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On Monday, an animal shelter housed 55 cats and dogs, and by Friday

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On Monday, an animal shelter housed 55 cats and dogs, and by Friday  [#permalink]

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New post 07 Feb 2019, 06:34
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Question Stats:

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On Monday, an animal shelter housed 55 cats and dogs, and by Friday exactly 1/5 of the cats and 1/4 of the dogs had been adopted. If no new cats or dogs were brought to the shelter during this period, what is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and Friday?

A) 11
B) 12
C) 13
D) 14
E) 20

Please check a question I have in the spoiler:
Do we necessarily need to account for the divisibility of dogs/cats as mentioned below?
I understood the min/max element related to fractions, but just picked 50 dogs and 5 cats and rounded down 50/4 to a whole number. Using 50 dogs, 10 cats also yield 13 this way as does 45 dogs and 15 cats. Is it a fluke of the question or is it generally fine to round down to a whole number in Min/Max cases?

Official explanation:
The question asks you for the greatest number of animals that could have been adopted from the shelter within the parameters of the problem. Because a greater proportion of dogs than cats was adopted, you should seek a scenario that maximizes the number of dogs adopted. You must also satisfy the other conditions of the problem, however; the number of cats, for example, must be a multiple of 5, because that is the only way that 1/5 of the cats can be adopted. Because we want to maximize the number of dogs in the shelter, let’s start by assuming the minimum possible number of cats, 5. This would leave 50 dogs in the shelter. This solution, unfortunately, is impossible; because 50 is not evenly divisible by 4, there cannot be 50 dogs in the
shelter. Could there be 10 cats at the shelter? No, because this would leave 45 dogs, again making it impossible for exactly of the dogs to be adopted. 15 cats is the magic number, as it means there are 40 dogs. 1/5*15 + 1/4*40 = 3 + 10 = 13 animals. The correct answer is (C).
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Re: On Monday, an animal shelter housed 55 cats and dogs, and by Friday  [#permalink]

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New post 07 Feb 2019, 06:41
energetics wrote:
On Monday, an animal shelter housed 55 cats and dogs, and by Friday exactly 1/5 of the cats and 1/4 of the dogs had been adopted. If no new cats or dogs were brought to the shelter during this period, what is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and Friday?

A) 11
B) 12
C) 13
D) 14
E) 20

Please check a question I have in the spoiler:
Do we necessarily need to account for the divisibility of dogs/cats as mentioned below?
I understood the min/max element related to fractions, but just picked 50 dogs and 5 cats and rounded down 50/4 to a whole number. Using 50 dogs, 10 cats also yield 13 this way as does 45 dogs and 15 cats. Is it a fluke of the question or is it generally fine to round down to a whole number in Min/Max cases?

Official explanation:
The question asks you for the greatest number of animals that could have been adopted from the shelter within the parameters of the problem. Because a greater proportion of dogs than cats was adopted, you should seek a scenario that maximizes the number of dogs adopted. You must also satisfy the other conditions of the problem, however; the number of cats, for example, must be a multiple of 5, because that is the only way that 1/5 of the cats can be adopted. Because we want to maximize the number of dogs in the shelter, let’s start by assuming the minimum possible number of cats, 5. This would leave 50 dogs in the shelter. This solution, unfortunately, is impossible; because 50 is not evenly divisible by 4, there cannot be 50 dogs in the
shelter. Could there be 10 cats at the shelter? No, because this would leave 45 dogs, again making it impossible for exactly of the dogs to be adopted. 15 cats is the magic number, as it means there are 40 dogs. 1/5*15 + 1/4*40 = 3 + 10 = 13 animals. The correct answer is (C).


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Re: On Monday, an animal shelter housed 55 cats and dogs, and by Friday   [#permalink] 07 Feb 2019, 06:41
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On Monday, an animal shelter housed 55 cats and dogs, and by Friday

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