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avenus: Master | Next Rank: 500 Posts; Posts: 238; Joined: Tue Feb 10, 2009 8:44 am; Thanked: 9 times

by avenus » Mon May 04, 2009 9:52 am

Place your bets

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Source: Beat The GMAT — Problem Solving | Mon May 04, 2009 9:52 am

PussInBoots: Master | Next Rank: 500 Posts; Posts: 157; Joined: Tue Oct 07, 2008 5:47 am; Thanked: 3 times

by PussInBoots » Mon May 04, 2009 12:33 pm

The answer is D.

Square the whole equation => simplify => take a square root

Here are some hints you'll need to use at some point:
(a+b) (a-b) = a^2 - b^2
24^2 - 5^2 * 23 = 24^2 - 25 * 23 = 24^2 - (24+1) * (24 - 1)

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon May 04, 2009 1:02 pm

PussInBoots has a great solution above, and it's particularly useful to notice that you can compute 24^2 - 25*23 quickly using the difference of squares. Considering the answer choices here, however, if you notice that 5*sqrt(23) is almost equal to 24, then sqrt(24 - 5*sqrt(23)) must be very close to zero, while sqrt(24 + 5*sqrt(23)) must be very close in value to sqrt(48) ~ 7. So we're looking for an answer that is approximately equal to 7, and there's only one answer choice that's even remotely close.

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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