It is currently 22 Oct 2017, 00:09

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If PQRO is a square inside a Circle with centre at "O" and

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
User avatar
B
Status: Fighting hard
Joined: 04 Jul 2011
Posts: 69

Kudos [?]: 80 [0], given: 87

GMAT Date: 10-01-2012
If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

New post 16 Sep 2012, 03:17
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

88% (01:41) correct 12% (01:53) wrong based on 91 sessions

HideShow timer Statistics

Attachment:
File comment: Circle/Shaded Region
Image.png
Image.png [ 3.12 KiB | Viewed 1870 times ]
If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?


A. a^2((3pi-8)/12)
B. a^2((pi-2)/4)
C. a^2((9pi-16)/12)
D. a((3pi-1)/12)
E. a^2/11
[Reveal] Spoiler: OA

_________________

I will rather do nothing than be busy doing nothing - Zen saying

Kudos [?]: 80 [0], given: 87

Senior Manager
Senior Manager
avatar
Joined: 15 Jun 2010
Posts: 358

Kudos [?]: 453 [0], given: 50

Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Reviews Badge
Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

New post 16 Sep 2012, 03:26
1
This post was
BOOKMARKED
Pansi wrote:
If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?


A. a^2((3pi-8)/12)
B. a^2((pi-2)/4)
C.a^2((9pi-16)/12)
D.a((3pi-1)/12)
E.a^2/11


So the square should have a diagonal equal to length of radius of circle. Let x be the side of square.
Hence diagonal of a square with side x= x root2
=> x root2 = a (radius of circle)
=>x= a/root 2
Hence area of square = (a/root 2)^2 = a^2/2.
Now the area of circular quadrant is (pi * a^2)/4
So shaded area = (pi * a^2)/4 - a^2/2, by simplifying
=> a^2((pi-2)/4)
Hence Answer B.
_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Kudos [?]: 453 [0], given: 50

1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 610

Kudos [?]: 1059 [1], given: 43

WE: Science (Education)
Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

New post 16 Sep 2012, 06:26
1
This post received
KUDOS
1
This post was
BOOKMARKED
SOURH7WK wrote:
Pansi wrote:
If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?


A. a^2((3pi-8)/12)
B. a^2((pi-2)/4)
C.a^2((9pi-16)/12)
D.a((3pi-1)/12)
E.a^2/11


So the square should have a diagonal equal to length of radius of circle. Let x be the side of square.
Hence diagonal of a square with side x= x root2
=> x root2 = a (radius of circle)
=>x= a/root 2
Hence area of square = (a/root 2)^2 = a^2/2.
Now the area of circular quadrant is (pi * a^2)/4
So shaded area = (pi * a^2)/4 - a^2/2, by simplifying
=> a^2((pi-2)/4)
Hence Answer B.


Just a remark: For any quadrilateral with perpendicular diagonals (so obviously also for a square), the area is given by half the product of the diagonals.
(You can easily deduce it by expressing the areas of the triangles formed by the diagonals.)

So, when you know the diagonal of a square, you don't have to compute the side in order to find the area. You just have to square the diagonal and half it.
In the given question, the diagonal of the square is \(a\) (the radius of the circle), so the area of the square is \(a^2/2.\)
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Kudos [?]: 1059 [1], given: 43

Intern
Intern
User avatar
Joined: 07 Jan 2013
Posts: 26

Kudos [?]: 7 [0], given: 491

Location: Poland
GPA: 3.8
Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

New post 13 Nov 2013, 14:57
SOURH7WK wrote:
Pansi wrote:
If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?


A. a^2((3pi-8)/12)
B. a^2((pi-2)/4)
C.a^2((9pi-16)/12)
D.a((3pi-1)/12)
E.a^2/11


So the square should have a diagonal equal to length of radius of circle. Let x be the side of square.
Hence diagonal of a square with side x= x root2
=> x root2 = a (radius of circle)
=>x= a/root 2
Hence area of square = (a/root 2)^2 = a^2/2.
Now the area of circular quadrant is (pi * a^2)/4
So shaded area = (pi * a^2)/4 - a^2/2, by simplifying
=> a^2((pi-2)/4)
Hence Answer B.


???? my answer is a square (a square (pi -1)/4) or asquare pi - 4 a square.!!!

Kudos [?]: 7 [0], given: 491

Current Student
avatar
Joined: 03 Jan 2013
Posts: 185

Kudos [?]: 28 [0], given: 0

Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 750 Q48 V46
GPA: 3.02
WE: Engineering (Other)
GMAT ToolKit User
Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

New post 14 Nov 2013, 07:45
Area of one quarter of the circle: (pi*a^2)/4

Area of the square:

Diagonal is equal to radius a. Therefore s(sqrt2) = a --> s = a/(sqrt2)
s^2 = (a^2)/2

Area of the shaded region is area of one quarter of the circle minus area of the square:

(pi*a^2)/4 - (a^2)/2 = [(pi*a^2) - 2(a^2)]/4

Factor out a^2:

a^2[(pi-2)/4]

Answer is B

Kudos [?]: 28 [0], given: 0

Intern
Intern
avatar
Joined: 15 Jul 2012
Posts: 41

Kudos [?]: 25 [0], given: 7

Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

New post 09 May 2015, 02:36
Devon wrote:
Area of one quarter of the circle: (pi*a^2)/4

Area of the square:

Diagonal is equal to radius a. Therefore s(sqrt2) = a --> s = a/(sqrt2)
s^2 = (a^2)/2

Area of the shaded region is area of one quarter of the circle minus area of the square:

(pi*a^2)/4 - (a^2)/2 = [(pi*a^2) - 2(a^2)]/4

Factor out a^2:

a^2[(pi-2)/4]

Answer is B


You have reduced qone quadrant with area of Square, I am fine with it. But I have worked out complete Area of circle minus Area of Square which gives= a^2(Pi-1/2). What is wrong in this?

Kudos [?]: 25 [0], given: 7

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16576

Kudos [?]: 273 [0], given: 0

Premium Member
Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

New post 08 Jun 2016, 08:20
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Director
Director
User avatar
B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 570

Kudos [?]: 2691 [0], given: 220

Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)
Re: If PQRO is a square inside a Circle with centre at "O" and [#permalink]

Show Tags

New post 08 Jun 2016, 10:20
Pansi wrote:
Attachment:
Image.png
If PQRO is a square inside a Circle with centre at "O" and radius "a", what is the area of the shaded portion ?


A. a^2((3pi-8)/12)
B. a^2((pi-2)/4)
C. a^2((9pi-16)/12)
D. a((3pi-1)/12)
E. a^2/11



OQ=a,So OR=\(\frac{a}{\sqrt{2}}\),So area of the Square=(\(\frac{a}{\sqrt{2}}\))^2=\(\frac{a^2}{2}\)

OQ=a,So area of the \(\frac{1}{4}\)th of the Circle=\(\pi\)\(a^2\)/4

So the area of the shaded portion=(\(\pi\)\(a^2\)/4)-\(\frac{a^2}{2}\)=\(a^2\)(\(\pi\)-2/4)

Correct Answer B
_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Kudos [?]: 2691 [0], given: 220

Re: If PQRO is a square inside a Circle with centre at "O" and   [#permalink] 08 Jun 2016, 10:20
Display posts from previous: Sort by

If PQRO is a square inside a Circle with centre at "O" and

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.