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Source: — Problem Solving |
Junior | Next Rank: 30 Posts
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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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by Brent@GMATPrepNow » Thu Jan 01, 2009 9:27 am
Nice work/solution
Here's my full solution with graphics:

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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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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.
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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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by maihuna » Fri Jan 02, 2009 4:54 am
i hope it has been already solved correctly and perfectly
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