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## Official Guide Explanation:Problem Solving #56

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 56
Page: 69
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Data Interpretation >

Explanation: If you don't know how to do this problem, it's an easy one to guess on: to show the distance between all of those cities, do you think you can do it with 6 table entries or less? However, it's useful to know how the math works in case the answer choices are more carefully chosen next time you see it.

This is essentially a combinations problem. Given a population of six cities, how many pairs of cities can be selected from the population? The combinations formula is ((n!)/(k!(n - k)!)), where n is the population (in this case, 6), and k is the number in each subgroup (in this case, 2). Plugging in:

((n!)/(k!(n - k)!)) = ((6!)/(2!(6 - 2)!)) = ((6(5)(4!))/(2!(4!))) = ((6(5))/2) = 15, choice (A).

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