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In the figure above, a circle is inscribed in square WXYZ. What is the

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Joined: 02 Sep 2009
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Kudos [?]: 129158 [0], given: 12194

In the figure above, a circle is inscribed in square WXYZ. What is the [#permalink]

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New post 06 Jun 2017, 11:27
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A
B
C
D
E

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  25% (medium)

Question Stats:

80% (00:55) correct 20% (00:27) wrong based on 31 sessions

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[img]https://gmatclub.com/forum/download/file.php?id=35666[img]
In the figure above, a circle is inscribed in square WXYZ. What is the area of the shaded region?

(1) The shortest distance between point W and point Y is 4 inches.

(2) The area of the circle is 2π square inches.

[Reveal] Spoiler:
Attachment:
InscribedWXYZ.png
InscribedWXYZ.png [ 5.38 KiB | Viewed 635 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 129158 [0], given: 12194

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Re: In the figure above, a circle is inscribed in square WXYZ. What is the [#permalink]

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New post 06 Jun 2017, 17:36
The answer should be D.

We just need to figure out the diameter of the circle, as that will be the same length as the side of the square. Once we have these numbers, we can solve for the areas.

Statement one tells us that the diagonal is 4 inches. We can solve for the side length (and therefore the diameter of the circle) by knowing that the diagonal = side length * sqrt(2). Sufficient.

Statement two allows us to solve for radius, which we then double to get the diameter. Since diameter = side length, we can also solve with this info.

Both statements ALONE are sufficient. D

Kudos [?]: 0 [0], given: 71

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Re: In the figure above, a circle is inscribed in square WXYZ. What is the [#permalink]

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New post 06 Sep 2017, 19:50
Bunuel wrote:
[img]https://gmatclub.com/forum/download/file.php?id=35666[img]
In the figure above, a circle is inscribed in square WXYZ. What is the area of the shaded region?

(1) The shortest distance between point W and point Y is 4 inches.

(2) The area of the circle is 2π square inches.

[Reveal] Spoiler:
Attachment:
InscribedWXYZ.png


You can calculate the area of a square by squaring the diagonal of the square and dividing it by 2.

St 1

This just illustrates the diagonal of wxyz

suff

St 2

From this we can derive the length of the diagonal of wxyz

suff

D

Kudos [?]: 35 [0], given: 164

Re: In the figure above, a circle is inscribed in square WXYZ. What is the   [#permalink] 06 Sep 2017, 19:50
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In the figure above, a circle is inscribed in square WXYZ. What is the

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