1002*998 1001*999

[Ibn Abbas]

I got a problem in Poweprep similar to this but the numbers were larger. I forgot the numbers but the principal is same.

1002*998 or 1001*999 Which one is larger?
We are NOT expected to calculate. So what is the shortcut?

[rkhanna]

1002 * 998 = (1000+2) (1000-2)= 1000^2 - 2^2

1001 * 999 = (1000+1) (1000-1) = 1000^2 - 1 larger than the above

[Ibn Abbas]

Thanks!
It was itching me to think that there was a shortcut and I didn't know it.

[look_hd]

1002*998 =1001*998+998
1001*999 =1001*998+1001

thats another way

[sairam]

1002*998 1001*999
(1000+2)(990+8) <(1000+1)(990+9)

[Ibn Abbas]

Well, this was the Powerprep problem I actually faced and seems like I cannot solve it no matter how hard I think:
100210*90021 or 100021*90210

[seagull]

100210*90021 = 100021*90021+189*90021
100021*90210 = 100021*90021+100021*189

so column B

[apprentice]

is there any special formulae to extract the factors of the number? How you did the seagull, please explain to us.

Thanks

[seagull]

100210*90021 = (100021+189)*90021 = 100021*90021+189*90021
100021*90210 = 100021*(90021+189) = 100021*90021+100021*189

hope it looks clear