

GMAT Word Problems: Introduction, Strategies, and Practice QuestionsYou 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. No matter what your feelings are about this problem type, though, Magoosh’s experts have put together everything you need to know (and practice!) GMAT word problems in order to master them before test day. Table of Contents
What to Expect from GMAT Word ProblemsThink of GMAT word problems as questions that ask you to turn realworld 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. Think about it this way: the reason human beings created algebra was to solve problems about realworld situations, and the GMAT loves asking math problems about numbers and about realworld situations, a.k.a. word problems! Even folks who can do algebra in the abstract sometimes find word problems challenging. You’ll find GMAT word problems in the GMAT Quant section. How much of the GMAT is word problems? Within the Quant section, actually a whole lot! A study of official GMAT questions from actual tests show that word problems account for 58.2% of all GMAT math questions. In other words, testtakers should anticipate a word problem cropping up (on average) in three out of every five questions you’ll see in Quant. Because of GMAT word problems’ prevalence, you can expect to see both Data Sufficiency and Problem Solving questions in this format. The question format and answer choices may look different, but the basic premise will be the same. You may be feeling the pressure, 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 in that be?). The good news: by using and combining a variety of strategies, you can put together the tools you need to ace even the most complex GMAT word problems, every single time! With that in mind, here are the four key strategies you’ll need. 1. Translate from Words to MathSuppose we have the following sentence in a word problem:”Threefifths of x is 14 less than twice y squared.” How do we change words to math? Here’s a quick guide:
With that in mind, let’s go back to the sentence from the hypothetical problem above.
Altogether, the equation we get is: 2. Learn to Work with VariablesWorking with Variables Part I: Assigning Variables 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 saving each month. With what she has left each month, she spend 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 hypervigilant and overthetop 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
Andrew and Beatrice each have their own savings account. Beatrice’s account has $600 less than three times what Andrew’s account has. If Andrew had $300 more dollars, then he would have exactly half what is currently in Beatrice’s account. How much does Beatrice have?
Click here for a text answer and explanationThe obvious choices for variables are A = the amount in Andrew’s account and B = the amount in Beatrice’s account. The GMAT will be good about giving you word problems involving people whose names start with a different letter so that it’s easier to assign variables. We can turn the second & third sentences into equations. second sentence: B = 3A – 600 Both equations are solved for B, so simply set them equal. 3A – 600 = 2(A + 300) 3A – 600 = 2A + 600 A – 600 = 600 A = 1200 We can plug this into either equation to find B. (BTW, if you have time, an excellent check is to plug it into both equations, and make sure the value of B you get is the same!) B = 3000 Thus, Andrew has $1200 in his account, and Beatrice, $3000 in hers.
Working with Variables Part II: Choosing Your Approach 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 superbasic 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? 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 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:
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 WeaknessesWith 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:
Your answers to these questions can help you craft a better strategy for word problems, identifying exactly what you need to review to get better! GMAT Word Problem Practice QuestionsNow that you’ve learned how to approach word problems, we’ve put together a collection of them, direct from Magoosh’s product, for you to try! Video and text answers and explanations follow each question.
A. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. Click here for a video answer and explanation to GMAT Word Problem 1! Click here for a text answer and explanation to GMAT Word Problem 1!Our task is to determine the ratio of Bob’s trees to Ann’s trees. Let’s label these numbers of trees with variables: Bob’s trees→B, Ann’s trees→A With these variables, we can express the ratio we want to determine: \(B/A\) =? Statement 1: Let’s translate this into an equation using A and B: \( A=B+20 \) Now we can substitute this into our ratio, replacing A: \(B/A\) = \( B/(B+20) \) No matter what simplifications we make, we cannot find a numerical value for this fraction. We would need a value for B. We cannot determine the ratio. Statement 1 by itself is not sufficient. Statement 2: Let’s translate this into an equation using A and B: \(A=1.10 x B \) Again, let’s substitute this in for A in our ratio: \(B/A\) = \( B/(1.10B) \) = \(1/1.1 \) We found a value for the ratio of Bob’s trees to Ann’s trees. Statement 2 alone is sufficient.
A. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. Click here for a video answer and explanation to GMAT Word Problem 2! Click here for a text answer and explanation to GMAT Word Problem 2!If x is the number of visitors on the first day, then:
A. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. Click here for a video answer and explanation to GMAT Word Problem 3! Click here for a text answer and explanation to GMAT Word Problem 3!This question is really about common multiples and the LCM (note that it is different than finding the set of all multiples, though!). If Ms. Ames can give each of her 24 students k cookies, so that they all get the same and none are left over, then 24k = N. Similarly, in Mr. Betancourt’s class, 18s = N. Statement #1: if N<100, the only possibility is N = 72. This statement, alone and by itself, is sufficient. Statement #2: if N > 50, then N could be 72, or 144, or 216, or etc. Many possibilities. This statement, alone and by itself, is not sufficient.
A. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. Click here for a video answer and explanation to GMAT Word Problem 4! Click here for a text answer and explanation to GMAT Word Problem 4!A short way to do this problem. The prompt gives us ratio information. Each statement gives use some kind of count information, so each must be sufficient on its own. From that alone, we can conclude: answer = D. This is all we have to do for Data Sufficiency. A Final Word on Word ProblemsSo, what is the trick to GMAT word problems? As you’ve seen in this post, there’s no onesizefitsall 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. With them, you’ll be able to find everything from average speed to total distance traveled, from total time to total amount. 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. You can also check out our posts on compound interest and Venn diagrams for more practice with GMAT word problems. Good luck! This post was written with contributions from our Magoosh content creator, Rachel KapelkeDale. The post GMAT Word Problems: Introduction, Strategies, and Practice Questions appeared first on Magoosh GMAT Blog. 
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