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

It is currently 22 Feb 2019, 05:11

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 in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

What is the circumference of the circle above?

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

Hide Tags

 
Manager
Manager
avatar
Joined: 10 Dec 2005
Posts: 88
What is the circumference of the circle above?  [#permalink]

Show Tags

New post 21 Dec 2005, 23:54
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (01:32) correct 34% (02:14) wrong based on 119 sessions

HideShow timer Statistics

Image
What is the circumference of the circle above?

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

Attachment:
geo.jpg
geo.jpg [ 3.92 KiB | Viewed 2354 times ]

Attachments

DS- Geometry 2.doc [19.5 KiB]
Downloaded 474 times

To download please login or register as a user


_________________

JAI HIND!

Director
Director
avatar
Joined: 14 Sep 2005
Posts: 942
Location: South Korea
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 00:29
1
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 4685 times ]


_________________

Auge um Auge, Zahn um Zahn :twisted: !

SVP
SVP
avatar
Joined: 14 Dec 2004
Posts: 1593
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post Updated on: 22 Dec 2005, 01:23
2
But what if it is like this?
Attachments

possibility.JPG
possibility.JPG [ 6.19 KiB | Viewed 4670 times ]


Originally posted by vivek123 on 22 Dec 2005, 00:54.
Last edited by vivek123 on 22 Dec 2005, 01:23, edited 1 time in total.
Senior Manager
Senior Manager
avatar
Joined: 11 Nov 2005
Posts: 303
Location: London
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 01:08
1
good question...

Ans. C

Stat 1 is insufficient, does not provide enough info to determine the circumference.

Stat 2 suggest, the triangle is equilayeral so all the side are same in lenght, therefore all the 3 arc of the circle is same.... insufficient,

However combining togethe, it is possible to determine the circumferene, in this case it is 27.
Senior Manager
Senior Manager
avatar
Joined: 11 Nov 2005
Posts: 303
Location: London
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 01:11
Can you please label the angle and points?

vivek123 wrote:
But what if it is like this?
SVP
SVP
avatar
Joined: 24 Sep 2005
Posts: 1782
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 02:17
vivek123 wrote:
SunShine wrote:
Can you please label the angle and points?

vivek123 wrote:
But what if it is like this?


Done!


Uhm, i don't know whether there will normally be "not drawn to scale" to indicate that the figure are not exactly what we perceive ...Anyways, you're right to stem such a possibility!! :) . In that case, your original answer of E is correct.
Senior Manager
Senior Manager
avatar
Joined: 11 Nov 2005
Posts: 303
Location: London
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 02:23
vivek123 wrote:
But what if it is like this?


Thanks for the labels

in this case also the answer is C.

Stat 1 is insufficient, to calculate the circumference

statement 2 suggest the traingle is equilateral and hence r=60o
therefore the arc xz = 1/3 of the circumference.

combining together stat 1&2, circumference can be determined
Senior Manager
Senior Manager
avatar
Joined: 11 Nov 2005
Posts: 303
Location: London
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 02:31
well.. the measure of arc of a circle is double the angle it (arc) forms.

in this case 60o , arc=120, and hence 120/360 =1/3 of circumference
SVP
SVP
avatar
Joined: 24 Sep 2005
Posts: 1782
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 02:39
Sorry, I was double-minded but this time, i'm sure it's C and i'm gonna prove why 8-)
SVP
SVP
avatar
Joined: 24 Sep 2005
Posts: 1782
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 02:48
what matters here is that the angle of the arc XYZ is constant!
Attachments

why.doc [23.5 KiB]
Downloaded 172 times

To download please login or register as a user

Director
Director
avatar
Joined: 17 Dec 2005
Posts: 530
Location: Germany
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 02:49
Can you please explain the meaning of arc XYZ to me?

Is it the edge from X via Y to Z?

Or the arc opposite of Y?

Thx
SVP
SVP
avatar
Joined: 14 Dec 2004
Posts: 1593
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 02:53
AGREE!!! :-D

Thank you folks!
Senior Manager
Senior Manager
avatar
Joined: 03 Nov 2005
Posts: 319
Location: Chicago, IL
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 19:54
Combining (1) and (2), it follows that arc XY=ZY=ZX (they are fomed by equal angles)

===> XY=(XY+ZX)/2=9

Circumference=sum of 3 arcs=3*9=27
_________________

Hard work is the main determinant of success

SVP
SVP
avatar
Joined: 24 Sep 2005
Posts: 1782
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 19:56
rlevochkin wrote:
Combining (1) and (2), it follows that arc XY=ZY=ZX (they are fomed by equal angles)

===> XY=(XY+ZX)/2=9

Circumference=sum of 3 arcs=3*9=27


uhm, this we're not sure as vivek pointed out in his illustration
Senior Manager
Senior Manager
avatar
Joined: 03 Nov 2005
Posts: 319
Location: Chicago, IL
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 20:13
laxieqv wrote:
what matters here is that the angle of the arc XYZ is constant!


Thanks, I reviewed you attachment. Very nice. But I believe The following principle.....

We have : XOY= 2 *XZY coz this is a principle in geometry.

....applies only if the point O is a point of intersection of three perpendicular bisectors. We don't know if it is. Can we really apply this principle in that case?
_________________

Hard work is the main determinant of success

SVP
SVP
avatar
Joined: 24 Sep 2005
Posts: 1782
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 22 Dec 2005, 20:25
rlevochkin wrote:
laxieqv wrote:
what matters here is that the angle of the arc XYZ is constant!


Thanks, I reviewed you attachment. Very nice. But I believe The following principle.....

We have : XOY= 2 *XZY coz this is a principle in geometry.

....applies only if the point O is a point of intersection of three perpendicular bisectors. We don't know if it is. Can we really apply this principle in that case?


Yes, O is coz O is the centre of the circle! ...the distances from O to X, Y and Z are the same(= the radius) --> O lies on the perpendicular bisectors of XY, YZ and XZ.
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1796
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 30 Jan 2011, 11:08
3
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
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 725
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 13 Mar 2017, 21:56
What is the circumference of the circle above?

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

In order to solve this question, we need to know the radius.

Statement (1) allows us to parse out a formula we need to solve the problem- x/360 times the circumference of the circle or 2pir equals 18; however, there are two variables so we cannot solve this question.

Statement (2) implies an equilateral triangle- we can further the inscribed angle theorem; however, we need a radius length in order to calculate the circumference- we still have two variables

Statement (1) and (2) together are sufficient because they provide each other's missing variable. Hence, Statement (1) and (2) are sufficient.
Manager
Manager
avatar
B
Joined: 06 Dec 2016
Posts: 245
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 14 Mar 2017, 09:55
I understand the first one to be sufficient because an arc is 2/3 of circumference of a circle.
Can someone explain why the second statement is sufficient.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53066
Re: What is the circumference of the circle above?  [#permalink]

Show Tags

New post 14 Mar 2017, 11:20
matthewsmith_89 wrote:
I understand the first one to be sufficient because an arc is 2/3 of circumference of a circle.
Can someone explain why the second statement is sufficient.


The correct answer is C, not D. Please check solution here: https://gmatclub.com/forum/what-is-the- ... ml#p860848
_________________

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

GMAT Club Bot
Re: What is the circumference of the circle above?   [#permalink] 14 Mar 2017, 11:20

Go to page    1   2    Next  [ 24 posts ] 

Display posts from previous: Sort by

What is the circumference of the circle above?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.