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

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by BTGmoderatorDC » Thu Dec 27, 2018 6:31 pm

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Answers

A

B

C

D

E

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Image

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 2Ï€ square inches.

OA D

Source: Veritas Prep
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Fri Dec 28, 2018 2:07 am
BTGmoderatorDC wrote:Image

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 2Ï€ square inches.

OA D

Source: Veritas Prep
Note that the radius of the circle is half of the side of the square and Side of the square is 1/√2 times the diagonal of the square. Also, note that the shortest distance between W and Y is the diagonal. So from Statement 1, we have diagonal = WY. Thus, we can have the value of side as well as the radius, thereby we can calculate the areas of the square and the circle. The area of the shaded region = Area of the square - Area of the circle. Statement 1 is sufficient.

From Statement 2 (The area of the circle is 2Ï€ square inches.), we can have the radius, thus, the side of the square. In a similar vein, we can get the value of the area of the shaded region.

The correct answer: D

Hope this helps!

-Jay
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