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There 3 kinds of books in the library physics, chemistry and

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There 3 kinds of books in the library physics, chemistry and [#permalink] New post 14 Nov 2009, 00:04
00:00
A
B
C
D
E

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  25% (low)

Question Stats:

71% (02:54) correct 28% (01:33) wrong based on 52 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Jun 2013, 02:28, edited 2 times in total.
Edited the question and added the OA
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Re: Total number of books [#permalink] New post 14 Nov 2009, 00:23
Expert's post
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.

Answer: A
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Re: Total number of books [#permalink] New post 14 Nov 2009, 00:44
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.
Re: Total number of books   [#permalink] 14 Nov 2009, 00:44
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