One I am having trouble with...

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optimisticsam: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Wed Aug 22, 2007 8:29 pm; Location: Atlanta, GA

by optimisticsam » Tue Dec 11, 2007 4:04 am

Came across this last night taking a GMATPrep -

(1001^2 - 999^s) / (101^2 - 99^2)

I know I am missing something simple here...

Choices are -

10

20

40

80

100

Answer - 10

Can someone educate me on the simple way to solve this?

Thanks In Advance! ~Sam

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Source: Beat The GMAT — Problem Solving | Tue Dec 11, 2007 4:04 am

sankruth: Master | Next Rank: 500 Posts; Posts: 195; Joined: Sun Oct 21, 2007 4:33 am; Thanked: 10 times

by sankruth » Tue Dec 11, 2007 4:59 am

I assume here that 999^s is wrong, instead it is 999^2

Here is how I solved it

[(1000+1)^2 - (1000-1)^2]/[(100+1)^2 - (100-1)^2]

you end up with 4000/400 = 10

However I would like to know if there is a easier way to solve this?

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gabriel: Legendary Member; Posts: 986; Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member; Location: India; Thanked: 51 times

by gabriel » Tue Dec 11, 2007 5:29 am

First things first .. this should be in the PS section .. so moved to the PS section

An easier way to solve this is to use the formula (a^2-b^2) = (a-b)(a+b)

So, 1001^2-999^2 = (1001+999)(1001-999) = 2000*2 and 101^2-99^2 = (101+99)(101-99) = 200*2

Therefore (1001^2-999^2)/(101^2-99^2) = 4000/400 = 10 ..

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optimisticsam: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Wed Aug 22, 2007 8:29 pm; Location: Atlanta, GA

by optimisticsam » Tue Dec 11, 2007 3:59 pm

Thanks Gabriel! I should have gotten that one!

Thanks for moving it as well!

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