Do You Have a "Word Problem" Problem?

Written by Kelly Granson. Posted in GMAT Study Guide

math clip_art_02We get used to the idea that math includes only numbers, formulas and symbols, but not words that need to be translated. In GMAT Word Problems, you face this problem, where words must first be translated into numbers and symbols before a solution can be found. Figuring out quickly how to approach the problem in a fast and efficient way is one of the key skills the GMAT is testing. Quite often, you may be afraid that you will interpret a word problem incorrectly, but word problems are no harder than regular problems if you are attentive and can transform those words into mathematical expressions, usually equations or inequalities.

Some common English-to-Math translations of words into symbols can make your work easier as you break down word problems:

1) ADDITION (+): increased by, more than, combined, together, total of, sum, added to, and, plus;

2) SUBTRACTION (–): decreased by, minus, less/fewer than, subtracted from;

3) MULTIPLICATION (×): times, multiplied by, product of;

4) DIVISION (÷): per, ratio of, divided by;

5) EQUALS (=): is, are, gives, adds up to, is the same as, is as much as.

Several approaches to solving word problems can help you avoid confusion when you first see such a question. Here are some tips that will lead you step by step to successful solutions:

STEP 1 – Read the question carefully. Try to understand what information you have and what you need to derive. Make sure you have completely understood exactly what it is you have to find.

STEP 2 – Assign a variable to each unknown. To avoid confusion, it's a good strategy to pick variables associated with the unknowns in the question itself (instead of using the traditional x and y in every problem). For example, you can mark Jason's age with J, Mary's age with M, and combined ages with C. This will help you avoid the confusion and distraction of trying to remember which variable was assigned to which unknown.

STEP 3 – Convert words into numbers and variables. For example, if you are told that Jason is twice as old as Mary, write J=M × 2 or J = 2M. If you are told that Jason is 5 years older than Mary, write J = M+5 or M = J-5. It can be tricky, but it can be done correctly if you are attentive.

STEP 4 – Solve the equation(s) you've created, and check your answer.

Now that you understand how to break down word problems, let's go through a simple example that applies this knowledge in practice.

Example:

Jason invested all his money in lottery tickets and, surprisingly, doubled his initial investment, and spent $10 of his winnings to take a cab home. If by the time Jason got home, he had $380 more than he had before buying the lottery tickets. How much money did Jason have before buying the lottery tickets?

Solution:

• STEP 1 – You know that between the time Jason bought his tickets and the time he got home he doubled his money and spent $10. You also know that Jason got home with $380 more than he had when he bought lottery tickets. You need to find how much money he had before buying the lottery tickets.

• STEP 2 – Let x be the amount of money Jason had initially.

• STEP 3 – (a) You know that he doubled this amount (2x) and then spent $10, so he got home with 2x–10 dollars. (b) You also know that by the time he got home he had $380 more than he had initially, or x + 380. (c) Since x + 380 and 2x-10 represent the same amount of money (the amount of money Jason came home with), you can set these two expressions equal: x + 380 = 2x – 10.

• STEP 4 – Do the math: x + 380 = 2x – 10; 390 = x. Then check it. If Jason had $390 dollars, doubled it to $780 and then spent $10, $780 – 10 = $770 remained. If he started with $390 and came home with $380 more, then he came home with a total of $380 + 390 = $770. Since 390 works in both equations, it is the correct answer.

You see, if you approach it methodically, a Word Problem isn't as hard as it looks. With everyday practice, you can become fluent in reducing words to equations. If you're still struggling with English-to-Math translations, you just need more drill. Eventually, with practice, decoding word problems should come naturally.

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