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## Official Guide Explanation:Data Sufficiency #98

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: 98
Page: 281
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Remainder
Category 2: Arithmetic > Properties of Integers > Other

Explanation: To know the sum of the remainders, we'll need to know either the exact numbers, or some properties of the numbers as they relate to 7.

Statement (1) is insufficient. The largest possible remainder when divided by 7 is 6, and the smallest is 0, so if the range of the remainders is 6, we know that at least one remainder is 0 and one remainder is 6. However, there are 7 numbers, and we don't know anything about the other 5 remainders.

Statement (2) is sufficient. Consecutive numbers have consecutive remainders; for instance, the set {10,11,12,13,14,15,16} has, when divided by 7, the remainders {3,4,5,6,0,1,2}. Depending on the first number, the first and last remainders won't always be the same, but in a set of seven consecutive integers, exactly one of the integers will have each of the remainders from 0 to 6. Thus, the sum of the remainders must be:

0 + 1 + 2 + 3 + 4 + 5 + 6 = 21

Choice (B) is correct.

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