VeritasKarishma wrote:
Walkabout 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 the upper shelf.
(2) There are 24 books on the lower shelf.
Upper Shelf - Book with max no of pages has 400 pages. So all other books have less than 400 pages, say 350 pages (just an example)
Lower Shelf - Book with min no of pages has 475 pages. So all other books have more than 475 pages, say 500 pages (just an example)
Using both statement, there are 25 books on the upper shelf and 24 on the lower shelf.
So
Upper Shelf - There are total 25 books here. So one book has 400 pages and 24 others have 350 pages.
Lower Shelf - There are total 24 books here. So one book has 475 pages and 23 other books have 500 pages.
Now say we are going to arrange the 49 books in increasing order of pages to get the median. The median will be the number of pages in the 25th book:
350, 350, ... 350, 400, 475, 500, 500, .... 500, 500
There are 24 books with 350 pages each. The 25th book is the one with 400 pages.
So median = 400
VeritasKarishmaThanks for the explanation with kudos!
Can we consider that every books with the Upper Shelf carries 400 pages and every books with the Lower Shelf carries 475 pages?
Like....
For the Upper Shelf it is.....
400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400,
For the Lower Shelf it is.......
475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475,
So, if we combine both statements, we get.....
400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400,
400,
475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475, 475.So, median is 400.
Thanks__
Yes, you can. From its wording, the question seems to imply that there is one book with 400 pages and one with 475 but no such constraints are actually mentioned. So even the case given by you shouldn't change the answer.