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cats and dogs

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cats and dogs

by maria » Wed May 21, 2008 11:17 am
on Monday, a certain animal shelter housed 55 cats and dogs. by Friday, exactly 1/5 of the cats and 1/4 of the dogs had been adopted; no new cats and 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

Thanks.
Maria
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by VP_RedSoxFan » Wed May 21, 2008 12:03 pm
To solve the maximum number of animals adopted, we want to maximize the number of dogs in the adoption center since a higher percentage of them were adopted. Therefore, we want the highest integer 55 or less that is perfectly divided by 4 where the number of cats are divisible by 5.

Maximizing the number of dogs is the same as minimizing the number of cats. That is to say that 1 cat adoption means there were 5 cats there and therefore 50 dogs. That doesn't work though because 50 isn't divisible by 4. Then we'll step up the number of cat adoptions until it leaves a number of dogs divisible by 4

0 cat adoptions (0 cats) = 55 dogs
1 cat adoption (5 cats) = 50 dogs
2 cat adoptions (10 cats) = 45 dogs
3 cat adoptions (15 cats) = 40 dogs *** this works.

To answer the question then, the answer is 13 [C], 3 cats and 10 dogs.
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by netigen » Wed May 21, 2008 1:39 pm
5 x dogs+ 4 x cats = 55

cat's number will end in digit zero so the only possibility are 0, 20 and 40

if 0 then adopted=11
if 20 then adopted=12
if 40 then adopted=13
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