Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Jul 2014, 16:01

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If points A and B are randomly placed on the circumference

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1318
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 56

Kudos [?]: 453 [1] , given: 157

GMAT ToolKit User GMAT Tests User
If points A and B are randomly placed on the circumference [#permalink] New post 19 Jun 2010, 13:14
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

56% (01:46) correct 44% (01:27) wrong based on 89 sessions
If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 5/6

_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

Get the best GMAT Prep Resources with GMAT Club Premium Membership

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 175

Kudos [?]: 890 [0], given: 235

GMAT Tests User Reviews Badge
Re: Probability of length of chord AB [#permalink] New post 19 Jun 2010, 14:08
1
This post was
BOOKMARKED
IMO D - 2/3

Probability = required length of arc/ circumference

Take chord AB and join A and B with the center.
Find the angle subtended by the chord AB at the center

It will be 60 degrees as sin(AOD) = 1/2 => angle AOD = 30
=> angle AOB = 60
Where D is mid point of the chord

Now for the AB > 2 the angle subtended by the chord will be > 60 on one half of the circle and 60 degree on other half of the circle.
Total angle = 120 = 2π/3
So total excluded arc = angle * radius = 2πr/3
So required arc = 2πr - 2πr/3 = 4πr/3

Probability = (4πr/3) / ( 2πr) = 2/3
hence D

_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html


Last edited by gurpreetsingh on 19 Jun 2010, 14:10, edited 1 time in total.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18683
Followers: 3232

Kudos [?]: 22200 [0], given: 2601

Re: Probability of length of chord AB [#permalink] New post 19 Jun 2010, 14:09
Expert's post
Hussain15 wrote:
If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4


Not a GMAT question. Looks like: [Bertrand paradox]

One of the solutions:

Let C be the center of the circle.

Place point A on any place on the circumference. Now, if \angle{ACB}=60, then chord AB=raius=2, so if \angle{ACB}<60, AB<raius=2. But point B can be placed either clockwise or anticlockwise from A. Which means that if B falls in 60 degrees in either of direction from A, AB will be less than radius. Total circumference 360 degrees restricted area 60*2=120 degrees so P(AB>2)=\frac{360-120}{360}=\frac{2}{3}.

But answer can also be \frac{3}{4} or \frac{\sqrt{3}}{2}.

Don't worry about this question.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 175

Kudos [?]: 890 [0], given: 235

GMAT Tests User Reviews Badge
Re: Probability of length of chord AB [#permalink] New post 19 Jun 2010, 14:12
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 175

Kudos [?]: 890 [0], given: 235

GMAT Tests User Reviews Badge
Re: Probability of length of chord AB [#permalink] New post 19 Jun 2010, 14:16
Bunnel, could you analyze this question...
how-many-times-swimmers-meet-93953.html#p722693

Is this GMAT question? The user has not posted the OA and OE, though I have solved it but need expert comments.

_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18683
Followers: 3232

Kudos [?]: 22200 [0], given: 2601

Re: Probability of length of chord AB [#permalink] New post 19 Jun 2010, 14:22
Expert's post
gurpreetsingh wrote:
how 3/4 is possible?


http://mathforum.org/library/drmath/view/66793.html
http://mathworld.wolfram.com/BertrandsProblem.html

Again, please don't worry about this question.

gurpreetsingh wrote:
Bunnel, could you analyze this question...
how-many-times-swimmers-meet-93953.html#p722693

Is this GMAT question? The user has not posted the OA and OE, though I have solved it but need expert comments.


