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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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New post Updated on: 31 Jul 2014, 02:03
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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

Originally posted by araspai on 16 Aug 2003, 05:56.
Last edited by Bunuel on 31 Jul 2014, 02:03, 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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New post 31 Jul 2014, 02:11
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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

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

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New post 16 Aug 2003, 06:06
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
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Re: A pet store holds cats and dogs. If the difference between  [#permalink]

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New post 18 Aug 2003, 02:17
1
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.

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

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New post 30 Jul 2014, 20:53
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!
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Re: A pet store holds cats and dogs. If the difference between  [#permalink]

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New post 08 Aug 2014, 22:19
1
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.
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Re: A pet store holds cats and dogs. If the difference between  [#permalink]

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New post 09 Aug 2014, 01:35
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

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Siva 8-)
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Re: A pet store holds cats and dogs. If the difference between  [#permalink]

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New post 28 Oct 2015, 12:59
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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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New post 28 Oct 2015, 22:41
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).

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

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New post 28 Oct 2015, 23:53
1
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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Re: A pet store holds cats and dogs. If the difference between  [#permalink]

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New post 18 Dec 2017, 07:44
If you realise, the question is indirectly talking about multiples of 13. Then you will be able to see only option E adjusts for the difference.

Cats : Dogs
13*4 : 13*5

52 : 65

65 - 52 = 13


If its any other option, difference will become much greater than 13. Hence E is the answer
Re: A pet store holds cats and dogs. If the difference between &nbs [#permalink] 18 Dec 2017, 07:44
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