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. Options: A . &nbsp if the question can be answered by one of the statements alone but not by the other B . &nbsp if the question can be answered by using either statement alone C . &nbsp if the question can be answered by using both the statements together but cannot be answered using either statement alone D . &nbsp if the question cannot be answered even by using both the statements A and B.

A certain bookcase has 2 shelves of books. On the upper shelf, the book with t

Question

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.

Options:

A . if the question can be answered by one of the statements alone but not by the other

B . if the question can be answered by using either statement alone

C . if the question can be answered by using both the statements together but cannot be answered using either statement alone

D . if the question cannot be answered even by using both the statements A and B.

Answer: Option C
:
C

Statement (1) Insufficient: The information given says nothing about the number of books on the lower shelf. If there are fewer than 25 books on the lower shelf, then the median number of pages will be the number of pages in one of the books on the upper shelf or the average number of pages in two books on the upper shelf. Hence, the median will be at most 400. If there are more than 25 books on the lower shelf, then the median number of pages will be the number of pages in one of the books on the lower shelf or the average number of pages in two books on the lower shelf. Hence, the median will be at least 475; NOT sufficient.

Statement (2) Insufficient: An analysis very similar to that used in (1) shows the information given is not sufficient to determine the median; NOT sufficient. Given both (1) and (2), it follows that there is a total of 49 books. Therefore, the median will be the 25th book when the books are ordered by number of pages. Since the 25th book in this ordering is the book on the upper shelf with the greatest number of pages, the median is 400. Therefore, (1) and (2) together are sufficient. The correct answer is C; both statements together are sufficient

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