Number puzzle 2

Top row 2 x 3 = 6, 6 x 3 = 18
 
Second row 4 x 5 = 20,  20 x 5 = 100
 
Bottom row 3 x 7 = 21, 21 x 7 = 147
 
Answer = 3

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

Let X = number of cats
 
X =  999919 / X
 
X₂ = 999919
 
X = Square root of 999919
 
X = 991

Bummers I read you answer wrong

Answer: A) 1009

Explanation:
Given total number of rats = 999919



999919 = 1000000 - 81 = (10002 − 92) = (1000+9)(1000-9) = 1009 x 991.
Since there were more rats than there were cats, 991 cats killed 1009 rats each.

It seems I misread the question, you wanted the number of rats, i gave you the number of cats.

Let X = number of cats
 
X =  999919 / X
 
X₂ = 999919
 
X = Square root of 999919
 
X = 991 cats
 
No of rats = 999919 / 991
 
No of rats = 1009

At what time between 2 and 3 O'clock, do the hands of a clock coincide ?

In the previous question 991 is not the square root of 999919 but is a prime number so the only solution as one cat did not kill the lot.

Myg, are you suggesting my equations for the number of cats is wrong?
 
Let X = number of cats
 
X =  999919 / X
 
X₂ = 999919
 
X = Square root of 999919
 
X = 991
 
I won’t argue with you as you are a much better mathematician than me.
 
The square root of 999919 is not a whole number, but 991 is the nearest whole number.

Not arguing Ray
rxc=999919
but Lolly's explanation of the difference between two squares is required
a squared +b squared =(a+b)(a-b) which in the example is obviously (1000+9)(1000-9)=1000000-81
as both these factors are prime numbers there are no other solutions with smaller factors
e.g had the number been 999951( 1000 squared -7 squared) then more than one answer is possible

Myg, thanks for the explanation, but it might well be in Serbo Croat LOL !!!!!!!   

999919 is a product of two prime numbers
its only 4 factors are 1,991,1009 and 999919

25 75 9 8 8 1 = 531

(75-25+8)x9+8+1=531

50 100 4 7 3 5 =297

50 x 4 = 200
 
100 – 3 = 97
 
200 + 97 = 297

My answer : 297

50 + 100 = 150
150 x 4 = 600
7 - 5 = 2
600 ÷ 2 = 300
300 - 3 = 297



25 100 6 2 8 7 =486

(100-25+2x7-8)x6=486

My answer : 486

25 + 100 = 125
125 x 2 = 250
250 - 7 = 243
8 - 6 = 2
2 x 243 = 486

25 75 8 9 3 2 =378

(25+75+2)x3+(8x9)=378

Your're too quick


25 100 50 7 2 8= 452

(8x25)+(7x50)-100+2=452

Well done you

75 2 7 1 4 3 = 103

(75+7x4)x(3-1)/2=103