# To find the number of cats.

A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were?
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anirban_goswami

• Member Since Feb-2008 | Mar 11th, 2008

No. of cats = x(say)
Therefore, no. of mice killed by each cat = 999919/x (since, they killed equal no. of mice)
Now, given that

(999919/x) is greater than x, i.e

999919/x > x, implies x*x<999919

Therefore,  x <  999.95(approx). Now, the only no. which is nearest to but less than 999.95 and is a factor of 999919 is 991.

Thus,  x = 991 and no. of mice = 999919/991 = 1009.

#### anirban_goswami Profile Answers by anirban_goswami

• Mar 11th, 2008

No. of cats = x(say)
Therefore, no. of mice killed by each cat = 999919/x (since, they killed equal no. of mice)
Now, given that

(999919/x) is greater than x, i.e

999919/x > x, implies x*x<999919

Therefore,  x <  999.95(approx). Now, the only no. which is nearest to but less than 999.95 and is a factor of 999919 is 991.

Thus,  x = 991 and no. of mice = 999919/991 = 1009.

#### amith.aec Profile Answers by amith.aec

• Oct 29th, 2010

Observing the num 999919 which is the total num of rats being eaten..we can write it as

(1000000-81) =   (1000^2-9^2)   =   (1000+9)(1000-9)   =  (1009)(991)

so total num of rats killed =(1009)(991)

and given that each cat kills more num of rats than the total num of cats
hence each cat kills 1009 num of rats
and there are 991 num of cats