Square roots problem

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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 » Wed Jan 28, 2009 8:38 am

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 | Wed Jan 28, 2009 8:38 am

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Wed Jan 28, 2009 8:53 am

I multiplied both p and q by their respective conjugates to come up with

p= (sqrt(14) + sqrt(13))

q= (sqrt(14) - sqrt(13))

3pq = 3(14-13) = 3

now we have:

(sqrt(14) + sqrt(13))^2 + 3 + (sqrt(14) - sqrt(13))
27 + 2sqrt(14x13) + 3 + 27 - 2sqrt(14x13)

27 + 3 + 27
57

Fixed my silly mistake

Last edited by dmateer25 on Wed Jan 28, 2009 9:28 am, edited 1 time in total.

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sacx: Master | Next Rank: 500 Posts; Posts: 139; Joined: Wed Oct 22, 2008 4:36 am; Thanked: 17 times

by sacx » Wed Jan 28, 2009 8:55 am

p^2 + 3pq +q^ = p^2 + 2pq + q^2 + pq

= (p+q)^2 + pq

substituting values give B as answer

SACX

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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 » Wed Jan 28, 2009 9:19 am

sacx wrote:p^2 + 3pq +q^ = p^2 + 2pq + q^2 + pq

= (p+q)^2 + pq

substituting values give B as answer

Nice, the answer is B.
I posted this question to note that it is sometimes beneficial to know how to simplify rational expressions involving roots. In this question, I think it speeds up the process. See what you think.

Brent Hanneson - Creator of GMATPrepNow.com

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DeepakR: Master | Next Rank: 500 Posts; Posts: 158; Joined: Tue Sep 30, 2008 8:47 amFollowed by: 1 member; Thanked: 23 times; GMAT Score:660

by DeepakR » Wed Jan 28, 2009 8:01 pm

Hi Brent,

The question image isn't showing up for me. I tried it in Firefox and IE. Can someone help ? It may be an isolated case for me. :roll:

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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 » Wed Jan 28, 2009 8:34 pm

DeepakR wrote:Hi Brent,

The question image isn't showing up for me. I tried it in Firefox and IE. Can someone help ? It may be an isolated case for me. :roll:

Hey DeepakR,
This is a jpeg, just like all of my other posts.
I'm not sure what to suggest.
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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DeepakR: Master | Next Rank: 500 Posts; Posts: 158; Joined: Tue Sep 30, 2008 8:47 amFollowed by: 1 member; Thanked: 23 times; GMAT Score:660

by DeepakR » Thu Jan 29, 2009 7:14 am

Hi Brent,

Now i am able to view the image and i get 57. Not sure what was the issue previously anyway Thanks.

- Deepak

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aroon7: Master | Next Rank: 500 Posts; Posts: 160; Joined: Sat Dec 20, 2008 9:12 pm; Thanked: 11 times

by aroon7 » Thu Jan 29, 2009 9:07 pm

Brent Hanneson wrote:
Nice, the answer is B.
I posted this question to note that it is sometimes beneficial to know how to simplify rational expressions involving roots. In this question, I think it speeds up the process. See what you think.

Thanks Bernt
I get reminded about conjugates that i learnt in school...
may be it helps me at the test

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