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