Last visit was: 14 Dec 2024, 10:53 It is currently 14 Dec 2024, 10:53
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
555-605 Level|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Dec 2024
Posts: 97,877
Own Kudos:
685,839
 []
Given Kudos: 88,270
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,877
Kudos: 685,839
 []
In the diagram above, point B is the center of Circle #1 and point D i 10 Mar 2015, 06:00
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

73% (01:58) correct 27% (02:17) wrong based on 240 sessions

History

Date
Time
Result
Not Attempted Yet
Attachment:
gpp_img7.png
gpp_img7.png [ 15.74 KiB | Viewed 6900 times ]
In the diagram above, point B is the center of Circle #1 and point D is the center of Circle #2. If the ratio of the area of Circle #2 to the area of Circle #1 is 3:2, what is the ratio CE:BC?

A. 1.5
B. \(\sqrt{3}\)
C. 3
D. \(\sqrt{6}\)
E. 6

Kudos for a correct solution.
ShowHide Answer
Official Answer
D
User avatar
iamdp
User avatar
Joined: 05 Mar 2015
Last visit: 01 Jul 2016
Posts: 172
Own Kudos:
691
Given Kudos: 258
Status:A mind once opened never loses..!
Location: India
MISSION : 800
WE:Design (Manufacturing)
Posts: 172
Kudos: 691
In the diagram above, point B is the center of Circle #1 and point D i 10 Mar 2015, 06:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi

let's say R1 is the radius of smaller circle and R2 is of the bigger circle

According to question
A1/A2 = 3/2
[pi(R1)^2 ] / [pi(R2)^2] = 3/2
R1/R2 = root3 / root 2

Now CE= 2[R2] & BC =R1

therefore CE/BC = [2(root3)] / root2 = root6
User avatar
lipsi18
User avatar
Joined: 26 Dec 2012
Last visit: 30 Nov 2019
Posts: 132
Own Kudos:
54
 []
Given Kudos: 4
Location: United States
Concentration: Technology, Social Entrepreneurship
WE:Information Technology (Computer Software)
Posts: 132
Kudos: 54
 []
In the diagram above, point B is the center of Circle #1 and point D i 10 Mar 2015, 19:01
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Assume radius of circle 1 = R & radius of circle 2 = r;
given, Area of Circle 1/Area of Circle 2 = 3/2 = R^2/r^2; therefore R/r = Root 3/Root 2
Required, CE:BC = 2*R: r = 2 * Root 3/Root 2; simplify (multiply numerator and denominator by root 2), and answer = Root 6
Therefore answer choice D Root 6
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Dec 2024
Posts: 97,877
Own Kudos:
685,839
Given Kudos: 88,270
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,877
Kudos: 685,839
In the diagram above, point B is the center of Circle #1 and point D i 15 Mar 2015, 21:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

In the diagram above, point B is the center of Circle #1 and point D is the center of Circle #2. If the ratio of the area of Circle #2 to the area of Circle #1 is 3:2, what is the ratio CE:BC?

A. 1.5
B. \(\sqrt{3}\)
C. 3
D. \(\sqrt{6}\)
E. 6

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

This is tricky. We are given the ratio of areas, and we want to know a ratio involving the radii. Let R be the radius of the bigger circle, and r be the radius of the smaller circle.
\(ratio \ of \ areas = \frac{3}{2} = \frac{\pi{R^2}}{\pi{r^2}}=\frac{\pi{R^2}}{\pi{r^2}}\).

Take the square root and rationalize the denominator:
\(\frac{R}{r}=\frac{\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{6}}{2}\)

Well, CE = 2R, and BC = r, so CE/BC = 2R/r, which is twice this ratio \(\frac{CE}{BC}=\sqrt{6}\).

Answer = (D)
User avatar
kashifgolf
User avatar
Joined: 13 Sep 2015
Last visit: 19 Dec 2015
Posts: 9
Own Kudos:
7
Posts: 9
Kudos: 7
In the diagram above, point B is the center of Circle #1 and point D i 20 Oct 2015, 09:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[quote="Bunuel"]
Attachment:
gpp_img7.png
In the diagram above, point B is the center of Circle #1 and point D is the center of Circle #2. If the ratio of the area of Circle #2 to the area of Circle #1 is 3:2, what is the ratio CE:BC?

A. 1.5
B. \(\sqrt{3}\)
C. 3
D. \(\sqrt{6}\)
E. 6


Solution :

Lets assume radius of circle 1 - r, and circle 2 as - R

Area of circle 1 - pi r*2
Area of circle 2 - pi R*2

Therfore pi R*2/pi r*2 = 3/2
R*2/r*2 = 3/2
R/r = root 3/ root 2

We have to find out the ratio of the diameter of circle 2/ radius of circle 1, which can be written mathematically as 2R/r

2R/r = 2* root 3/ root 2
= root 2 * root 3
= root 6

Answer : D
User avatar
shashankism
User avatar
Joined: 13 Mar 2017
Last visit: 09 Dec 2024
Posts: 619
Own Kudos:
624
 []
Given Kudos: 88
Affiliations: IIT Dhanbad
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy)
Posts: 619
Kudos: 624
 []
In the diagram above, point B is the center of Circle #1 and point D i 06 Apr 2018, 02:36
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
Attachment:
gpp_img7.png
In the diagram above, point B is the center of Circle #1 and point D is the center of Circle #2. If the ratio of the area of Circle #2 to the area of Circle #1 is 3:2, what is the ratio CE:BC?

A. 1.5
B. \(\sqrt{3}\)
C. 3
D. \(\sqrt{6}\)
E. 6

Kudos for a correct solution.

Area(C2) : Area (C1) = 3 :2
Diameter(C2) : Diameter(C1) = \(\sqrt{(3/2)}\)
CE: AB = \(\sqrt{(3/2)}\)
CE: 2BC = \(\sqrt{(3/2)}\)
CE:BC = 2*\(\sqrt{(3/2)}\) = \(\sqrt{4*(3/2)}\) = \(\sqrt{6}\)

Answer D
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 35,820
Own Kudos:
930
Posts: 35,820
Kudos: 930
In the diagram above, point B is the center of Circle #1 and point D i 28 Aug 2022, 09:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderator:
Bunuel
Math Expert
97877 posts