OG 12, Median problem <Urgent>

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vaishalijain7: Master | Next Rank: 500 Posts; Posts: 102; Joined: Sun Mar 29, 2009 7:21 pm; Location: toronto; Thanked: 5 times

OG 12, Median problem <Urgent>

by vaishalijain7 » Mon Jun 29, 2009 4:42 pm

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 upper shelf.
2. There are 24 books on lower shelf.

Can anyone please explain how to solve it? Please take it as urgent as I have my GMAT exam after 2 days.

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Source: Beat The GMAT — Data Sufficiency | Mon Jun 29, 2009 4:42 pm

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Re: OG 12, Median problem <Urgent>

by Ian Stewart » Mon Jun 29, 2009 6:07 pm

vaishalijain7 wrote: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 upper shelf.
2. There are 24 books on lower shelf.

Can anyone please explain how to solve it? Please take it as urgent as I have my GMAT exam after 2 days.

Neither statement is sufficient alone, because we have no information about the other shelf.

Taking both together, we know we have 49 books. The median book will therefore have the 25th highest number of pages. The 24 books with the most pages are all on the bottom shelf, so the book with the 25th most pages is the book on the upper shelf with the greatest number of pages, and the question tells us that book has 400 pages. So the median must be 400. C.

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Domnu: Master | Next Rank: 500 Posts; Posts: 385; Joined: Sun May 24, 2009 3:55 pm; Thanked: 11 times; GMAT Score:740

by Domnu » Mon Jun 29, 2009 6:08 pm

The answer should be C. Here's why:

[spoiler]1) isn't complete, since this tells us nothing about the second shelf. Same thing for 2). Now, when we combine both shelves, we know that the ordering is going to be something like this:

_ _ _ _ _ _... 400 475 _ _ _ ... _ _

where there are 24 books before the 400 and 23 books after the 475. We are looking for the 25th book in this order, since, in a list of 49 books, the 25th element is the median. Since there are 24 books before the 400, the book with 400 pages is the median. This information is derivable from both 1) and 2).[/spoiler]

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