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

It is currently 18 Jun 2019, 01:06

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

Two identical circles of area 36π overlap as shown above. If the dista

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55662
Two identical circles of area 36π overlap as shown above. If the dista  [#permalink]

Show Tags

New post 14 Sep 2018, 01:16
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (02:54) correct 36% (02:20) wrong based on 21 sessions

HideShow timer Statistics

Image
Two identical circles of area 36π overlap as shown above. If the distance from point A to point B is 6, what is the area of the shaded region?


A. 6π

B. 12π

C. \(18\sqrt{3} – 6π\)

D. \(6π – 9\sqrt{3}\)

E. \(12π – 18\sqrt{3}\)


Attachment:
image020.jpg
image020.jpg [ 2.53 KiB | Viewed 681 times ]

_________________
Intern
Intern
avatar
B
Joined: 22 Oct 2016
Posts: 19
GMAT 1: 590 Q47 V25
GMAT 2: 640 Q49 V27
Reviews Badge
Re: Two identical circles of area 36π overlap as shown above. If the dista  [#permalink]

Show Tags

New post 14 Sep 2018, 02:03
distance between point A and B is given to assume an equilateral triangle with 6m sides, sinch area = 6^2xpie

Hence, Area of shaded region = 2(area of 60 deg sector - Area of Equilateral Triangle )
Ans = 12pie-18sqrt3
Intern
Intern
avatar
B
Joined: 04 Oct 2016
Posts: 17
Re: Two identical circles of area 36π overlap as shown above. If the dista  [#permalink]

Show Tags

New post 16 Sep 2018, 08:11
1
swapnilce.nitdgp wrote:
distance between point A and B is given to assume an equilateral triangle with 6m sides, sinch area = 6^2xpie

Hence, Area of shaded region = 2(area of 60 deg sector - Area of Equilateral Triangle )
Ans = 12pie-18sqrt3


Hi,
Can someone please provide a lil more detailed explanation...
Intern
Intern
avatar
Joined: 16 Sep 2018
Posts: 2
Location: Italy
Schools: LBS MiM '20 (A)
GMAT 1: 660 Q39 V41
GMAT 2: 690 Q42 V42
GPA: 3.6
Re: Two identical circles of area 36π overlap as shown above. If the dista  [#permalink]

Show Tags

New post 16 Sep 2018, 10:16
mischiefmanaged wrote:
swapnilce.nitdgp wrote:
distance between point A and B is given to assume an equilateral triangle with 6m sides, sinch area = 6^2xpie

Hence, Area of shaded region = 2(area of 60 deg sector - Area of Equilateral Triangle )
Ans = 12pie-18sqrt3


Hi,
Can someone please provide a lil more detailed explanation...


ibb.co/iyL3zz (copy-paste this to see the picture I drew for you, it won't let me attach it for some reason...)

Basically, AB = 6 which happens to be = r (you can reverse engineer "r" looking at the area that is 36pi. Area of a circle = pi*r^2, therefore 36*pi means that r = 6).

You can now build an equilateral triangle with side = 6, and find its area since it's a 30-60-90 triangle.

You can also compute the "sector's area" using the formula in the image I posted (it's just a proportional fraction of the whole circle's area).

Now you can find the difference between the two, which will give you the area of half the shaded region. Multiply that by 2 and you get the result.
Manager
Manager
User avatar
S
Joined: 10 Jun 2014
Posts: 67
Location: India
Concentration: Operations, Finance
WE: Manufacturing and Production (Energy and Utilities)
CAT Tests
Two identical circles of area 36π overlap as shown above. If the dista  [#permalink]

Show Tags

New post 16 Sep 2018, 12:39
For only one circle

Area = 36\(\pi\)
So Radius = 6
Distance between A to B = 6

So Origin,A & B form a equilateral Triangle
Area of \(\triangle\) = 9\(\sqrt{3}\)

\(\angle\) AOB= 60\(^{o}\) , Since Equilateral Triangle [ O= Origin]

Area of Circular segment OAB =(36\(\pi\) / \(360^{\circ}\)) x \(60^{\circ}\) = 6\(\pi\)

Shaded Portion by only one Circle = 6\(\pi\)-9\(\sqrt{3}\)

Shaded Portion by two circle = 12\(\pi\)-18\(\sqrt{3}\)
_________________
KUDOS PLEASE IF IT HELPED
GMAT Club Bot
Two identical circles of area 36π overlap as shown above. If the dista   [#permalink] 16 Sep 2018, 12:39
Display posts from previous: Sort by

Two identical circles of area 36π overlap as shown above. If the dista

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


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