Official Guide Explanation:
Data Sufficiency #147

Background

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Solution and Metadata

Question: 147
Page: 286
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Descriptive Statistics > other

Explanation: If we were to rank all of the books on the two shelves in order of their number of pages, the book with the median number of pages would be the one in the middle of that ranking. While we know that some of the books have no more than 400 pages and others have no fewer than 475, we don't know how many books are on each shelf, so we don't know whether the median falls in one of the groups or the other.

Statements (1) and (2) are insufficient on their own. Knowing how many books are on one of the two shelves is not enough. For instance, if we know that 25 books have no greater than 400 pages, we still don't know whether the median is greater than 400 (if, for instance, there are 30 books on the other shelf) or the median is less than 400 (if there are 20 books on the lower shelf).

Taken together, the statements are sufficient. There are 25 books with 400 or fewer pages and 24 with 475 or greater. If we rank all of those, the book in the middle of the list will be the one with the greatest number of pages among the 25 with 400 or fewer. The question tells us that one of those books has exactly 400 pages. None of those books have more, so the book with the greatest number of pages on the upper shelf--and thus, the book with the median number of pages--has exactly 400 pages. Choice (C) is correct.

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