GMAT Exam: A Simple Guide To GMAT Problem-Solving Questions

About Problem-Solving Questions
The GMAT problem-solving questions are multiple-choice questions. Each question provides five answer choice options. Most of the questions present a problem situation that requires a single response. Some of the question stems will have Roman numeral options. The five answer options will include various combinations of the Roman numeral options. In either case, you must select the one best answer choice from the five answer choice options.

Strategies for Problem-Solving Questions
Start by reading the question stem. Determine what the question is asking. Skim through the answer choices. Decide on an optimum approach for answering the question.

Here are some strategic ways to attack problem-solving questions.

Write and Solve an Equation
For many questions, writing and solving an equation is a straightforward method for determining the answer. Let the variable represent the unknown in the question. When you have more than one unknown in a problem question, you might be able to express one in terms of the other. For instance, if a first unknown is described in terms of a second unknown, it is usually easier to let the variable equal the second unknown. For such problems, you also can choose to assign a variable name to each unknown. Just remember that you will need as many equations as you have variables in order to determine specific values for the variables.

Here is an example.

A rectangular swimming pool is twice as long as it is wide. If the perimeter of the pool is 180 feet, what is the length, in feet, of the pool?
A. 30
B. 60
C. 70
D. 80
E. 90

The perimeter, P, of a rectangle is P = 2l + 2w = 2(l + w), where l is the rectangle’s length and w is its width. 

Method 1: Use one variable.
The length of the pool is described in terms of its width. Let w = the width, in feet, of the pool. Then 2w = the length, in feet, of the pool. Write an equation that represents the facts given in the question.
180 feet = 2(2w + w) or, equivalently, 2(2w + w) = 180 feet

Solve the equation, omitting the units for convenience.

The length of the pool is 60 feet. The correct response is B.

Tip: Make sure you answer the question asked. In this question, after you obtain w, you must calculate 2w to answer the question.

Method 2: Use two variables.
Let w = the width, in feet, of the pool and l = the length, in feet, of the pool. Write two equations that represent the facts given in the question. (1) l = 2w (2) 2(l + w) = 180 feet

Simultaneously solve the two equations, omitting the units for convenience.
Using the substitution method, substitute l = 2w from equation (1) into equation (2) to obtain
2(2w + w) = 180
Complete the solution as shown in Method 1.

Check the Answer Choices
When you are provided numerical answer choices, you might determine the correct choice by checking the answer choices.

Here is an example.

Henry must pay a 7% penalty tax on the portion of the total value of an item that exceeds $100. If Henry paid a penalty tax of $8.75, what was the total value of the item?
A. $185
B. $225
C. $240
D. $275
E. $300

Before you start checking the answer choices, write an equation to make sure you understand the question. Let x = the total value in dollars of the item. Then x – $100 is the portion of the item that is subject to the 7% penalty tax. Using the information in the question, set up an equation that represents the facts of the question.
7%(x – $100) = $8.75
x – $100) = $8.75

Now check the answer choices in the equation. The answers are listed in ascending order, so start with choice C. If choice C is incorrect, you might be able to use logical reasoning to eliminate other answer choices as well. This will enable you to determine the correct answer sooner and save time. Check C:

Choice C is too high, so eliminate choices D and E as too high as well.

Check B:

Choice B is the correct response.

Plug in 100 for an Unknown Base in Percentage Questions
When you have questions involving percentages in which the base is not given, you can usually plug in 100 for the base to make the problem easier to work out.

Here is an example.

Marvin invested in a stock whose value had increased 5% by the end of 2012, decreased 2% by the end of 2013, and increased 10% by the end of 2014. What is the percent increase in the value of the stock from the end of 2012 to the end of 2014?
A. 7.80%
B. 8.19%
C. 12.50%
D. 13.00%
E. 17.00%

The percent increase in the stock is


For convenience let $100 be the initial value of the stock. Then the value of the stock at the end of 2012 was 105%($100) = $105. By the end of 2013, the value of the stock was 98%($105) = $102.90. By the end of 2014, the value of the stock was 110%(102.90) = $113.19.

The percent increase is

The percent increase in the stock is 7.8%. Choice A is the correct response.

Evaluate Expressions Using Suitable Values for Variables
When the question stem and the answer choices both contain one or more variables, you might try evaluating the expressions given in the question stem and answer choices for suitable values of the variables. Make sure the values you select satisfy all the conditions presented in the question. Suitable values are small numbers such as 2, 3, and 4. Avoid using 0 or 1, because these numbers have special properties that might lead you to believe an incorrect answer choice is correct. Look for an answer choice that evaluates to the same value as the expression in the question stem.

Tip: You must evaluate all the answer choices to make sure two choices (or possibly more) do not evaluate to the same value as the expression in the question stem. If this occurs, start over and choose different values for the variables.

Here is an example.

Which expression is equivalent to

Let x = 3 and y =

2.
Check A:

Check B:

Check C:

Check D:

Check E:

Choice D is the correct response.

Do the Math
In many cases, the most efficient way to answer a problem-solving question is simply to do the math.

Here is an example.
4x2 – 8x – 5 = 0

What is the sum of the roots of the preceding quadratic equation?
A. –8
B. –2
C. 2
D. 4
E. 8

Solve the quadratic equation by factoring.

Compute the sum

.
Choice C is the correct response.

This question is an example of a way a test maker can compose a question to thwart the strategy of checking the answer choices.

Other Helpful Advice
- Use logical reasoning to eliminate answer choices. You can eliminate some answer choices from the outset based on logical reasoning. For instance, if you figure out the answer must be even, you can eliminate all odd answer choices.
- Make rough sketches for geometry questions. For geometry problems, sketches help you organize the question information. However, make quick rough sketches. Do not spend unnecessary time making them.
- Know your math. No matter which strategy you use in a problem-solving question, you will need to know and understand math. Most of the math concepts on the GMAT are ones you likely have encountered in the past. However, you might have forgotten some if not most of them. 

Directions for the Problem-Solving Questions
Select the best of the given answer choices.
Note: Unless otherwise stated, you can assume all of the following.

- All numbers used are real numbers.
- All figures lie in a plane.
- Lines shown as straight are straight lines, and straight lines might sometimes appear jagged.
- Figures are drawn accurately, but are NOT necessarily drawn to scale.
- All angle measures are greater than zero.
- The relative positions of points, angles, and regions are in the order shown.