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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 » Thu Jan 01, 2009 9:00 am

Brent Hanneson - Creator of GMATPrepNow.com

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Source: Beat The GMAT — Problem Solving | Thu Jan 01, 2009 9:00 am

daisy: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed Dec 31, 2008 2:20 pm; Location: London

by daisy » Thu Jan 01, 2009 9:18 am

Answer should be 2x^2 (i.e. D)

Outer square area = 4x^2
therefore, diameter of circle will be = 2x
therefore, diagonal of inner square = 2x (i.e equal to diameter of the circle).
Lets say length of side of inner square = y
therefore, y^2 + y^2 = (2x)^2

therefore, 2y^2 = 4x^2
therefore, y^2 = 2x^2 (i.e. the area of the inner square).

Hit (D)

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GMAT/MBA Expert

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 » Thu Jan 01, 2009 9:27 am

Nice work/solution
Here's my full solution with graphics:

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vivek.kapoor83: Legendary Member; Posts: 833; Joined: Mon Aug 04, 2008 1:56 am; Thanked: 13 times

by vivek.kapoor83 » Thu Jan 01, 2009 10:22 am

daisy wrote:Answer should be 2x^2 (i.e. D)

therefore, diameter of circle will be = 2x

Brent, daisy,
can u pls explain how dia will be 2x if side of sq is 2x

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GMAT/MBA Expert

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 » Thu Jan 01, 2009 10:34 am

If the area of the outer square is 4x^2, then we get (side)(side) = 4x^2
This tells us that each side of the outer square is 2x [since (2x)(2x)=4x^2]
Note that the length of the side of the outer square is equivalent to the diameter of the circle. To help see this, draw a center for the circle and draw the diameter through this center such that the diamater is drawn horizontally.

Hope that helps.

Brent Hanneson - Creator of GMATPrepNow.com

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mental: Master | Next Rank: 500 Posts; Posts: 145; Joined: Mon Sep 29, 2008 1:14 am; Thanked: 13 times

by mental » Fri Jan 02, 2009 4:34 am

side of square = 2x = dia of circle = diagonal of inner square

Formula: Area of Square = side^2 = (Diagonal^2)/2

area of inner square = (2x)^2/2 = 2*x^2

ans: D

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Fri Jan 02, 2009 4:54 am

i hope it has been already solved correctly and perfectly

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