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

It is currently 11 Dec 2019, 22:38

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

In the figure above, the radius of the circle with center S is twice

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59674
In the figure above, the radius of the circle with center S is twice  [#permalink]

Show Tags

New post 20 Nov 2017, 23:18
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:51) correct 39% (02:04) wrong based on 56 sessions

HideShow timer Statistics

Image
In the figure above, the radius of the circle with center S is twice the radius of the circle with center O, and the measure of angle RST is twice that of angle POQ. If the area of the shaded region of circle O is 3, what is the area of the shaded region of circle S?

(A) 24
(B) 12
(C) 6
(D) 3
(E) 3/2

Attachment:
2017-11-21_1004_001.png
2017-11-21_1004_001.png [ 13.25 KiB | Viewed 1347 times ]

_________________
Senior Manager
Senior Manager
User avatar
G
Joined: 17 Oct 2016
Posts: 305
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
GMAT ToolKit User
Re: In the figure above, the radius of the circle with center S is twice  [#permalink]

Show Tags

New post 20 Nov 2017, 23:35
A . 24

For smaller circle we have (a/180)*pi*r^2=3 where a is the angle POQ

Hence for larger circle angle RST = 2a and radius =2r

Hence for larger circle the shaded area is (2a/180)*pi*(2r)^2 = 8* shaded area of smaller circle.
8*3=24


Sent from my iPhone using GMAT Club Forum
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: In the figure above, the radius of the circle with center S is twice  [#permalink]

Show Tags

New post 27 Nov 2017, 11:52
3
Bunuel wrote:
Image
In the figure above, the radius of the circle with center S is twice the radius of the circle with center O, and the measure of angle RST is twice that of angle POQ. If the area of the shaded region of circle O is 3, what is the area of the shaded region of circle S?

(A) 24
(B) 12
(C) 6
(D) 3
(E) 3/2

Attachment:
2017-11-21_1004_001.png


We can let the degree measure of angle POQ = x and the radius of circle O = r. Thus the area of the shaded region of circle O = (x/360)πr^2. We are also given that this area is 3. Thus we have:

(x/360)πr^2 = 3

Furthermore, the degree measure of angle RST = 2x and the radius of circle S = 2r. Thus the area of the shaded region of circle S = (2x/360)π(2r)^2 = 2(x/360)π(4r^2) = 8(x/360)πr^2 = 8(3) = 24.

Alternate Solution:

Since the radius of the circle with center S is twice the radius of the circle with center O, the area of the circle with center S is four times the area of the circle with center O. Thus, had the angle RST been equal to the angle POQ, the area of the shaded region RST would have been 4 times the area of the shaded region POQ. However, since the angle RST is twice the angle POQ, the area RST will be twice as large, which makes it 8 times the area POQ. Since the area POQ is 3, area RST is 8 x 3 = 24.

Answer: A
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
avatar
B
Joined: 10 Sep 2019
Posts: 53
Location: India
Concentration: Social Entrepreneurship, Healthcare
GPA: 2.6
WE: Project Management (Non-Profit and Government)
CAT Tests
Re: In the figure above, the radius of the circle with center S is twice  [#permalink]

Show Tags

New post 22 Nov 2019, 04:20
The areas of the sectors are directly proportional to the angle and directly proportional to the square of the radius'.

=> Area of the shaded region in circle S = 2*(2)^2 = 8 times the area of the shaded region in circle O.

=> Area = 8*3 = 24

Ans A
GMAT Club Bot
Re: In the figure above, the radius of the circle with center S is twice   [#permalink] 22 Nov 2019, 04:20
Display posts from previous: Sort by

In the figure above, the radius of the circle with center S is twice

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





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