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Intern
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Books [#permalink] New post 04 Aug 2010, 19:31
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Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but one contained 8 books and the last shelf contained 11 books, how many shelves does the bookcase have?

(C) 2008 GMAT Club - m09#13

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Gmatclub manager,
Should the question be "the librarian took out 21 books and rearranged the remaining books so that each shelf contained 8 books and the last shelf contained 11 books"?

Thanks !
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Re: Books [#permalink] New post 04 Aug 2010, 19:48
dungtd wrote:
Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but one contained 8 books and the last shelf contained 11 books, how many shelves does the bookcase have?

(C) 2008 GMAT Club - m09#13

* 5
* 6
* 7
* 8
* 9

Gmatclub manager,
Should the question be "the librarian took out 21 books and rearranged the remaining books so that each shelf contained 8 books and the last shelf contained 11 books"?

Thanks !
.

The wording in the question is correct . If the "but one" is omitted like you mentioned, the details contradict with each other. If each shelf contains 8 books,last shelf also must contain 8 books and can't contain 11 books.
The "but one" indicates that each shelf except the last shelf has 8 books and the last shelf has 11 books.
Here is how we can solve the problem.

Let x be the number of shelves.
No of books in the beginning =12*x
After taking out 21 books No of remaining books = 12x -21
when the remaining books are rearranged, each shelf except the last shelf has 8 books and the last shelf has 11 books. So No of remaining books is also equal to 8*(x-1)+11

12x-21=8(x-1)+11
4x=24
x=6. Answer B
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Intern
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Re: Books [#permalink] New post 04 Aug 2010, 20:41
crack700 wrote:
dungtd wrote:
Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but one contained 8 books and the last shelf contained 11 books, how many shelves does the bookcase have?

(C) 2008 GMAT Club - m09#13

* 5
* 6
* 7
* 8
* 9

Gmatclub manager,
Should the question be "the librarian took out 21 books and rearranged the remaining books so that each shelf contained 8 books and the last shelf contained 11 books"?

Thanks !
.

The wording in the question is correct . If the "but one" is omitted like you mentioned, the details contradict with each other. If each shelf contains 8 books,last shelf also must contain 8 books and can't contain 11 books.
The "but one" indicates that each shelf except the last shelf has 8 books and the last shelf has 11 books.
Here is how we can solve the problem.

Let x be the number of shelves.
No of books in the beginning =12*x
After taking out 21 books No of remaining books = 12x -21
when the remaining books are rearranged, each shelf except the last shelf has 8 books and the last shelf has 11 books. So No of remaining books is also equal to 8*(x-1)+11

12x-21=8(x-1)+11
4x=24
x=6. Answer B


Thanks for your explanation!
Manager
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Joined: 27 Jun 2008
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Location: United States (AL)
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Re: Books [#permalink] New post 04 Aug 2010, 22:09
B for me as well,, nice explanation crack700
Re: Books   [#permalink] 04 Aug 2010, 22:09
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