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M09-13

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M09-13 [#permalink]

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New post 16 Sep 2014, 00:39
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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
[Reveal] Spoiler: OA

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New post 16 Sep 2014, 00:39
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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 \(x=6\).


Answer: B
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M09-13 [#permalink]

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New post 24 Oct 2014, 23:50
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 \(x=6\).


Answer: B


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

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M09-13 [#permalink]

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New post 25 Oct 2014, 06:41
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 \(x=6\).


Answer: B


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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M09-13 [#permalink]

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New post 10 Sep 2015, 19:35
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.

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New post 25 Jun 2017, 02:57
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.

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Re: M09-13 [#permalink]

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New post 30 Oct 2017, 17:52
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?

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Re: M09-13 [#permalink]

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New post 30 Oct 2017, 21:00
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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?


Answered here: https://gmatclub.com/forum/m09-183821.html#p1433061
_________________

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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: M09-13 [#permalink]

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New post 31 Oct 2017, 14:38
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.

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Re: M09-13   [#permalink] 31 Oct 2017, 14:38
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