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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]

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24 Sep 2014, 20:01
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Difficulty:

45% (medium)

Question Stats:

75% (02:10) correct 25% (02:09) wrong based on 92 sessions

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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

M09-13
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Re: Each shelf of a bookcase contained 12 books. If the librarian took out  [#permalink]

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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

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Re: Each shelf of a bookcase contained 12 books. If the librarian took out  [#permalink]

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25 Sep 2014, 02:11
anceer 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 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

M09-13

Say there are total of $$x$$ shelves, then: $$12*x=21+8*(x-1)+11$$, which gives $$x=6$$.

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Re: Each shelf of a bookcase contained 12 books. If the librarian took out  [#permalink]

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17 Dec 2014, 06:09
Although i am able to understand the solution but still not confident if I will be able to solve similar question. Confusion is

" so that all shelves but the last one contained 8 books " -- last shelf has 8 Books ??

But the question says " last shelf contained 11 books "

Is the language wrong , can someone post a better explanation ?
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Re: Each shelf of a bookcase contained 12 books. If the librarian took out  [#permalink]

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17 Dec 2014, 06:24
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aashu4uiit wrote:
Although i am able to understand the solution but still not confident if I will be able to solve similar question. Confusion is

" so that all shelves but the last one contained 8 books " -- last shelf has 8 Books ??

But the question says " last shelf contained 11 books "

Is the language wrong , can someone post a better explanation ?

All shelves but the last one contained 8 books and that last shelf contained 11 books means that all shelves but the last one contained 8 books, so if there are total of x shelves, then the number of shelves with 8 books is x - 1.

Hope it's clear.
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Re: Each shelf of a bookcase contained 12 books. If the librarian took out  [#permalink]

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21 Dec 2014, 20:02
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.

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.

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Each shelf of a bookcase contained 12 books. If the librarian took out  [#permalink]

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21 Dec 2014, 22:15
right equation is:

12x-21=8(x-1)+11
x=6
shelves and books in both sides are equal

wrong equation is:

12x-21=8x+11
x=8
in this case right side has one shelf more
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Re: Each shelf of a bookcase contained 12 books. If the librarian took out  [#permalink]

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16 Jul 2017, 23:00
anceer 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 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

M09-13

Let the number of shelves be $$x$$. So, total number of books = $$12x$$.

Removing $$21$$ books would leave $$(12x-21)$$ books to be rearranged.

Last $$2$$ shelves would contain $$(11+8) = 19$$ books, that would leave $$(12x-21-19) = (12x-40)$$ books to be re-arranged into $$(x-2)$$ shelves equally.

$$\frac{12x-40}{x-2} = n$$ ($$n$$ must be an integer)

A. $$5$$
$$\frac{12(5) - 40}{5-2} = \frac{20}{3}$$ - not an integer.

B. $$6$$
$$\frac{12(6) - 40}{6-2} = \frac{32}{4} = 8$$. YES.

C. $$7$$
$$\frac{12(7) - 40}{7-2} = \frac{44}{5}$$ - not an integer.

D. $$8$$
$$\frac{12(8) - 40}{8-2} = \frac{56}{6}$$ - not an integer.

E. $$9$$
$$\frac{12(9) - 40}{9-2} = \frac{68}{7}$$ - not an integer.

So, the ans is B.
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Re: Each shelf of a bookcase contained 12 books. If the librarian took out  [#permalink]

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16 Jul 2017, 23:14
12x -21 = 8(x-1)+11
X=6

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Re: Each shelf of a bookcase contained 12 books. If the librarian took out  [#permalink]

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14 Apr 2019, 05:54
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Re: Each shelf of a bookcase contained 12 books. If the librarian took out   [#permalink] 14 Apr 2019, 05:54
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