A certain bookcase has 2 shelves of books

A certain bookcase has 2 shelves of books. On the upper shelf, the book with the greatest number of pages has 400 pages. On the lower shelf, the book with the least number of pages has 475 pages. What is the median number of pages for all of the books on the 2 shelves? (1) There are 25 books on the upper shelf. (2) There are 24 books on the lower shelf. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient., Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient., BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient., EACH statement ALONE is sufficient., Statements (1) and (2) TOGETHER are not sufficient.

1 Explanation

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Mike McGarry, Magoosh Tutor

Nov 11, 2012 • Comment

The main issue I have with this question is nowhere does it state that the books are in any kind of order. Book 25 could just as well have 200 pages because it is less than 400. Book 26 could have 1000 pages because it is more than 475. I feel it is worded poorly or maybe I just missed something. How can we assume information when its not given from the GMAT question?

Feb 9, 2019 • Reply

Adam

Hey there!
Indeed, nothing tells us that the books are in order on the shelf, and they don't have to be.
However, we are asked to find the median number of pages. The median is defined as the number in the middle of a list when that list is put in order. So whenever you calculate the median of any list, the first step is to place the list in order from least to greatest.
The median number of pages, then, is the number of pages in the middle of a list where all the books are in order from least number of pages to most number of pages. So while the books aren't in order on the shelf, we're not finding the middle book on the shelf. We're finding the median number of pages, and to do this, we first order the books.
Hope that helps!

Feb 13, 2019 • Reply