GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 07 Dec 2019, 01:51

### 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

# A is the center of the circle, and the length of AB is . The blue shad

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59587
A is the center of the circle, and the length of AB is . The blue shad  [#permalink]

### Show Tags

20 Mar 2015, 07:07
1
2
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:46) correct 21% (01:59) wrong based on 123 sessions

### HideShow timer Statistics

Attachment:

areashade_q2.png [ 10.15 KiB | Viewed 7370 times ]
A is the center of the circle, and the length of AB is $$4\sqrt{2}$$. The blue shaded region is a square. What is the area of the shaded region?

A. 4(4 - π)
B. 4(8 - π)
C. 8(2 - π)
D. 8(8 - π)
E. 16(4 - π)

Kudos for a correct solution.

_________________
Senior Manager
Joined: 02 Mar 2012
Posts: 268
Schools: Schulich '16
Re: A is the center of the circle, and the length of AB is . The blue shad  [#permalink]

### Show Tags

20 Mar 2015, 12:37
1
correct choice is E

side of square =2r

4sqt2=r *sqt2

r=4

so we can calculate the area of square and circle and minus
which boils down to option E for the correct answer
Manager
Joined: 19 Apr 2013
Posts: 68
Concentration: Entrepreneurship, Finance
GMAT Date: 06-05-2015
GPA: 3.88
WE: Programming (Computer Software)
Re: A is the center of the circle, and the length of AB is . The blue shad  [#permalink]

### Show Tags

20 Mar 2015, 12:54
1
consider radius of circle = r
so side of square = 2r

r^2+r^2 = {4sqrt(2)}^2
2r^2 = 32
r^2 = 16

so area of circle = pi*r^2 => pi*16
area of square = 4*r^2 = 4*16
so area of shaded region == area of square - area of cirlce == 16(4-pi)
Intern
Joined: 20 Mar 2015
Posts: 17
Location: Italy
GMAT 1: 670 Q48 V34
GPA: 3.7
A is the center of the circle, and the length of AB is . The blue shad  [#permalink]

### Show Tags

Updated on: 21 Mar 2015, 03:07
2
Since AB is half the diagonal of the square, the diagonal is $$8\sqrt{2}$$, which is $$\sqrt{2}$$ the side of the square. The side of the square is then $$\frac{8\sqrt{2}}{\sqrt{2}}=8$$.

The area of the square is then $$8^2=64$$.

The side of the square equals twice the radium of the circle. Therefore, the area of the circle is $$\pi\cdot4^2=16\pi$$

The shaded area is $$64-16\pi=16(4-\pi)$$

Originally posted by ngie on 20 Mar 2015, 13:22.
Last edited by ngie on 21 Mar 2015, 03:07, edited 1 time in total.
Senior Manager
Joined: 28 Feb 2014
Posts: 289
Location: United States
Concentration: Strategy, General Management
Re: A is the center of the circle, and the length of AB is . The blue shad  [#permalink]

### Show Tags

20 Mar 2015, 20:45
Bunuel wrote:
Attachment:
A is the center of the circle, and the length of AB is $$4\sqrt{2}$$. The blue shaded region is a square. What is the area of the shaded region?

A. 4(4 - π)
B. 4(8 - π)
C. 8(2 - π)
D. 8(8 - π)
E. 16(4 - π)

Kudos for a correct solution.

The line segment AB forms a 45 45 90 triangle with a hypotenuse of $$4\sqrt{2}$$
As a result both a side of the square and the radius is 4.
8^2 - (4^2)π
16(4 - π)

Math Expert
Joined: 02 Sep 2009
Posts: 59587
Re: A is the center of the circle, and the length of AB is . The blue shad  [#permalink]

### Show Tags

23 Mar 2015, 05:08
Bunuel wrote:

A is the center of the circle, and the length of AB is $$4\sqrt{2}$$. The blue shaded region is a square. What is the area of the shaded region?

A. 4(4 - π)
B. 4(8 - π)
C. 8(2 - π)
D. 8(8 - π)
E. 16(4 - π)

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

areashade_explanation.png [ 46.82 KiB | Viewed 5998 times ]

_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
A is the center of the circle, and the length of AB is . The blue shad  [#permalink]

### Show Tags

26 Mar 2015, 19:32
There is a direct relation between area of inscribed circle & area of square

$$Area of circle = Area of square * \frac{\pi}{4}$$

Diagonal of square $$= 2 * 4\sqrt{2} = 8\sqrt{2}$$

Side of square $$= \sqrt{\frac{(8\sqrt{2})^2}{2}} = 8$$

Area of square $$= 8^2 = 64$$

Area of circle $$= 64 * \frac{\pi}{4} = 16\pi$$

Area of shaded region $$= 64 - 16\pi = 16(4-\pi)$$
Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 563
Location: India
GMAT 1: 780 Q51 V46
Re: A is the center of the circle, and the length of AB is . The blue shad  [#permalink]

### Show Tags

26 Mar 2015, 22:59
Hi All,
Area of the shaded region = Area of the square – area of the circle.
Since line segment AB forms the 45-45-90 triangle with square.
It gives side of the square as 8. And radius of the circle as 4.
Area of the shaded region = 64 – 16pi.
= 16(4-Pi).
You can also approach this question using POE.
the shaded region should be slightly less than 1/4th of the area of the square. Since area of the square is 64. We are looking some answer close to 16.
Let pi = 3.1
A. 4(4 - π) this is less than 4 eliminate.
B. 4(8 - π) this is more than 16 eliminate.
C. 8(2 - π) this is negative eliminate.
D. 8(8 - π) this is more than 16 eliminate.
E. 16(4 - π) this is very close to 16. So answer is E.
POE is just in case if you don’t know how to solve.
_________________
- CrackVerbal Prep Team

Register for the Free GMAT Kickstarter Course : http://bit.ly/2DDHKHq

Register for our Personal Tutoring Course : https://www.crackverbal.com/gmat/personal-tutoring/

Join the free 4 part GMAT video training series : http://bit.ly/2DGm8tR
Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 265
Re: A is the center of the circle, and the length of AB is . The blue shad  [#permalink]

### Show Tags

02 Mar 2019, 05:32
Bunuel wrote:
Attachment:
A is the center of the circle, and the length of AB is $$4\sqrt{2}$$. The blue shaded region is a square. What is the area of the shaded region?

A. 4(4 - π)
B. 4(8 - π)
C. 8(2 - π)
D. 8(8 - π)
E. 16(4 - π)

Kudos for a correct solution.

okay

since the length of AB is 4√2, the diagonal of the square is 8√2, and thus each side of the square measures 8 and radius of the circle measures 4

now the shaded area = 64 - pi 4^2 = 16(4-pi) = E the answer

thanks
Re: A is the center of the circle, and the length of AB is . The blue shad   [#permalink] 02 Mar 2019, 05:32
Display posts from previous: Sort by