Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 00:33

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56300
In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

26 Aug 2015, 00:47
1
6
00:00

Difficulty:

5% (low)

Question Stats:

85% (01:03) correct 15% (01:07) wrong based on 141 sessions

### HideShow timer Statistics

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.

Attachment:

circle-in-square-dr-tri-yel.GIF [ 2.61 KiB | Viewed 4306 times ]

_________________
Manager
Joined: 13 Mar 2013
Posts: 162
Location: United States
GPA: 3.5
WE: Engineering (Telecommunications)
Re: In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

26 Aug 2015, 02:18
1
1
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
_________________
Regards ,
Manager
Joined: 14 Mar 2014
Posts: 145
GMAT 1: 710 Q50 V34
Re: In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

26 Aug 2015, 10:14
IMO : C

Attachment:

Capture.JPG [ 16.94 KiB | Viewed 3788 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
_________________
I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯
Intern
Joined: 09 May 2012
Posts: 18
In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

27 Aug 2015, 03:29
1
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.
Manager
Joined: 29 May 2013
Posts: 100
Location: India
Concentration: Technology, Marketing
WE: Information Technology (Consulting)
Re: In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

27 Aug 2015, 08:42
1
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!
Manager
Joined: 29 May 2013
Posts: 100
Location: India
Concentration: Technology, Marketing
WE: Information Technology (Consulting)
Re: In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

27 Aug 2015, 08:42
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!
Manager
Joined: 04 May 2015
Posts: 71
Concentration: Strategy, Operations
WE: Operations (Military & Defense)
In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

27 Aug 2015, 20:36
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

_________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps
Manager
Joined: 14 Jul 2014
Posts: 164
Location: United States
Schools: Duke '20 (D)
GMAT 1: 600 Q48 V27
GMAT 2: 720 Q50 V37
GPA: 3.2
Re: In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

27 Aug 2015, 21:07
Ah please don't tell me that I got it wrong because the detail about the center is not explicitly mentioned.
Math Expert
Joined: 02 Sep 2009
Posts: 56300
Re: In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

30 Aug 2015, 09:38
1
Bunuel wrote:

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.

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.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 56300
Re: In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

30 Aug 2015, 09:40
1
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.
_________________
Manager
Joined: 04 May 2015
Posts: 71
Concentration: Strategy, Operations
WE: Operations (Military & Defense)
Re: In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

30 Aug 2015, 12:04
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?
_________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps
Math Expert
Joined: 02 Sep 2009
Posts: 56300
Re: In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

30 Aug 2015, 12:09
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.
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42
GPA: 3.82
In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

31 Aug 2015, 07:20
1
1
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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Non-Human User
Joined: 09 Sep 2013
Posts: 11713
Re: In the figure above, a circle is inscribed in a square. What is the ar  [#permalink]

### Show Tags

16 Dec 2017, 23:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In the figure above, a circle is inscribed in a square. What is the ar   [#permalink] 16 Dec 2017, 23:15
Display posts from previous: Sort by