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## Question

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In one room there are certain cats and rats.

Count of rats is 999919.

Cats started eating the rats.

Each cat had the same number of rats as the other cats.

Also the count of cats is more than the number of rats they had

Now the question is how many cats are there in the room and how many rats each cat had?

PS: Mind you there is more than 1 cat and each cat had more than 1 rat.

## 7 answers to this question

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Guest
In one room there are certain cats and rats.

Count of rats is 999919.

Cats started eating the rats.

Each cat had the same number of rats as the other cats.

Also the count of cats is more than the number of rats they had

Now the question is how many cats are there in the room and how many rats each cat had?

PS: Mind you there is more than 1 cat and each cat had more than 1 rat.

the factors of 999919 are {1, 991, 1009, 999919}.

As each cat has more than 1 rat and the number of cats is more than the number of rats:

991 rats and 1009 cats.

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the factors of 999919 are {1, 991, 1009, 999919}.

As each cat has more than 1 rat and the number of cats is more than the number of rats:

991 rats and 1009 cats.

bingo brahn

I would like to know your approach on this. how you factored this number

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bingo brahn

I would like to know your approach on this. how you factored this number

Some time ago I had a post with a title Lyran III inhabitants ... and with those prime numbers on hand, it is not difficult to do the factorization stuff in excel.

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Some time ago I had a post with a title Lyran III inhabitants ... and with those prime numbers on hand, it is not difficult to do the factorization stuff in excel.

See this solution instead of finding the factors

Let there be x cats

Let there be y rats each cat had

so by question we have x*y=999919

Instead of finding factors for 999919 which are primes,

x*y=(1000000 - 81)

you must have read the formula a^2-b^2=(a+b)(a-b)

x*y=(1000^2)-(9^2)

x*y=(1000+9)(1000-9)

x*y=1009*991

Hope this is clear.

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Guest
See this solution instead of finding the factors

Let there be x cats

Let there be y rats each cat had

so by question we have x*y=999919

Instead of finding factors for 999919 which are primes,

x*y=(1000000 - 81)

you must have read the formula a^2-b^2=(a+b)(a-b)

x*y=(1000^2)-(9^2)

x*y=(1000+9)(1000-9)

x*y=1009*991

Hope this is clear.

Waw, that is a very elegant way. Good one, and thanx for sharing.

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Guest

1009 cats and with 991 rats each cat has.

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Guest
See this solution instead of finding the factors

Let there be x cats

Let there be y rats each cat had

so by question we have x*y=999919

Instead of finding factors for 999919 which are primes,

x*y=(1000000 - 81)

you must have read the formula a^2-b^2=(a+b)(a-b)

x*y=(1000^2)-(9^2)

x*y=(1000+9)(1000-9)

x*y=1009*991

Hope this is clear.

Wow! What a simple and smart way. Thanks for sharing.

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