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Ratio and exponents

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by jimmytwoshoes » Sun Jul 27, 2008 1:52 pm
What is the fastest way to solve this problem?

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by Ian Stewart » Sun Jul 27, 2008 2:41 pm
Definitely by using the difference of squares:

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

I can guarantee that you will see a difference of squares on your real GMAT- I just can't tell you where you'll see it. It may be in an algebra problem, but it can also appear in geometry, number theory, even percent increase and decrease- in almost any subject area. Be sure you can recognize it when it shows up.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by sibbineni » Tue Jul 29, 2008 5:47 pm
It is just application of the formula

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

Apply the formula

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