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E
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Difficulty:
45%
(medium)
Question Stats:
71% (02:06) correct
29%
(02:30)
wrong
based on 914
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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
A. 1:3
B. 1:4
C. 1:5
D. 2:5
E. 4:5
31 Jul 2014, 02:11
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Reni
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.
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.
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.
