greater than” mean addition. Ex. “5 greater than x” means (x + 5) and “7 more than y” means (y + 7)
4. The words “less than” means subtraction. Ex. “8 less than Q” means (Q – 8). Notice that the first element is always subtracted: in other words, “J less than K” means (K – J).

With that in mind, let’s go back to the sentence from the hypothetical problem above.

• “three fifths of x” means [(3/5)*x]
• “is” marks the location of the equal sign
• “twice y squared” means 2(y^2)
• “14 less than twice y squared” means 2(y^2) – 14

Altogether, the equation we get is:

Using this strategy, it’s straightforward to translate from a verbal statement about numbers to an equation.

2. Learn to Work with Variables

Working with Variables Part I: Assigning Variables

Most GMAT word problems concern real world quantities and are stated in real world terms, and we need to assign algebraic variables to these real-world quantities.

Sometimes, one quantity is directly related to every other quantity in the problem. For example:

“Sarah spends 2/5 of her monthly salary on rent, 1/12 of her monthly salary on auto costs including gas and insurance, and 1/10 of her monthly salary automatically goes into savings each month. With what she has left each month, she spends $800 on groceries and …”

In that problem, everything is related to “monthly salary,” so it would make a lot of sense to introduce just one variable for that, and express everything else in terms of that variable. Also, please don’t always use the boring choice of x for a variable! If we want a variable for salary, you might use the letter S, which will help you remember what the variable means! If we are given multiple variables that are all related to each other, it’s often helpful to assign a letter to the variable with the lowest value, and then express everything else in terms of this letter.

If there are two or more quantities that don’t depend directly on each other, then you may well have to introduce a different variable for each. Just remember that it’s mathematically problematic to litter a problem with a whole slew of different variables. You see, for each variable, you need an equation to solve it. If we want to solve for two different variables, we need two different equations (this is a common Word Problem scenario). If we want to solve for three different variables, we need three different equations (considerably less common). While the mathematical pattern continues to extend upward from there, more than three completely separate variables is almost unheard of on GMAT math.

When you assign variables, always be hyper-vigilant and over-the-top explicit about exactly what each variable means. Write a quick note to yourself on the scratch paper: T = the price of one box of tissue, or whatever the problem wants. What you want to avoid is the undesirable situation of solving for a number and not knowing what that number means in the problem!

Practice Question
Here’s a word problem practice question that’s a bit easier than what you might see on the GMAT!

Working with Variables Part II: Choosing Your Approach

When questions have variables in the answer choices, you can decide whether you’d rather take an algebraic approach or a numerical approach. Neither one of these is “better” than the other— it all depends on what works best for you.

An algebraic approach is what you most likely learned back in high school. This means that, to solve the problem, you’ll manipulate the variables according to mathematical rules. For a super-basic example, to solve \( 2x = y \), you would divide both sides by two and end up with \( x = y/2 \).

However, you could also to a numerical approach to this (and many other!) problems. This means putting numbers into both the question and the answer choices. So let’s take the previous example—which, again, is much, much easier than anything you’d see on the GMAT:

If \( 2x = y \), what is x in terms of y?
 
A. \(y/20\)
B. \(y/2\)
C. \(4/y\)
D. \(20/y\)
 
Here, you could pick a number to stand in for x in the original equation. Let’s say x is 2. If x = 2, then the original equation tells us that y = 4.

Now, plug that into the question and the answer. The question becomes: “What is 2 in terms of 4?” It’s ½, or .5. Then, look for the answer choice that gives you this answer. Plugging in the numbers, you get:

A. \(y/20\) = 0.2
B. \(y/2\) = 0.5
C. \(4/y\) = 1
D. \(20/y\) = 5

So B must be correct.

3. Plug in Numbers (the Smart Way)

If you choose to use the numerical approach described above, keep in mind that there are some key tips for plugging in numbers that you should use!

Here’s a quick summary of how to quick the best numbers for a particular problem:

• Remember that the GMAT has a broad definition of “number” that goes beyond positive integers! Zero, fractions, and negatives are all included. Work on developing number sense to help select the best numbers in a given scenario.
• For percent problems, think outside the box: GMAT test writers know lots of students pick 100. Try 500 or 1000 instead.
• Don’t try to pick numbers for questions involving more than one percent increase or decrease.
• Pay attention to units and convert them appropriately. This is particularly important in solutions and mixing problems!
• Don’t pick 1 as a number—it has too many unique properties.

A separate case involving plugging in, rather than picking, numbers: When all the answer choices are numerical, one further strategy we have at our disposal is backsolving. Using this strategy, we can pick one answer, plug it into the problem, and see whether it works. If this choice is too big or too small, it guides us in what other answer choices to eliminate. Typically, we would start with answer choice (C), but if another answer choice is a particularly convenient choice, then we would start there.

4. Understand Your Strengths and Weaknesses

With all of the above strategies at your disposal, you have everything you need to improve your answers to GMAT word problems. The most efficient way to do this is to keep an error log of word problems you’ve answered wrong in your practice, then review it. As you go through, think about the following:

• What concept or concepts was the question testing?
• What was tricky about the wording of the question?
• Were you already familiar with the methods used in the explanation video?
• Once you watched the explanation video, could you explain how to solve the problem to somebody else?

Your answers to these questions can help you craft a better strategy for GMAT Math word problems, identifying exactly what you need to review to get better!

A Final Word on Word Problems

So, what is the trick to GMAT word problems? As you’ve seen in this post, there’s no one-size-fits-all trick—but there are plenty of strategies!

The strategies you’ve read about here can be used to take the given information and identify key words in a question. The key now is to put them into practice. Jot down these techniques or bookmark this post so you can come back as you continue your practice with GMAT word problems. Also, check out our posts on work rate problems and Venn diagrams for more practice with GMAT word problems!

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