Again not a GMAT question but 13 seems to be a correct answer.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 12 Feb 2012
Posts: 106
Followers: 1

Kudos [?]: 9 [0], given: 28

Re: Probability of length of chord AB [#permalink] New post 03 Sep 2012, 10:23
This is the way I did it:

I drew a circle and drew a line from the center to the point, forming the radius. I asked myself, if I were to pick a another point on the circle for which the chord is equal to 2, what would the angle be of the radius to the first point and the second point? Well the radius of the circle is 2, so if I wanted to make a chord of length two, all I would have to do it draw a 60,60,60, equaliteral triangle from the center to the first point and two the first point making a 60 degree angle between them. The same long is used again, If I were to draw a third point, in the other direction to form a chord of length two, the angle between the center and the first and third point would be 60*. Hence for any single point on the circle, the two point that can be possible be drawn to generate a length of 2, from that first point span 60+60=120*. Everything above that degree and we have a chord bigger than 2. Now 1-(120/360*2*pi*r)=1/3. Hope that made sense
Senior Manager
Senior Manager
avatar
Joined: 15 Jun 2010
Posts: 363
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Followers: 6

Kudos [?]: 134 [0], given: 50

GMAT Tests User Reviews Badge
Re: Probability of length of chord AB [#permalink] New post 03 Sep 2012, 10:46
Hussain15 wrote:
If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 5/6


I don't know whether I am correct or not.

Probability of chord greater than 2 = 1- probability of chord less than or equal to 2.
Probability of chord less than or equal to 2 = (Length of circumference of shaded circle)/ Length of circumference = [(60/360)2*pi*2] / [2*pi*2] ie. [(4/6)*pi]/[4*pi] ie 1/6.
Hence, Probability of chord greater than 2 = 1-1/6 =5/6. Choice E.

Attachments

123.JPG
123.JPG [ 11.15 KiB | Viewed 3116 times ]


_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Current Student
avatar
Joined: 18 Jun 2012
Posts: 145
Concentration: Healthcare, General Management
GMAT Date: 09-14-2012
Followers: 1

Kudos [?]: 14 [0], given: 1

Re: Probability of length of chord AB [#permalink] New post 03 Sep 2012, 17:17
2/3. There are only 2 chords of 2 in that can be drawn..on adjacent equilateral triangles. These triangles take up 120 degrees of the circle...leaving 240 degrees outside the probable area...hence 240/360=2/3.
Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4558
Location: Pune, India
Followers: 1028

Kudos [?]: 4449 [2] , given: 162

Re: Probability of length of chord AB [#permalink] New post 03 Sep 2012, 20:59
2
This post received
KUDOS
Expert's post
SOURH7WK wrote:
Hussain15 wrote:
If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 5/6


I don't know whether I am correct or not.

Probability of chord greater than 2 = 1- probability of chord less than or equal to 2.
Probability of chord less than or equal to 2 = (Length of circumference of shaded circle)/ Length of circumference = [(60/360)2*pi*2] / [2*pi*2] ie. [(4/6)*pi]/[4*pi] ie 1/6.
Hence, Probability of chord greater than 2 = 1-1/6 =5/6. Choice E.


There is one little point you missed (using the method you have used to find the way the chord is chosen). Say you put the first point anywhere on the circumference. Now, you have found that if you put the other point on 1/6th of the circumference (right next to the first point), the chord length will be less than or equal to 2. But you have to consider the 1/6th of the circle on the other side of the point too. Say, in your diagram, the left vertex of the triangle lying on the circle is A, the first point. Now B can be to the right of A or to the left of A. So you can put B on 1/3rd of the circle and still get a chord less than or equal to 2. So answer will be 2/3.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior Manager
avatar
Joined: 15 Jun 2010
Posts: 363
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Followers: 6

Kudos [?]: 134 [0], given: 50

GMAT Tests User Reviews Badge
Re: Probability of length of chord AB [#permalink] New post 04 Sep 2012, 00:27
VeritasPrepKarishma wrote:
SOURH7WK wrote:
Hussain15 wrote:
If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 5/6


I don't know whether I am correct or not.

Probability of chord greater than 2 = 1- probability of chord less than or equal to 2.
Probability of chord less than or equal to 2 = (Length of circumference of shaded circle)/ Length of circumference = [(60/360)2*pi*2] / [2*pi*2] ie. [(4/6)*pi]/[4*pi] ie 1/6.
Hence, Probability of chord greater than 2 = 1-1/6 =5/6. Choice E.


