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

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

VeritasKarishma
Thanks 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__
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Re: A certain bookcase has 2 shelves of books. On the upper [#permalink]
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Asad wrote:
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

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


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

VeritasKarishma
Thanks 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.

Quote:
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.

VeritasKarishma
Thanks...
One more question:
What if the scenario is something like the following?
Quote:
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 2 books on the upper shelf.
(2) There are 1 book on the lower shelf.

Can we choose median from statement 2?
What will be the solution of this problem?
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Re: A certain bookcase has 2 shelves of books. On the upper [#permalink]
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Asad wrote:
One more question:
What if the scenario is something like the following?
Quote:
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 2 books on the upper shelf.
(2) There are 1 book on the lower shelf.

Can we choose median from statement 2?
What will be the solution of this problem?



The answer will still be (C).

Statement 2 alone is not sufficient.
Knowing there is only 1 book on lower shelf and that has 475 pages, you do not know the median. The median will be the number of pages in some book on upper shelf or if the upper shelf has only 1 book too, then it will be the average of 400 and 475.
For example, using stmnt 2 alone, you get
370, 390, 395, 400, 475 (median 395)
390, 400, 475 (median 400)
400, 475 (median = 437.5)
etc


Using both statements, we know that it will look like this:
390(for example), 400, 475
So median will be 400.
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Re: A certain bookcase has 2 shelves of books. On the upper [#permalink]
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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.


Solution:

We are given that a bookcase has 2 shelves of books. We are also given that the book with the greatest number of pages on the upper shelf has 400 pages and that the book with the least number of pages on the lower shelf has 475 pages. This tells us that all of the books on the upper shelf have fewer pages than all of the books on the lower shelf.

We must determine the median number of pages of the books on the two shelves. Thus, if we were to order books on both shelves from the books with the least numbers pages to the books with the greatest number of pages, we must determine the number of pages in the middle book.

Statement One Alone:

There are 25 books on the upper shelf.

Using the information in statement one, we know that the 25th book on the top shelf, when the books are ordered by the least number of pages to the greatest number of pages, has 400 pages. However, without knowing the number of books on the lower shelf, we still cannot determine the median number of pages for all the books on the two shelves. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

There are 24 books on the lower shelf.

Using the information in statement two, we know that the first book on the bottom shelf, when the books are ordered by the least number of pages to the greatest number of pages, has 475 pages. However, we still cannot determine the median number of pages for all the books on the two shelves. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From statements one and two, we know that there is a total of 49 books on the two shelves. Thus, we can determine which book, when the books are ordered by least number of pages to the greatest number of pages, is the median. To determine the median book we can follow the rule:

If a set of numbers is in numerical order and has n terms and if n is odd, the median is the value at the (n+1)/2 position.

position of median = (49 + 1)/2

position of median = 25

Thus, the 25th book is the median.
From our two statements, we also know that the book with the greatest number of pages on the upper shelf has 400 pages, and the book with the least number of pages on the lower shelf has 475 pages. This means that all the books on the upper shelf have fewer pages than the books on the lower shelf. So if we ordered the books on both shelves from the least number of pages to the greatest number of pages, we see that the book on the top shelf, with the greatest number of pages, or the 25th book, would be the median. Since we know that the 25th book has 400 pages, we know the median is 400 pages.

Answer: C

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Re: A certain bookcase has 2 shelves of books. On the upper [#permalink]
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Video solution from Quant Reasoning:
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Re: A certain bookcase has 2 shelves of books. On the upper [#permalink]
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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.


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Re: A certain bookcase has 2 shelves of books. On the upper [#permalink]
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
VeritasKarishma when considering the median number of pages. I understand that the 25th book is the "median book" but I am a little confused about the "median page" as that would be determined by the distribution/spread of pages in each book. How do we know whether the question is talking about pages or books? Please help. Thanks!
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Re: A certain bookcase has 2 shelves of books. On the upper [#permalink]
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Sidharth003 wrote:
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
VeritasKarishma when considering the median number of pages. I understand that the 25th book is the "median book" but I am a little confused about the "median page" as that would be determined by the distribution/spread of pages in each book. How do we know whether the question is talking about pages or books? Please help. Thanks!



We are finding the median of "number of pages". Whenever we find the median, we first arrange all elements in increasing or decreasing order. When you arrange the books, you arrange them in increasing order of the number of pages. So you start with the lowest number of pages (the book that has say 100 pages), then put the book with 115 pages, then the book with 142 pages and so on till at the end you put the book with 1000 pages.
The median will be the number of pages in the book in the middle, say 400 pages.

Statistically, the "median book" doesn't make any sense. Median is a number.
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Re: A certain bookcase has 2 shelves of books. On the upper [#permalink]
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