Last visit was: 18 Nov 2025, 15:46 It is currently 18 Nov 2025, 15:46
Home
GMAT
Messages
Tests
Schools
Events
Rewards
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
605-655 Level|   Geometry|      
User avatar
JAI HIND
User avatar
Joined: 10 Dec 2005
Last visit: 19 Feb 2006
Posts: 52
Own Kudos:
530
 [17]
Posts: 52
Kudos: 530
 [17]
What is the circumference of the circle above? 22 Dec 2005, 00:54
2
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

63% (01:33) correct 37% (01:33) wrong based on 350 sessions

History

Date
Time
Result
Not Attempted Yet

What is the circumference of the circle above?

(1) The length of arc XYZ is 18.
(2) r = s

Show Spoiler
Attachment:
2022-10-02_20-12-28.png
2022-10-02_20-12-28.png [ 8.06 KiB | Viewed 4498 times ]
ShowHide Answer
Official Answer
C
User avatar
gamjatang
User avatar
Joined: 14 Sep 2005
Last visit: 07 Jul 2007
Posts: 523
Own Kudos:
1,235
 [2]
Location: South Korea
Posts: 523
Kudos: 1,235
 [2]
What is the circumference of the circle above? 22 Dec 2005, 01:29
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
The length of arc XYZ is the sum of the below two arcs
- the length of arc XY
- the length of arc YZ

Statement1)

We need to know degree of s in order to find out the length of the arc XY or the arc YZ.

Since we do not know s, statement 1 alone is not sufficient.

Statement2)

If r = s, then r = s = 60. However, we do not know the radius of the circle, and so we cannot find out the circumference of the circle.

Thus statement2 alone is not sufficient.

Statement1 and 2)

Since r = s = 60 and the length of the arc XY is 9, we know the following;

- The length of the arc XY is 9.
- The length of the arc YZ is 9.
- The length of the arc XZ is 9.
--------------------------------
The circumference of the circle is 27.

Thus statement 1 and 2 combined are sufficient.
Attachments

PastedImage.jpg
PastedImage.jpg [ 8.57 KiB | Viewed 13308 times ]

User avatar
vivek123
User avatar
Joined: 14 Dec 2004
Last visit: 03 Jun 2012
Posts: 880
Own Kudos:
1,100
 [4]
Posts: 880
Kudos: 1,100
 [4]
What is the circumference of the circle above? Updated on: 22 Dec 2005, 02:23
Originally posted by vivek123 on 22 Dec 2005, 01:54.
Last edited by vivek123 on 22 Dec 2005, 02:23, edited 1 time in total.
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
But what if it is like this?
Attachments

possibility.JPG
possibility.JPG [ 6.19 KiB | Viewed 13227 times ]

User avatar
fluke
User avatar
Retired Moderator
Joined: 20 Dec 2010
Last visit: 24 Oct 2013
Posts: 1,099
Own Kudos:
5,094
 [4]
Given Kudos: 376
Posts: 1,099
Kudos: 5,094
 [4]
What is the circumference of the circle above? 30 Jan 2011, 12:08
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Q: What is the radius of circle.
\(Circumference=2*\pi*radius\)
\(\pi\) is a constant.

1. \(\stackrel{\frown}{XYZ}=18\)
\(\stackrel{\frown}{XYZ}=(\theta/360)*2*\pi*radius\)
\(\stackrel{\frown}{XYZ}\)=length of the arc XYZ
\(18=(\theta/360)*2*\pi*radius\)
\(\theta\) angle subtended by major arc \(\stackrel{\frown}{XYZ}\) at the center of the circle
\(\theta\) unknown
NOT SUFFICIENT.

2. \(\angle r = \angle s\)
The triangle is an equilateral triangle and \(\angle r = 60^{\circ}\)
Minor arc \(\stackrel{\frown}{XZ}\) makes an angle of \(60^{\circ}\) with the point Y, which lies on the circumference.
Theorem,The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
So if the minor arc XZ is making an angle of r with a point on the circumference of the circle, minor arc XZ will make an angle of 2r with the centre of the circle. Now we know angle of minor arc XZ is \(2r=120^{\circ}\)
And angle subtended by major arc XYZ at the center is \(\theta=360-120=240\)
However, with this information also we won't be able to find the radius of the circle because the length of the arc is not known. NOT SUFFICIENT.

Combining both of the above;
We know, length of major arc \(\stackrel{\frown}{XYZ}\) and angle made by the arc from the center i.e. \(\theta\)

Put these into the formula now;
\(\stackrel{\frown}{XYZ}=(\theta/360)*2*\pi*radius\)
\(\theta=240^{\circ} \hspace \hspace \stackrel{\frown}{XYZ}=18\)
\(18=(240/360)*2*\pi*radius\)
\(radius=27/(2*\pi)\)

\(Circumference=2*\pi*radius=(2*\pi)*27/(2*\pi)=27\)
SUFFICIENT.


Answer: C
OA: C
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,586
Own Kudos:
1,079
Posts: 38,586
Kudos: 1,079
What is the circumference of the circle above? 02 Aug 2024, 10:58
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.
Moderators:
Bunuel
Math Expert
105355 posts
kingbucky
496 posts