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

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

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New post 25 Aug 2015, 23:47
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In the figure above, a circle is inscribed in a square. What is the area of the shaded region?

(1) The perimeter of the square equals 32.
(2) x = 35


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[Reveal] Spoiler:
Attachment:
circle-in-square-dr-tri-yel.GIF
circle-in-square-dr-tri-yel.GIF [ 2.61 KiB | Viewed 2805 times ]
[Reveal] Spoiler: OA

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

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New post 26 Aug 2015, 01:18
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Ans C.

from st. 1 we will only get radius of circle .
But to cal. area of yellow part = angle/360(pie r*r)

angle is not available . hence not A.

From statement 2 . We get the angle
As the angle subtends by yellow part is =2x=70
But r =?

hence not B.

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

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New post 26 Aug 2015, 09:14
IMO : C

Attachment:
Capture.JPG
Capture.JPG [ 16.94 KiB | Viewed 2434 times ]


St 1: The perimeter of the square equals 32
Clearly not suff

St 2: x = 35
Angle subtended at the center by a chord PQ = 2* Angle subtended by the same chord at the circumference of the circle
Thus Angle subtended at center will be 70\(^{\circ}\)
Area of the shaded region = area of sector OPQ of circle
area of sector of circle = (Ө/360˚)πr²
r is unknown.
Hence not suff

Combined:
We will get the value of r=8
Thus area of sector is calculated.
Hence Suff
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In the figure above, a circle is inscribed in a square. What is the ar [#permalink]

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New post 27 Aug 2015, 02:29
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Area of a Sector = \(\pi r^2 \frac{Q}{360^o}\)

Statement 1 provides us only the radius (r).
Statement 2 provides the angle.
We need to know both the radius and the angle. Since both statements are required to find the Area, Hence C.

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

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New post 27 Aug 2015, 07:42
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but why is it that you are assuming the shaded region is drawn from the centre of the circle?..It has not been stated in the question anywhere!

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

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New post 27 Aug 2015, 07:42
VenoMfTw wrote:
IMO : C

Attachment:
Capture.JPG


St 1: The perimeter of the square equals 32
Clearly not suff

St 2: x = 35
Angle subtended at the center by a chord PQ = 2* Angle subtended by the same chord at the circumference of the circle
Thus Angle subtended at center will be 70\(^{\circ}\)
Area of the shaded region = area of sector OPQ of circle
area of sector of circle = (Ө/360˚)πr²
r is unknown.
Hence not suff

Combined:
We will get the value of r=8
Thus area of sector is calculated.
Hence Suff



Hey,

but why is it that you are assuming the shaded region is drawn from the centre of the circle?..It has not been stated in the question anywhere!

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

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New post 27 Aug 2015, 19:36
I think we can infer that the central line divides the square vertically because it intersects the top and bottom edge at the same point as the perimeter of the circle, however there is nothing that says that the intersection of the shaded region and the vertical line is at the origin (it could be higher or lower).

(1) Gives us the radius of the circle, but nothing regarding angles or origins. insufficient
(2) IF if we knew that inside angle of the shaded was at the origin we would know that angle r is 70, however this cannot be inferred so to my knowledge and even if we could this statement alone is insufficient

(1) & (2) IF we knew that angle r was on the circle origin (the centre of the vertical line segment) we would have sufficient information to solve. but since this can not be inferred or deduced. This is also insufficient

My answer is: E
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Re: In the figure above, a circle is inscribed in a square. What is the ar [#permalink]

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New post 27 Aug 2015, 20:07
Ah please don't tell me that I got it wrong because the detail about the center is not explicitly mentioned. :(

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

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Bunuel wrote:
Image
In the figure above, a circle is inscribed in a square. What is the area of the shaded region?

(1) The perimeter of the square equals 32.
(2) x = 35


Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
circle-in-square-dr-tri-yel.GIF


GROCKIT OFFICIAL SOLUTION:

Statement 1 seems irrelevant to the question, but we can determine r by knowing that the length of the square’s side. If s = 32/4 = 8, then d = 8 and r = 4. This is insufficient, since we do not know the interior angle.

Statement 2 provides information about x, and from this, we know that the interior angle of the shaded region is 2(35) = 70. This is insufficient, since we do not know the size of the circle.

Together, we know both the size of the circle and the degree measure of the interior sector angle.

A(shaded) = (2x/360) * πr² = 70/360 * 16π, whatever the hell that comes out to. Remember, since it’s a Data Sufficiency question, we don’t actually need to calculate the number.

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

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jayanthjanardhan wrote:
but why is it that you are assuming the shaded region is drawn from the centre of the circle?..It has not been stated in the question anywhere!


Little r in the shaded region indicates that the line is a radius, thus shaded region is drawn from the center.
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New post 30 Aug 2015, 11:04
Bunuel wrote:
jayanthjanardhan wrote:
but why is it that you are assuming the shaded region is drawn from the centre of the circle?..It has not been stated in the question anywhere!


Little r in the shaded region indicates that the line is a radius, thus shaded region is drawn from the center.


Hmmmm... Maybe its's just me but I think it could be made a little clearer that the small r indicates that it is in fact a radius... Maybe an O stating origin or something? Thoughts?
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Re: In the figure above, a circle is inscribed in a square. What is the ar [#permalink]

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New post 30 Aug 2015, 11:09
DropBear wrote:
Bunuel wrote:
jayanthjanardhan wrote:
but why is it that you are assuming the shaded region is drawn from the centre of the circle?..It has not been stated in the question anywhere!


Little r in the shaded region indicates that the line is a radius, thus shaded region is drawn from the center.


Hmmmm... Maybe its's just me but I think it could be made a little clearer that the small r indicates that it is in fact a radius... Maybe an O stating origin or something? Thoughts?


Don't worry, on the real test this would be stated more clearly.
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In the figure above, a circle is inscribed in a square. What is the ar [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.



In the figure above, a circle is inscribed in a square. What is the area of the shaded region?

(1) The perimeter of the square equals 32.
(2) x = 35

==> In the original condition for the sector, there are 2 variables (center angle and the radius). Since we need to match the number of variables and equations, we need 2 equations. There is 1 each in 1) and 2), therefore C is likely the answer, and it turns out that C actually is the answer.

Using both 1) & 2), if x=35 then the center angle is 2*35=70 and since the length of the square is the radius of the circle, 4d=32, d=18. Thus the colored region has the are of pi*8^2*70/360. Therefore the answer is C.
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Re: In the figure above, a circle is inscribed in a square. What is the ar   [#permalink] 16 Dec 2017, 22:15
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