Official Guide Explanation:
Problem Solving #5




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Solution and Metadata

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

Remember to add 20 back to the answer:

3.9 + 20 = 23.9

Convert back to thousands of dollars for $23,900, choice (C).

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