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

Question

https://gmatclub.com/forum/download/file.php?id=27669 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 . circle-in-square-dr-tri-yel.GIF

TheKingInTheNorth · Answer

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.
Ans

VenoMfTw · Answer

IMO : C 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

scorpionkapoor77 · Answer

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.

jayanthjanardhan · Answer

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!

jayanthjanardhan · Answer

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!

DropBear · Answer

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

dina98 · Answer

Ah please don't tell me that I got it wrong because the detail about the center is not explicitly mentioned.

Bunuel · Answer

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.

Bunuel · Answer

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

DropBear · Answer

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?

Bunuel · Answer

Don't worry, on the real test this would be stated more clearly.

MathRevolution · Answer

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.

bumpbot · Answer

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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

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