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Each shelf of a bookcase contained 12 books. If the librarian took out

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Each shelf of a bookcase contained 12 books. If the librarian took out [#permalink] New post   24 Sep 2014, 20:01
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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 the last one contained 8 books and that last shelf contained 11 books, how many shelves does the bookcase have?

A. 5
B. 6
C. 7
D. 8
E. 9

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B
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Re: Each shelf of a bookcase contained 12 books. If the librarian took out [#permalink] New post   24 Sep 2014, 22:07
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Let the total shelf's = x

Books in each shelf = 12

Total Books = 12x .............. (1)

Books removed = 21 ............. (2)

Rearrangement = 8(x-1) + 11 (1) ............... (3)

Setting up the equation (1) = (2) + (3)

12x = 21 + 8x - 8 + 11

4x = 24

x = 6

Answer = B
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Re: Each shelf of a bookcase contained 12 books. If the librarian took out [#permalink] New post   21 Dec 2014, 20:02
Expert Reply
Hi All,

This question can be solved by TESTing THE ANSWERS.

We know from the prompt that we have a certain number of bookshelves and each shelf contains 12 books. We're then told that a librarian takes away 21 books and we're left with a bunch of shelves with 8 books each and one shelf with 11 books. We're asked for the number of bookshelves.

Here's how you can TEST THE ANSWERS....We just need to find an answer that "fits" with all of the given information...

If there were 5 shelves....
5(12) = 60 total books
Take 21 away = 60 - 21 = 39
Take 11 away = 39 - 11 = 28
Is 28 the sum of a "bunch" of 8s? 8+8+8 = 24, but not 28.
Eliminate Answer A.

If there were 6 shelves...
6(12) = 72 total books
Take 21 away = 72 - 21 = 51
Take 11 away = 51 - 11 = 40
Is 40 the sum of a "bunch" of 8s? 8+8+8+8+8 = 40. YES IT IS.
This MUST be the answer.

Final Answer:
Show Spoiler
B


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Re: Each shelf of a bookcase contained 12 books. If the librarian took out [#permalink] New post   16 Oct 2023, 10:47
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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 the last one contained 8 books and that last shelf contained 11 books, how many shelves does the bookcase have?

A. 5
B. 6
C. 7
D. 8
E. 9


Assuming there are \(x\) shelves in total, the initial count of books is \(12x\). After removing 21 books, this count becomes \(12x - 21\).

We are told that, after the rearrangement of that number of books, all shelves, except the last one, have 8 books each, and the last shelf contains 11 books. This implies that there are \((x - 1)\) shelves, each holding 8 books, while the final shelf accommodating 11 books. Therefore, the total number of books is \(8(x - 1) + 11\).

Equating these two expressions, we arrive at the equation \(12x - 21 = 8(x - 1) + 11\). Solving for \(x\) yields \(x = 6\).

Hence, there are a total of 6 shelves in the bookcase.


Answer: B
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Re: Each shelf of a bookcase contained 12 books. If the librarian took out [#permalink]
16 Oct 2023, 10:47
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