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How to simplyfy it?

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by Brent@GMATPrepNow » Sat Jul 16, 2011 9:58 am
Ashetty wrote: [1001^2 - 999^2] / [101^2 - 99^2]= 10 (How??)
This is a common question type on the GMAT
It requires you to factor the difference of squares in the numerator and denominator.

Aside: a^2 - b^2 = (a+b)(a-b)

[1001^2 - 999^2] / [101^2 - 99^2]
= [(1001+999)(1001-999)] / [(101+99)(101-99)]
=[(2000)(2)] / [(200)(2)]
=[4000] / [400]
= 10

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Brent
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by sana.noor » Thu May 09, 2013 5:58 am
very simple question
1001= 1000+1
999= 1000-1
101 = 100+1
99 = 100-1

now for a shortcut and to ave time
represent 1000= a....100 = b and 1= c
the above equation will be

(1000+1)^2 - (1000-1)^2/ (100+1)^2 - (100-1)^2 the final equation will be
(a+c)^2 - (a-c)^2/ (b+c)^2 - (b-c)^2---Main equation
open these equation as we know the general rule (a+b)^2 = a^2 +2ab + b^2
open the main equation and cancel out variables
in the end u will be left with ac/bc = 1000/100 = 10 answer...it took me few seconds to solve this question
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