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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] New post 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] New post 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
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Re: A pet store holds cats and dogs. If the difference between [#permalink] New post 18 Aug 2003, 01:17
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] New post 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!
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Re: A pet store holds cats and dogs. If the difference between [#permalink] New post 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

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] New post 08 Aug 2014, 21:19
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] New post 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 8-)
Re: A pet store holds cats and dogs. If the difference between   [#permalink] 09 Aug 2014, 00:35
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