It is currently 13 Dec 2017, 14:55

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


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

As the figure above shows, four identical circles are inscri

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

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 10 Feb 2011
Posts: 112

Kudos [?]: 382 [1], given: 10

As the figure above shows, four identical circles are inscri [#permalink]

Show Tags

New post 17 Feb 2011, 14:04
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:20) correct 0% (00:00) wrong based on 12 sessions

HideShow timer Statistics

185. As the figure above shows, four identical circles are inscribed in a square. If the distance between centers of circle A and В is 4sq2 , what is the area of the shaded region?
(A) 256 – 72п
(B) 256 – 64п
(C) 256 – 32п
(D) 128 – 32п
(E) 64 – 16п
Attachments

Doc1.docx [10.31 KiB]
Downloaded 82 times

To download please login or register as a user

Kudos [?]: 382 [1], given: 10

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42583

Kudos [?]: 135541 [1], given: 12697

Re: As the figure above shows, four identical circles are inscri [#permalink]

Show Tags

New post 17 Feb 2011, 14:19
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
banksy wrote:
185. As the figure above shows, four identical circles are inscribed in a square. If the distance between centers of circle A and В is 4sq2 , what is the area of the shaded region?
(A) 256 – 72п
(B) 256 – 64п
(C) 256 – 32п
(D) 128 – 32п
(E) 64 – 16п
Attachment:
untitled.PNG
untitled.PNG [ 2.74 KiB | Viewed 3415 times ]
As you can see on the diagram above AB is the hypotenuse of the isosceles right triangle with legs equal to 2r (45-45-90 right triangle --> ratio of the sides \(1:1:\sqrt{2}\)). Now, as \(AB=hypotenuse=4\sqrt{2}\) then \(2r=leg=\frac{4\sqrt{2}}{\sqrt{2}}=4\) --> \(r=2\).

Shades region = are of the square - area of the circles = \((4r)^2-4*\pi{r^2}=64-16\pi\).

Answer: E.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135541 [1], given: 12697

TOEFL Forum Moderator
avatar
Joined: 16 Nov 2010
Posts: 1586

Kudos [?]: 607 [0], given: 40

Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: As the figure above shows, four identical circles are inscri [#permalink]

Show Tags

New post 19 Apr 2011, 18:36
AB = 4root(2)

So The diameter of circle = 4

Area of aquare = 4+4 = 8

Area of shaded part = 64 - 4*pi*4 = 64 - 16pi

Answer - E
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 607 [0], given: 40

1 KUDOS received
Intern
Intern
avatar
Joined: 19 Apr 2011
Posts: 9

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

Re: As the figure above shows, four identical circles are inscri [#permalink]

Show Tags

New post 19 Apr 2011, 19:04
1
This post received
KUDOS
Distance AB = 4sq2
So each side of triangle = 4
Radius of circle = 2
Each side of Square = 8

Area of shaded portion = area of square - area of 4 circles
= (8*8) - 4*pi(2)square
= 64 - 16 pi

Correct Answer E

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14869

Kudos [?]: 287 [0], given: 0

Premium Member
Re: As the figure above shows, four identical circles are inscri [#permalink]

Show Tags

New post 20 Aug 2017, 04:29
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 [?]: 287 [0], given: 0

Re: As the figure above shows, four identical circles are inscri   [#permalink] 20 Aug 2017, 04:29
Display posts from previous: Sort by

As the figure above shows, four identical circles are inscri

  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®.