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## Official Guide Explanation:Data Sufficiency #86

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: 86
Page: 280
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Discrete Probability >
Category 2: Word Problems > Other >

Explanation: If 31 or more people were involved, then its guaranteed that at least one number was written down more than once. (There are only 30 numbers to go around.) If between 2 and 30 people participated, then it's possible, but not guaranteed, that a number was written down more than once. So, the question is really asking, "Were there 31 or more people?"

Statement (1) is enough information: if there were more than 40 people, there must have been more than 31. Statement (2) is not enough: if there were fewer than 70 people, it's not clear whether there were more or less than 31. So, choice (A) is correct.

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