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A certain bookcase has 2 shelves of books. On the upper

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A certain bookcase has 2 shelves of books. On the upper  [#permalink]

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New post 13 Dec 2012, 08:17
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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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Re: A certain bookcase has 2 shelves of books. On the upper  [#permalink]

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New post 13 Dec 2012, 08:27
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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?

Notice that we are told that all books on the upper shelf have fewer pages than all books on the lower shelf.

(1) There are 25 books on the upper shelf. No info about the lower shelf. Not sufficient.
(2) There are 24 books on the lower shelf. No info about the upper shelf. Not sufficient.

(1)+(2) There are total of 25+24=49 books, thus the median number of pages for all of the books will be the book with 25th largest number of pages. Now, since on the upper shelf which has 25 books, the book with the greatest number of pages has 400 pages, then median=400 pages (recall that all books from the lower shelf have more pages than all books on the upper shelf, so if we order all books in ascending number of pages, then we'll have 25 books from the upper shelf and then 24 books from the lower shelf). Sufficient.

Answer: C.
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Re: A certain bookcase has 2 shelves of books. On the upper  [#permalink]

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New post 02 May 2013, 04:08
Thanks for the reply, Banuel. So are we assuming that the books in the shelves are ordered by the number of pages?

This information wasn't provided in the original question...?
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Re: A certain bookcase has 2 shelves of books. On the upper  [#permalink]

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New post 02 May 2013, 04:46
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Re: A certain bookcase has 2 shelves of books. On the upper  [#permalink]

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New post 02 May 2013, 16:14
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Yeah, you are right, that shouldn't matter! Duh :) early morning jitters!!
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A certain bookcase has 2 shelves of books. On the upper  [#permalink]

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New post Updated on: 21 Jan 2017, 19:52
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Hello All,

From Question we can infer. Correct me if you think otherwise.

If Upper Shelf Books > Lower Shelf = Median = 400
If Upper Shelf Books < Lower Shelf = Median = 475
If Upper Shelf Books = Lower Shelf = Median = 400+475/2

S-1) Not sufficient
S-2) Not Sufficient
S-3) Upper Shelf 25> Lower 24. So Median is 400

So C is the correct Answer
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Originally posted by coolkl on 21 Jan 2017, 09:28.
Last edited by coolkl on 21 Jan 2017, 19:52, edited 1 time in total.
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Re: A certain bookcase has 2 shelves of books. On the upper  [#permalink]

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New post 01 Apr 2017, 11:17
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 GREATEST number of pages has 400 pages i.e. it will come in the end of the shelf if the books are arranged in ascending order according to the number of pages.
Lower shelf: Book with the least number of pages has 475 pages i.e. it will come in the starting if the books are arranged in ascending order.

(1) Total 25 books on upper shelf. Not sufficient to understand the number of books at the lower shelf.

BCE

(2) Again, not sufficient for the same reason.

Both statement together:
Total number of books in the two shelfs= 25+24=49 (ODD)

The median would be the 25th book. Therefore the median number of pages are 400.


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Re: A certain bookcase has 2 shelves of books. On the upper  [#permalink]

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New post 31 Dec 2017, 02:23
Bunuel 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?

Notice that we are told that all books on the upper shelf have fewer pages than all books on the lower shelf.

(1) There are 25 books on the upper shelf. No info about the lower shelf. Not sufficient.
(2) There are 24 books on the lower shelf. No info about the upper shelf. Not sufficient.

(1)+(2) There are total of 25+24=49 books, thus the median number of pages for all of the books will be the book with 25th largest number of pages. Now, since on the upper shelf which has 25 books, the book with the greatest number of pages has 400 pages, then median=400 pages (recall that all books from the lower shelf have more pages than all books on the upper shelf, so if we order all books in ascending number of pages, then we'll have 25 books from the upper shelf and then 24 books from the lower shelf). Sufficient.

Answer: C.



How do we know that all books on the upper shelf have fewer pages than the lower one? This info is not given and can change the answer if the lower shelf has books with less than 400 pages, right? Can you clarify me, please?
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Re: A certain bookcase has 2 shelves of books. On the upper  [#permalink]

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New post 27 Jul 2018, 00:59
The assumption is not required because of reason as below:
the median should be the 25th in sequence

(small -> big)
U (25): ........... 400 (25th)
L (24): 475....... (the smallest in Lower shelf is 475, thus rest of the others must be greater than both 475 and 400)
Therefore, 400 must be the 25th greatest/smallest among these 49 books
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Re: A certain bookcase has 2 shelves of books. On the upper  [#permalink]

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New post 05 Aug 2018, 10:41
analuisa wrote:
Bunuel 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?

Notice that we are told that all books on the upper shelf have fewer pages than all books on the lower shelf.

(1) There are 25 books on the upper shelf. No info about the lower shelf. Not sufficient.
(2) There are 24 books on the lower shelf. No info about the upper shelf. Not sufficient.

(1)+(2) There are total of 25+24=49 books, thus the median number of pages for all of the books will be the book with 25th largest number of pages. Now, since on the upper shelf which has 25 books, the book with the greatest number of pages has 400 pages, then median=400 pages (recall that all books from the lower shelf have more pages than all books on the upper shelf, so if we order all books in ascending number of pages, then we'll have 25 books from the upper shelf and then 24 books from the lower shelf). Sufficient.

Answer: C.



How do we know that all books on the upper shelf have fewer pages than the lower one? This info is not given and can change the answer if the lower shelf has books with less than 400 pages, right? Can you clarify me, please?


Agree with you. How this was understood?
I know now that sequence matters in this case, but still I wanna know what I missed.
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Re: A certain bookcase has 2 shelves of books. On the upper &nbs [#permalink] 05 Aug 2018, 10:41
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