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Manager  Joined: 30 Aug 2009
Posts: 220
Location: India
Concentration: General Management
There 3 kinds of books in the library physics, chemistry and  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 69% (02:11) correct 31% (02:39) wrong based on 325 sessions

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There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total of the book?

A. 3003
B. 3027
C. 3024
D. 3021
E. 3018

Originally posted by kp1811 on 14 Nov 2009, 01:04.
Last edited by Bunuel on 24 Jun 2013, 03:28, edited 2 times in total.
Edited the question and added the OA
Math Expert V
Joined: 02 Sep 2009
Posts: 58395
Re: Total number of books  [#permalink]

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kp1811 wrote:
There 3 kinds of books in the library physics,chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000?which one of following can be the total of the book?

A. 3003
B. 3027
C. 3024
D. 3021
E. 3018

Given: P:C=3:2 and C:B=4:3. Equate C's by finding the LCM of 2 and 4 so that to be able to write down one ratio for all three kinds of books: P:C=6:4 and C:B=4:3 --> P:C:B=6:4:3. Now, 6+4+3=13, which means that we have total of 13 parts, thus the total number must be divisible by 13, only answer divisible by 13 is 3003.

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Name: Ronak Amin
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Re: Total number of books  [#permalink]

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True.

P:C = 3:2, C:B = 4:3 ( multiply P:C by 4 and C:B by 2 so that we have same C )
P:C = 12:8, C:B = 8:6
P:C:B = 12:8:6 = 6:4:3
6x+4x+3x= total =13x, so the total number of books should be divisible by 13, only 3003 is a possibility.
Manager  Joined: 21 Oct 2013
Posts: 178
Location: Germany
GMAT 1: 660 Q45 V36 GPA: 3.51
There 3 kinds of books in the library physics, chemistry and  [#permalink]

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First, you have to find the common ratio for all 3 books. You have:
P:C:B
3:2 --> multiply by 2 (gives you row 3)
4:6
6:4:3

Hence:
P:C:B:T(Total)
6:4:3:13 ----> This means, the Total Number must be a multiple of 13.

Answer A is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).
Intern  Joined: 21 Mar 2014
Posts: 22
Re: There 3 kinds of books in the library physics, chemistry and  [#permalink]

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Bunuel if p/c=3/2 .... i.e 2p=3c
and c/b=4/3 .... i.e 3c=4b.
why cant we say that, 2p=3c=4b?
what am i missing here?
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Re: There 3 kinds of books in the library physics, chemistry and  [#permalink]

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Yes we can say that - 2p= 3c=4b . In order to calculate the total no of books, we need to find the add all of the same parameters (by taking one book as "x") In this case (considering this relation) - all the variables add upto "13 parts" .

Find the "lowest common positive multiple" of 2,3,4. Answer will be 12. And then represent every variable accordingly. This calculation will lead to

6+4+3= 13 parts.
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Re: There 3 kinds of books in the library physics, chemistry and  [#permalink]

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kp1811 wrote:
There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total of the book?

A. 3003
B. 3027
C. 3024
D. 3021
E. 3018

P:C = 3:2
C:B = 4:3
P:C:B = 6:4:3

so we have 6+4+3 parts, or total 13 parts.
the answer must be a multiple of 13.
1300 is a multiple of 13
2600 is a multiple of 13
390 is a multiple of 13
add 2600 and 390
2990 is a multiple of 13.
2990+13 = 3003. multiple of 13. A works.
3003+13 = 3016. 3016+13 = 3029
as we can see, there are no other options but A.
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Re: There 3 kinds of books in the library physics, chemistry and  [#permalink]

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_________________ Re: There 3 kinds of books in the library physics, chemistry and   [#permalink] 12 Jan 2018, 23:24
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