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Median number of pages for all books on 2 shelves?

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by Striver » Tue May 29, 2012 4:07 pm
#47

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.
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by Jim@StratusPrep » Tue May 29, 2012 4:21 pm
1 and 2 are each insufficient individually because you do not know the total number of books in either case.

Together, you know that the 25th longest (or shortest) book is the median. On the upper shelf you know that the longest book of the 25 has to have 400 pages, placing it at the median.
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