There is one little point you missed (using the method you have used to find the way the chord is chosen). Say you put the first point anywhere on the circumference. Now, you have found that if you put the other point on 1/6th of the circumference (right next to the first point), the chord length will be less than or equal to 2. But you have to consider the 1/6th of the circle on the other side of the point too. Say, in your diagram, the left vertex of the triangle lying on the circle is A, the first point. Now B can be to the right of A or to the left of A. So you can put B on 1/3rd of the circle and still get a chord less than or equal to 2. So answer will be 2/3.


Thanks Karishma!!!. I have not thought of that possibility. So I have to add another 1/6.

_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Intern
Intern
avatar
Joined: 23 Oct 2012
Posts: 2
Schools: LBS '14
GMAT 1: 720 Q50 V37
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: If points A and B are randomly placed on the circumference [#permalink] New post 10 Nov 2012, 23:18
kapsycumm wrote:
If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?
A. \frac{1}{4}
B. \frac{1}{3}
C. \frac{1}{2}
D. \frac{2}{3}
E. \frac{3}{4}


I think one way of answering this question is:

Let us assume that the center is A and the two ends of the chord are B and C.

Let us first assume that the length of the chord is 2.

If the length of the chord has to be 2 to start with. The triangle created by drawing lines from the two ends of the chord to the center would be an equilateral triangle.

Which means angle BAC would be 60 degrees. If the angle BAC is less than 60 then the length of the chord would be less than 2 and if it is more than 60 it would be greater than 2.

This means that there are 120 possibilities for angle BAC where the length of BC would be greater than 2.

The probability would therefore be 120/180 = > 2/3
Senior Manager
Senior Manager
avatar
Joined: 10 Apr 2012
Posts: 265
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 2

Kudos [?]: 78 [0], given: 318

GMAT ToolKit User Premium Member CAT Tests
If points A and B are randomly placed on the circumference [#permalink] New post 29 Nov 2013, 22:18
If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?
A)1/4
B)1/3
C)1/2
D)2/3
E)3/4
Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1226
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 61

Kudos [?]: 623 [0], given: 116

GMAT Tests User Premium Member
Re: If points A and B are randomly placed on the circumference [#permalink] New post 29 Nov 2013, 22:26
If the length of the chord is 2, then the radii joining the ends of the chord to the centre form an equilateral triangle. i.e the angle between A & B from the centre has to be 60.

If A is a random point on the circumference then B can be any point further than 60 degrees of A on either side of A.
i.e 60 degrees on either side of A is out of bounds.
i.e 120 degress of the circumference is out of bounds.
So probability = 360-120/360 = 240/360 = 2/3

Answer is D

_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18683
Followers: 3232

Kudos [?]: 22200 [0], given: 2601

Re: If points A and B are randomly placed on the circumference [#permalink] New post 30 Nov 2013, 03:03
Expert's post
guerrero25 wrote:
If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?
A)1/4
B)1/3
C)1/2
D)2/3
E)3/4


Merging similar topics. Please refer to the solutions above.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: If points A and B are randomly placed on the circumference   [#permalink] 30 Nov 2013, 03:03
    Similar topics Author Replies Last post
Similar
Topics:
7 Experts publish their posts in the topic Point P(a,b) is randomly selected in the region enclosed by jellybean23 3 26 Sep 2013, 22:51
2 Six numbers are randomly selected and placed within a set. DeepGagan 3 01 Jun 2011, 17:17
1 If points A and B are randomly placed AKProdigy87 1 20 Sep 2009, 18:39
How many points on the circumference of a circle represented ritula 7 27 Jun 2008, 03:39
Six numbers are randomly selected and placed within a set. Caas 11 04 Apr 2007, 07:21
Display posts from previous: Sort by

If points A and B are randomly placed on the circumference

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.