What's the shortcut here?

I feel like there should be some shortcut here rather than having to do the actual math....

But, what is it? Couldn't really simplify by factoring since 101 is prime. Any ideas here?

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Mon Nov 29, 2010 2:59 pm

WilliamGCash wrote:

I feel like there should be some shortcut here rather than having to do the actual math....

But, what is it? Couldn't really simplify by factoring since 101 is prime. Any ideas here?

This question is testing the following quadratic identity:

xÂ² - yÂ² = (x+y)(x-y)

Thus:
(1001Â² - 999Â²)/(101Â² - 99Â²)
= (1001+999)(1001-999)/(101+99)(101-99)
= (2000)(2)/(200)(2)
= 10.

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WilliamGCash: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Wed Nov 03, 2010 12:56 pm; GMAT Score:740

by WilliamGCash » Mon Nov 29, 2010 4:49 pm

Thanks. I knew I had to missing something.

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