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# A pet store holds cats and dogs. If the difference between

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A pet store holds cats and dogs. If the difference between [#permalink]

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16 Aug 2003, 04:56
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A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 13. What could be the ratio of Cats to dogs in the pet store?

A. 1:3
B. 1:4
C. 1:5
D. 2:5
E. 4:5
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Jul 2014, 01:03, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: A pet store holds cats and dogs. If the difference between [#permalink]

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31 Jul 2014, 01:11
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Reni wrote:
araspai wrote:
1. A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 13. What could be the ratio of Cats to dogs in the pet store?
a. 1:3 b. 1:4 c. 1:5 d. 2:5 e. 4:5

I got this same exercise but with diff options:
a)4:1
b)3:1
c)4:3
d)5:2
e)5:3

Thank you!

A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 13. What could be the ratio of Cats to dogs in the pet store?

A. 1:3
B. 1:4
C. 1:5
D. 2:5
E. 4:5

Say the ratio of cats to dogs is a/b. Then the number of cats would be ax and the number of dogs bx, for some positive integer x.

We are told that ax - bx = 13 --> x(a - b) = 13. Since 13 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*13.

The above implies that either x = 1 and a - b = 13 or x = 13 and a - b = 1.

Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13.

For the original question only option which fits is E, 4:5. Cats = 13*4 = 52 and dogs = 13*5 = 65.

For your question the answer would be C, 4:3, for the same reason.
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Re: A pet store holds cats and dogs. If the difference between [#permalink]

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28 Oct 2015, 11:59
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The logic I used to answer this question is this: I thought about the difference between both C - D = 13
Which means that (if you didn't look at the answer choices) you could technically pick any ratio where the differences were 13. For instance: 7:20 , 6:19 , 1:14 , etc etc, All of these ratios are correct, but the problem here is that we do not have any answer choices that will match this, which is why it is safe to multiply each answer choice by 13 to see which ones will give you a difference of 13 when you subtract them by one another.

D) 4:5 ---> (13)* 4:5 *(13) ===> 52:65 , which when you subtract these it gives you 65-52 = 13.

This is a much easier way to tackle this problem just by looking at the problem statement and realizing that your answer is not amongst one of them.
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Re: A pet store holds cats and dogs. If the difference between [#permalink]

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28 Oct 2015, 22:53
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Expert's post
araspai wrote:
A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 13. What could be the ratio of Cats to dogs in the pet store?

A. 1:3
B. 1:4
C. 1:5
D. 2:5
E. 4:5

This question tests your understanding of the ratio scale vs actual values. If you recognise it, it takes you a few secs to get to your answer.
This concept has been discussed in detail here:
http://www.veritasprep.com/blog/2011/03 ... of-ratios/

We all are aware that to convert ratio scale values to actual values, we multiply the ratio by the multiplier. We have also often used the sum of values concept for the "total" of actual values.
This question tests the same concept with the difference between values.
If the actual difference between values is 13, what could be the difference in values on the ratio scale? To get 13, the multiplier could have been 1 or 13. In case it was 1, then the difference between the values on ratio scale would be 13. If instead, the multiplier is 13, the difference between the values on the ratio scale would be 1.
Only option (E) satisfies this condition (difference between values on ratio scale is 1)
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 14 Aug 2003 Posts: 88 Location: barcelona Followers: 1 Kudos [?]: 0 [0], given: 0 Re: A pet store holds cats and dogs. If the difference between [#permalink] ### Show Tags 16 Aug 2003, 05:06 e? we have c cats and d dogs... d=c+13... so our ratio is c/d=c/(c+13)... if we plug every answer (not very elegant, i admit it), we see that the only way to get an integer for c is 4/5 Manager Joined: 27 Jul 2003 Posts: 122 Location: Singapore Followers: 1 Kudos [?]: 50 [0], given: 0 Re: A pet store holds cats and dogs. If the difference between [#permalink] ### Show Tags 18 Aug 2003, 01:17 1 This post was BOOKMARKED yes E. 4:5 is the correct answer. the difference between the number of cats and dogs must be divisible by difference between the numbers that represent both animals in ratio. Since 13 is a prime number , it is only divisible by 1 and 13 .Therefore, the correct choice is the one where the difference between the numbers is 1. Regards, Ara Intern Joined: 24 May 2014 Posts: 13 Location: Brazil Followers: 0 Kudos [?]: 73 [0], given: 6 Re: A pet store holds cats and dogs. If the difference between [#permalink] ### Show Tags 30 Jul 2014, 19:53 araspai wrote: 1. A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 13. What could be the ratio of Cats to dogs in the pet store? a. 1:3 b. 1:4 c. 1:5 d. 2:5 e. 4:5 I got this same exercise but with diff options: a)4:1 b)3:1 c)4:3 d)5:2 e)5:3 The answer is C. Bunnuel, could you please help and explain it to us? Thank you! Intern Joined: 21 Jul 2014 Posts: 23 Followers: 0 Kudos [?]: 2 [0], given: 13 Re: A pet store holds cats and dogs. If the difference between [#permalink] ### Show Tags 08 Aug 2014, 21:19 1 This post was BOOKMARKED Bunuel wrote: Reni wrote: araspai wrote: 1. A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 13. What could be the ratio of Cats to dogs in the pet store? a. 1:3 b. 1:4 c. 1:5 d. 2:5 e. 4:5 I got this same exercise but with diff options: a)4:1 b)3:1 c)4:3 d)5:2 e)5:3 The answer is C. Bunnuel, could you please help and explain it to us? Thank you! A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 13. What could be the ratio of Cats to dogs in the pet store? A. 1:3 B. 1:4 C. 1:5 D. 2:5 E. 4:5 Say the ratio of cats to dogs is a/b. Then the number of cats would be ax and the number of dogs bx, for some positive integer x. We are told that ax - bx = 13 --> x(a - b) = 13. Since 13 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*13. The above implies that either x = 1 and a - b = 13 or x = 13 and a - b = 1. Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13. For the original question only option which fits is E, 4:5. Cats = 13*4 = 52 and dogs = 13*5 = 65. Answer: E. For your question the answer would be C, 4:3, for the same reason. I understood till this point : The above implies that either x = 1 and a - b = 13 or x = 13 and a - b = 1. But how can you deduce this from above : Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13. Please explain. Intern Status: Pursuit of happyness Joined: 07 Nov 2012 Posts: 31 Location: India Concentration: General Management, Leadership GMAT Date: 04-24-2013 WE: General Management (Energy and Utilities) Followers: 0 Kudos [?]: 6 [0], given: 506 Re: A pet store holds cats and dogs. If the difference between [#permalink] ### Show Tags 09 Aug 2014, 00:35 The answer options does not have 1 and has 13 and hence the difference is 13. The question says "could" be and hence 13 is the answer Regards Siva GMAT Club Legend Joined: 09 Sep 2013 Posts: 13493 Followers: 576 Kudos [?]: 163 [0], given: 0 Re: A pet store holds cats and dogs. If the difference between [#permalink] ### Show Tags 15 Aug 2015, 02:20 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. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8314 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 381 Kudos [?]: 2467 [0], given: 163 Re: A pet store holds cats and dogs. If the difference between [#permalink] ### Show Tags 28 Oct 2015, 21:41 Hi EricImasogie, That's a clever way to interpret this question and it showcases how paying attention to the answer choices (and using them to your advantage) can lead to quicker solutions to a given question (than just doing long-winded calculations). GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: A pet store holds cats and dogs. If the difference between   [#permalink] 28 Oct 2015, 21:41
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