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M09-13

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Math Expert
Joined: 02 Sep 2009
Posts: 52132

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15 Sep 2014, 23:39
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:17) correct 31% (01:21) wrong based on 108 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

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Math Expert
Joined: 02 Sep 2009
Posts: 52132

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15 Sep 2014, 23:39
Official Solution:

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

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

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Joined: 21 May 2013
Posts: 8

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24 Oct 2014, 22:50
Bunuel wrote:
Official Solution:

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

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

Hi Bunuel,

Thanks for the explanation. However, why do you subtract "1" from 8*(x-1)? Can you please verify?

Thank you so much.
Aram
Math Expert
Joined: 02 Sep 2009
Posts: 52132

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25 Oct 2014, 05:41
safaria25 wrote:
Bunuel wrote:
Official Solution:

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

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

Hi Bunuel,

Thanks for the explanation. However, why do you subtract "1" from 8*(x-1)? Can you please verify?

Thank you so much.
Aram

We are told that all shelves but the last one contained 8 books, so the number of shelves with 8 books is x - 1.
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Joined: 10 Aug 2014
Posts: 49
GMAT 1: 680 Q49 V34

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10 Sep 2015, 18:35
What if we plug in values?
For example we have 6 shelves, thus 6*12=72 books - remove 21 books=51-11 books=40/8=5 shelves left+1 with 11 books=6 justify
and 8 shelves, 8*12=96-21=75-11=64/8=8 shelves with 8 books + 1 shelf with 11 books=9 thus 8 doesn't equal 9. So we have only 6 is the correct choice.
Intern
Joined: 10 May 2017
Posts: 27

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25 Jun 2017, 01:57
1
I used this method.

Total books current = 12 x n (where n is no of shelves)

21 books removed and re-arranged,

12n-21 = 8n + 3 (Since the last shelf has additional 3 books)

n=6.
Intern
Joined: 25 Aug 2017
Posts: 32

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30 Oct 2017, 16:52
Could someone please help explain to me why the following equation would not work for this problem? I got 8, which is the wrong answer, but am trying to figure out where my thought process crapped out on me. Thanks for your help.

12 books per shelf minus 21 books = 8 books per shelf + 11 on the last shelf
12x - 21 = 8x + 11
x = 8

Are the 21 books removed from equation all together?
Math Expert
Joined: 02 Sep 2009
Posts: 52132

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30 Oct 2017, 20:00
1
Raffio wrote:
Could someone please help explain to me why the following equation would not work for this problem? I got 8, which is the wrong answer, but am trying to figure out where my thought process crapped out on me. Thanks for your help.

12 books per shelf minus 21 books = 8 books per shelf + 11 on the last shelf
12x - 21 = 8x + 11
x = 8

Are the 21 books removed from equation all together?

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Joined: 26 Mar 2013
Posts: 1996

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31 Oct 2017, 13:38
1
Raffio wrote:
Could someone please help explain to me why the following equation would not work for this problem? I got 8, which is the wrong answer, but am trying to figure out where my thought process crapped out on me. Thanks for your help.

12 books per shelf minus 21 books = 8 books per shelf + 11 on the last shelf
12x - 21 = 8x + 11
x = 8

Are the 21 books removed from equation all together?

The problem in highlighted part. You missed that All but one. So it should be 8(x -1). What you did is that you multiplied by 8x and add another self with 11.
Intern
Joined: 28 Oct 2017
Posts: 1
Location: India
GMAT 1: 670 Q44 V39
GPA: 2

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22 Apr 2018, 16:15
mika84 wrote:
What if we plug in values?
For example we have 6 shelves, thus 6*12=72 books - remove 21 books=51-11 books=40/8=5 shelves left+1 with 11 books=6 justify
and 8 shelves, 8*12=96-21=75-11=64/8=8 shelves with 8 books + 1 shelf with 11 books=9 thus 8 doesn't equal 9. So we have only 6 is the correct choice.

why isnt it +11 instead of +3?
Re: M09-13 &nbs [#permalink] 22 Apr 2018, 16:15
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