How can you solve this problem faster?

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oxvt: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Feb 02, 2009 9:21 am

by oxvt » Mon Mar 02, 2009 2:42 am

1001^2-999^2 / 101^2-99^2

A) 10
B) 20
C) 40
D) 80
E) 100

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Source: Beat The GMAT — Problem Solving | Mon Mar 02, 2009 2:42 am

farooq: Master | Next Rank: 500 Posts; Posts: 140; Joined: Sat Feb 28, 2009 8:51 amFollowed by: 3 members; Location: India; Thanked: 14 times

Re: How can you solve this problem faster?

by farooq » Mon Mar 02, 2009 2:56 am

oxvt wrote:1001^2-999^2 / 101^2-99^2

A) 10
B) 20
C) 40
D) 80
E) 100

I took 1 min

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

(1001-999)(1001+999)/(101-99)(101+99) =10.

Regards,
Farooq Farooqui.
London. UK

It is your Attitude, not your Aptitude, that determines your Altitude.

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krisraam: Master | Next Rank: 500 Posts; Posts: 221; Joined: Wed Jan 21, 2009 10:33 amFollowed by: 1 member; Thanked: 12 times

by krisraam » Mon Mar 02, 2009 6:39 am

(a+b)^2 + (a-b)^2 = 4ab

(1000 + 1)^2 + (1000 -1)^2 = 4*1000 *1

Thanks
raama

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kamu: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Fri Feb 27, 2009 12:41 amFollowed by: 3 members; Thanked: 44 times

by kamu » Mon Mar 02, 2009 8:15 am

krisraam wrote:(a+b)^2 + (a-b)^2 = 4ab

(1000 + 1)^2 + (1000 -1)^2 = 4*1000 *1

Thanks
raama

I think you meant (a+b)^2 - (a-b)^2 = 4ab

and

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

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