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There 3 kinds of books in the library fiction, non-fiction and biology

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imhimanshu
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There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   Updated on: 05 Jun 2017, 06:48
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There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000. Which one of following can be the total of the book?

A. 1001
B. 1009
C. 1008
D. 1007
E. 1006


Quote:
44. There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000?which one of following can be the total of the book?

A 1001 B. 1009 C.1008 D.1007 E.1006

Soln: fiction : non-fiction = 3 : 2 = 6 : 4
non-fiction : biology = 4 : 3

fiction : non-fiction : biology = 6 : 4 : 3

6x + 4x + 3x = 1000
x = 76 12/13
if we add 1, 13 will divide evenly (1001/13 = 77)
1000 + 1 = 1001


Hi Bunuel,

One more doubt,please help me out.

I was going through the question posted above-

This is how I approached this question -

Fiction:Non Fiction = 3:2 ---(A)
Non Fiction : Biology = 4:3 ---(B)
In order to make the ratios equal, I multiplied equation (A) with 4 and equation(b) with 2. But that's giving me the wrong answer. When I checked the solution, only equation (A) was multiplied by 2 in order to make the ratios equal.
Is it a rule that in order to make the ratios equal, one should multiply by the Lowest number that makes the ratio equal. Please help.
Thanks
H
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A

Originally posted by imhimanshu on 29 Mar 2012, 06:41.
Last edited by Bunuel on 05 Jun 2017, 06:48, edited 2 times in total.
Edited the question and added the OA
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   05 Jun 2017, 03:45
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   29 Mar 2012, 07:00
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There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000. Which one of following can be the total of the book?

A. 1001
B. 1009
C. 1008
D. 1007
E. 1006


Given: F:N=3:2 and N:B=4:3.

Equate N'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: F:N=3:2=6:4 and N:B=4:3 --> F:N:B=6:4:3. Now, 6+4+3=13, which means that we have total of 13 parts, thus the total number of books must be divisible by 13, only answer divisible by 13 is 1001.

Answer: A.

As for your question: you can equate N's in any other way (LCM is just easiest one). For example: F:N=3:2=30:20 and N:B=4:3=20:15 --> F:N:B=30:20:15=6:4:3, the same reduced ratio. Or the way you were doing: F:N=3:2=12:8 and N:B=4:3=8:6 --> F:N:B=12:8:6=6:4:3, the same reduced ratio.

Hope it's clear.
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   30 Mar 2012, 06:59
Thanks Bunuel. Your replies always clear the doubt.. :-)
Regards,
H
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   10 May 2014, 16:49
Easy.

F:NF:B
3:2
4: 3

Then ratio becomes 6x:4x:3x= 13x
Answer must be a multiple of 1000

1000/13=76.something

76*13=988+13 = 1001.

Answer: A

Hope it helps
Cheers
J :)
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   05 Jun 2017, 06:48
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Bunuel , there seems to be a page missing, along with the question.


Fixed it. Thank you.
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   05 Jun 2017, 09:17
imhimanshu wrote:
There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000. Which one of following can be the total of the book?

A. 1001
B. 1009
C. 1008
D. 1007
E. 1006
Attachment:
Capture.PNG
Capture.PNG [ 2.51 KiB | Viewed 15853 times ]


Since the total number of books will be a multiple of 13 the only possible answer will be (A) 1001..

Correct answer will hence be (A)
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   06 Jun 2017, 16:40
Expert Reply
imhimanshu wrote:
There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000. Which one of following can be the total of the book?

A. 1001
B. 1009
C. 1008
D. 1007
E. 1006


We are given:

Ratio of fiction to nonfiction = 3 : 2

Ratio of nonfiction to biology = 4 : 3

We can multiply the first ratio by 2 and we have:

fiction to nonfiction = 6 : 4

Thus, we now have a three-part ratio (which we can express using an x multiplier):

fiction to nonfiction to biology = 6x : 4x : 3x

We see that the total books must be a multiple of 6x + 4x + 3x = 13x, or a multiple of 13.

Of the answer choices, only 1001 is a multiple of 13.

Answer: A
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   12 Jul 2017, 05:22
imhimanshu wrote:
There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000. Which one of following can be the total of the book?

A. 1001
B. 1009
C. 1008
D. 1007
E. 1006


Quote:
44. There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000?which one of following can be the total of the book?

A 1001 B. 1009 C.1008 D.1007 E.1006

Soln: fiction : non-fiction = 3 : 2 = 6 : 4
non-fiction : biology = 4 : 3

fiction : non-fiction : biology = 6 : 4 : 3

6x + 4x + 3x = 1000
x = 76 12/13
if we add 1, 13 will divide evenly (1001/13 = 77)
1000 + 1 = 1001


Hi Bunuel,

One more doubt,please help me out.

I was going through the question posted above-

This is how I approached this question -

Fiction:Non Fiction = 3:2 ---(A)
Non Fiction : Biology = 4:3 ---(B)
In order to make the ratios equal, I multiplied equation (A) with 4 and equation(b) with 2. But that's giving me the wrong answer. When I checked the solution, only equation (A) was multiplied by 2 in order to make the ratios equal.
Is it a rule that in order to make the ratios equal, one should multiply by the Lowest number that makes the ratio equal. Please help.
Thanks
H

LF : NF = 3 : 2 = 6 : 4
NF : B = 4 : 3

LF : NF : B = 6 : 4: 3
13x > 1000
x> 1000/13
Since x is integer. so we will have to find the value which must be divisible by 13

1001 is divisible by 13.

Answer A
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   16 Jul 2017, 17:21
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Quote:
There 3 kinds of books in the library fiction, non-fiction and biology. Ratio of fiction to non-fiction is 3 to 2; ratio of non-fiction to biology is 4 to 3, and the total of the books is more than 1000. Which one of following can be the total of the book?

A. 1001
B. 1009
C. 1008
D. 1007
E. 1006


We are given that the ratios of:

fiction : non-fiction = 3 : 2

Multiplying the ratio by 2, we have:

fiction : non-fiction = 6 : 4

Non-fiction : biology = 4 : 3

Thus, our ratio is:

fiction : non-fiction : biology

6x : 4x : 3x

So, our total is 6x + 4x + 3x = 13x.

We need to find an answer choice that is a multiple of 13. Let’s test answer choice A:

1,001/13 = 77

So, 1,001 can be the total number of books.

Answer: A
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink] New post   29 Nov 2022, 05:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: There 3 kinds of books in the library fiction, non-fiction and biology [#permalink]
29 Nov 2022, 05:55
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