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## Official Guide Explanation:Problem Solving #5

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 5
Page: 152
Difficulty: 3 (Very Easy)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Word Problems > Data Interpretation >

Explanation: The textbook method for a question like this is to calculate the total salary for the 20 employees. For instance, you would start by multiplying 5 by \$20,000 for the total salary of those five employees, then do the same for the other three groups of employees.

There are two ways to shorten the time required to complete this question. First, disregard the thousands. Instead of \$20,000, \$22,000, etc., think in terms of 20, 22, 25, and 30. Next, all four of these numbers can be placed on a number line between 20 and 30. To make the calculations easier, subtract 20 from each of them--move them all 20 to the left on the number line. (Later, we'll add 20 to the answer, effectively moving 20 back in the other direction on the number line.

Thus, our new table looks something like this:

5    0

4    2

8    5

3    10

The calculations here are much quicker:

5(0) + 4(2) + 8(5) + 3(10)

= 0 + 8 + 40 + 30

= 78

There are 20 employees, so the average is:

(78/20) = (39/10) = 3.9