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# Given a circle that is inscribed in a rectangle so that the circle tou

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
Given a circle that is inscribed in a rectangle so that the circle tou  [#permalink]

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06 Sep 2018, 00:17
00:00

Difficulty:

35% (medium)

Question Stats:

64% (00:27) correct 36% (00:50) wrong based on 23 sessions

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Given a circle that is inscribed in a rectangle so that the circle touches all four sides of the rectangle as shown in the figure, what is the area of the shaded region?

(1) The rectangle shown is a square.
(2) The area of the shown circle is 10π.

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Re: Given a circle that is inscribed in a rectangle so that the circle tou  [#permalink]

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06 Sep 2018, 01:36
From statement 1:

No info about the side of a square or the radius of the circle.
Hence insufficient.

From statement 2:
Area = 10Pi
Pi*$$r^2$$ = 10Pi
r = $$\sqrt{10}$$

Diameter = 2r = 2$$\sqrt{10}$$ = Side of the square.

Area of the shaded region = area of the square - area of the circle.

Area of the shaded region = 4*10-10Pi = 40-10Pi.

Hence 2 is sufficient.

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Re: Given a circle that is inscribed in a rectangle so that the circle tou  [#permalink]

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06 Sep 2018, 02:05
Quote:
Given a circle that is inscribed in a rectangle so that the circle touches all four sides of the rectangle as shown in the figure, what is the area of the shaded region?

(1) The rectangle shown is a square.
(2) The area of the shown circle is 10π.

Statement 1: The rectangle shown is a square.
No new information.
If a circle touches all four sides of a rectangle, the rectangle has to be a square.
Insufficient.

Statement 2: The area of the shown circle is 10π.
We already know that the circle touches all four sides of the rectangle. Hence the rectangle is a square.
That means all the sides are equal.
In addition, this statement gives us the area of circle.
There is no need of calculations.
From Area, we can calculate the radius of the circle, r.
Also, from the figure we can see that the side of the square = dia of circle= 2xr
hence we can calculate the area of square.
Subtracting the area of Square from the area of circle, we get the area of shaded region.
Hence, Sufficient

Please Note that questions like above, are intentionally put up to make the test taker waste time.
There's no need of any calculation. We just have to check out the basics of Data sufficiency, ie if the information given is sufficient.

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Re: Given a circle that is inscribed in a rectangle so that the circle tou   [#permalink] 06 Sep 2018, 02:05
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