Sqrt(17+sqrt264) = sqrt(a) + sqrt(b)

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Jan 25, 2009 3:06 pm

Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.

Brent Hanneson - Creator of GMATPrepNow.com

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Source: Beat The GMAT — Problem Solving | Sun Jan 25, 2009 3:06 pm

piyush_nitt: Master | Next Rank: 500 Posts; Posts: 424; Joined: Sun Dec 07, 2008 5:15 pm; Location: Sydney; Thanked: 12 times

Re: Sqrt(17+sqrt264) = sqrt(a) + sqrt(b)

by piyush_nitt » Sun Jan 25, 2009 4:17 pm

Brent Hanneson wrote:

Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.

Sqrt(17+sqrt264) = sqrt(a) + sqrt(b)

squaring both sides

17+sqrt(264) = a + b + 2*sqrt(a)*(sqrt(b)

Comparing ll'ar parts

a + b = 17 - (1)
sqrt(264) = 2*sqrt(a)*sqrt(b) (2)

squaring 2 again

264 = 4*a*b

ab = 66 - (3)

solving 1 and 3

a =11 , b = 6

hence a-b = 5 , IMO E

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Jan 25, 2009 4:26 pm

Nice solution piyush. The answer is E.

Here's my solution as well.

Brent Hanneson - Creator of GMATPrepNow.com

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awesomeusername: Master | Next Rank: 500 Posts; Posts: 226; Joined: Tue Jan 13, 2009 1:27 pmFollowed by: 1 member; Thanked: 23 times

by awesomeusername » Sun Jan 25, 2009 9:29 pm

For some reason, I'm not understanding why we can say 17 = a+b and sqrt(264) = 2sqrt(ab).

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Jan 25, 2009 10:44 pm

awesomeusername wrote:For some reason, I'm not understanding why we can say 17 = a+b and sqrt(264) = 2sqrt(ab).

After squaring both sides of the equation we have: 17 + sqrt(264) = a+b+2sqrt(ab)

On both sides, we have terms that are inside the square root and terms outside the square root.

We can we can assume that the terms inside the square root are equal: sqrt(264)=2sqrt(ab) or sqrt(264)=sqrt(4ab)

And we can we can assume that the terms outside the square root are equal: a+b = 17

Brent Hanneson - Creator of GMATPrepNow.com

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awesomeusername: Master | Next Rank: 500 Posts; Posts: 226; Joined: Tue Jan 13, 2009 1:27 pmFollowed by: 1 member; Thanked: 23 times

by awesomeusername » Mon Jan 26, 2009 6:38 am

Thanks Brent, I think I understand it now

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