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There 3 kinds of books in the library physics, chemistry and [#permalink]

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14 Nov 2009, 01:04

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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?

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.

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.

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

Re: There 3 kinds of books in the library physics, chemistry and [#permalink]

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24 Oct 2016, 06:39

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.