Official Guide Explanation:
Data Sufficiency #86




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Solution and Metadata

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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