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ramyaravindran: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Mon Apr 28, 2008 5:33 am; Thanked: 2 times

by ramyaravindran » Tue Mar 09, 2010 12:02 pm

This may be a simple concept but it is eluding me now. How can you quickly estimate if sqrt(78*79*80*81) is greater than or less than 6400?

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Source: Beat The GMAT — Problem Solving | Tue Mar 09, 2010 12:02 pm

dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Tue Mar 09, 2010 1:46 pm

ramyaravindran wrote:This may be a simple concept but it is eluding me now. How can you quickly estimate if sqrt(78*79*80*81) is greater than or less than 6400?

(Root( 78, 79, 80, 81) )^2

(80 80 )^2

78 78 80 81

80 80 80 80

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kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Tue Mar 09, 2010 2:09 pm

ramyaravindran wrote:This may be a simple concept but it is eluding me now. How can you quickly estimate if sqrt(78*79*80*81) is greater than or less than 6400?

Remember that 81^2 * 79^2 =(80^2 - 1^2)^2 < 80^4

Alternatively, 81 x 79 =80^2 - 1^2 < 80^2

80 x 78 < 80^2

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

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happyzzim: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Fri Mar 05, 2010 4:09 pm; Thanked: 1 times

by happyzzim » Tue Mar 09, 2010 2:34 pm

Q. sqrt(78*79*80*81) is greater than or less than 6400?

A. sqrt(78*79*80*81) < sqrt(79*79*81*81) = sqrt(79^2*81^2) = 6399 < 6400

For the reason, sqrt(78*79*80*81) < 6400

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