GMAT Exam: A Simple Guide To Solving Word Problems - Representing Verbal Phrases and Statements

For many questions, writing and solving an equation is a straightforward method for determining the answer. When you use equations, you must represent verbal phrases and statements using mathematical symbolism.

Here are some general guidelines.

Example: Ten less than three times a number is five more than twice the number. What is the number?
Let n = the number. Write an equation that represents the facts.
3n – 10 = 2n + 5 (Keep in mind that “Ten less than three times a number” is not 10 – 3n.)

Solve the equation.

The number is 15.

Sometimes you have two or more unknowns in a problem. For this situation you can use a different variable name for each unknown. On the other hand, you might assign a variable name to one unknown and express the other unknowns in terms of that variable.

For instance, if a first unknown is described in terms of a second unknown, let the variable equal the second unknown. In most cases, you will need as many equations as you have variables in order to determine specific values for the variables.

No matter whether you go with one variable or two or more variables, ultimately, the process will culminate in a one-variable linear equation (or its equivalent).

Example: The length of a lawn is 6 feet longer than its width. The lawn’s perimeter is 68 feet. What is the lawn’s length, in feet?

Method 1: Use one variable.
The lawn’s length is described in terms of its width. Let w = the lawn’s width, in feet. Then w + 6 feet = the lawn’s length, in feet. Write an equation that represents the facts given in the question.
2[(w +6 feet) + w] = 68 feet

Solve the equation, omitting the units for convenience.

The lawn’s length is 20 feet.
Make sure you answer the question that was asked. In this question, after you obtain w, you must calculate (w + 6) to answer the question.

Method 2: Use two variables.
Let w = the lawn’s width, in feet, and l = the lawn’s length, in feet.

Write two equations that represent the facts given in the question.

Simultaneously solve the two equations, omitting the units for convenience.

Using the substitution method, substitute l = w + 6 from equation (1) into equation (2) to obtain
2[(w +6) + w] = 68

Complete the solution as shown in Method 1.