Official Guide Explanation:
Problem Solving #57




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Solution and Metadata

Question: 57
Page: 160
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Algebra > Linear Equations-One Unk >

Explanation: There are two ways to find the mean of 10, 30, and 50. The traditional way is to add them up and divide by three: ((10 + 30 + 50)/3) = (90/3) = 30. It works, it's reasonably fast, and it's easy. There's another way to instantly see that the average is 30. Any time a set of numbers is equally spaced (consecutive integers, consecutive evens, or numbers all spaced by 20s, like these), the average is equal to the median. The median is simply the middle number, so it's easy enough to spot.

The second step doesn't have a shortcut, unfortunately. If 30 is 5 more than the average of three other numbers, including 20 and 40, the equation can be given as follows:     ((20 + 40 + x)/3) = 25

60 + x = 75

x = 15, choice (A).

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