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## Official Guide Explanation:Data Sufficiency #66

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: 66
Page: 157
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Arithmetic > Properties of Integers > Evens and Odds

Explanation: Given the average of a set of consecutive odd integers, we have some idea of what the set looks like. If it contains 2 numbers, it is {9, 11}. If 4 numbers, it's {7, 9, 11, 13}. For every pair of numbers added, we simply add one to the bottom, one to the top.

Statement (1) is sufficient. If the range is 14, we can determine how many numbers there are. In the two examples I just gave, the ranges were 2 and 6, meaning that a set of 6 numbers has a range of 10 and a set of 8 numbers has a range of 14. No need to figure out exactly what those 8 numbers are, but suffice it to say we could do so.

Statement (2) is also sufficient. As suggested by the examples above, if a set of consecutive odds is to have an even average, there must be an even number of terms in the set. If 17 is the greater number in the set, we can determine that the set must consist of {3, 5, 7, 9, 11, 13, 15, 17}. Thus we know the least integer as well. Choice (D) is correct.

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