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

It is currently 10 Jul 2014, 16:07

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

In the diagram, points A, B, and C are on the diameter of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Director
Director
avatar
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 563
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 12

Kudos [?]: 208 [3] , given: 217

GMAT Tests User
In the diagram, points A, B, and C are on the diameter of [#permalink] New post 08 Feb 2012, 17:27
3
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

38% (03:23) correct 61% (02:42) wrong based on 202 sessions
Attachment:
Circle.png
Circle.png [ 4.27 KiB | Viewed 3275 times ]
In the diagram, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcs pictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the line YB to the area of the shaded region below the line YB? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)

(A) ¾
(B) 5/6
(C) 1
(D) 7/5
(E) 9/7
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(


Last edited by Bunuel on 14 Jul 2013, 10:01, edited 2 times in total.
Added the OA
Expert Post
12 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3187

Kudos [?]: 21200 [12] , given: 2537

Re: Area of shaded region [#permalink] New post 08 Feb 2012, 17:59
12
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
In the diagram, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcs pictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the line YB to the area of the shaded region below the line YB? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)
(A) ¾
(B) 5/6
(C) 1
(D) 7/5
(E) 9/7
Attachment:
untitled.PNG
untitled.PNG [ 4.59 KiB | Viewed 4703 times ]

According to the central angle theorem <ABY=2*(180-105)=150 (for more on this check Circles chapter of Math Book: math-circles-87957.html). Hence <CBY=180-150=30.

The area of sector ABY=\frac{150}{360}*\pi{r^2}=\frac{5}{12}\pi{r^2};
The area of sector CBY=\frac{30}{360}*\pi{r^2}=\frac{1}{12}\pi{r^2};

The area of each of two small semicircles is \frac{\pi{(\frac{r}{2})^2}}{2}=\pi{\frac{r^2}{8}} (as its radius is half of the radius of the big circle);

The are of the shaded region above BY is \frac{5}{12}\pi{r^2}-\pi{\frac{r^2}{8}=\frac{7}{24}\pi{r^2};
The are of the shaded region below BY is \frac{1}{12}\pi{r^2}+\pi{\frac{r^2}{8}=\frac{5}{24}\pi{r^2};

Ratio of the areas of the shaded regions is \frac{7}{5}.

Answer: D.
_________________

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

Director
Director
avatar
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 563
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 12

Kudos [?]: 208 [0], given: 217

GMAT Tests User
Re: In the diagram, points A, B, and C are on the diameter of [#permalink] New post 11 Feb 2012, 11:18
Hi Bunuel - can you please help? How did you get the area of two small semi circles??
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3187

Kudos [?]: 21200 [1] , given: 2537

Re: In the diagram, points A, B, and C are on the diameter of [#permalink] New post 11 Feb 2012, 12:15
1
This post received
KUDOS
Expert's post
enigma123 wrote:
Hi Bunuel - can you please help? How did you get the area of two small semi circles??


The radius of the small semicircles is r/2, where r is the radius of the large circle. Thus the area of each is half of the area of the circle with the radius of r/2: \frac{\pi{(\frac{r}{2})^2}}{2}=\pi{\frac{r^2}{8}}.

Hope it's clear.
_________________

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

Intern
Intern
avatar
Joined: 16 Dec 2011
Posts: 49
GMAT Date: 04-23-2012
Followers: 0

Kudos [?]: 0 [0], given: 12

Re: In the diagram, points A, B, and C are on the diameter of [#permalink] New post 23 Feb 2012, 06:51
thanks bunuel for nice explanation +1 kudos
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3187

Kudos [?]: 21200 [0], given: 2537

Re: In the diagram, points A, B, and C are on the diameter of [#permalink] New post 20 Jun 2013, 05:39
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


_________________

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: 14 Nov 2011
Posts: 147
Location: United States
Concentration: General Management, Entrepreneurship
Schools: Stanford '15
GPA: 3.61
WE: Consulting (Manufacturing)
Followers: 0

Kudos [?]: 16 [0], given: 97

GMAT ToolKit User
Re: In the diagram, points A, B, and C are on the diameter of [#permalink] New post 22 Jun 2013, 07:27
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE



Hi Bunnel,

Can we have more geometry questions please.
Thanks.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3187

Kudos [?]: 21200 [0], given: 2537

Re: In the diagram, points A, B, and C are on the diameter of [#permalink] New post 22 Jun 2013, 07:39
Expert's post
cumulonimbus wrote:
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE



Hi Bunnel,

Can we have more geometry questions please.
Thanks.


Links to more geometry questions are given in the post you are quoting.
_________________

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

Intern
Intern
avatar
Joined: 08 Sep 2012
Posts: 7
Followers: 0

Kudos [?]: 2 [0], given: 28

Re: Area of shaded region [#permalink] New post 30 Jun 2013, 04:09
Hi Bunel,

I didn't understand the below mentioned part. I did refer to the link provided by you. Can you please can explain this central angle theorem.

"According to the central angle theorem <ABY=2*(180-105)=150 (for more on this check Circles chapter of Math Book: math-circles-87957.html). Hence <CBY=180-150=30"

Thank you
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3187

Kudos [?]: 21200 [1] , given: 2537

Re: Area of shaded region [#permalink] New post 30 Jun 2013, 07:58
1
This post received
KUDOS
Expert's post
Genfi wrote:
Hi Bunel,

I didn't understand the below mentioned part. I did refer to the link provided by you. Can you please can explain this central angle theorem.

"According to the central angle theorem <ABY=2*(180-105)=150 (for more on this check Circles chapter of Math Book: math-circles-87957.html). Hence <CBY=180-150=30"

Thank you


Check the diagram below:
Attachment:
.png
.png [ 5.5 KiB | Viewed 3395 times ]


The same as here:
Image

Hope it's clear.
_________________

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

1 KUDOS received
Intern
Intern
avatar
Joined: 24 Jun 2013
Posts: 14
Followers: 0

Kudos [?]: 3 [1] , given: 2

Re: In the diagram, points A, B, and C are on the diameter of [#permalink] New post 12 Jun 2014, 01:36
1
This post received
KUDOS
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE



It can also be solved the following way:

Three new triangles can be formed which will be isosceles triangles (please refer the attachment)
Hence,
x+y = 105 (given)
2(x+y+z) = 360 since ACYX is a quadrilateral
x+y+z = 180
-> z = 75

in Triangle, BYC, <YBC will be 180 - 2*z = 180 - 2*75 = 30 degrees.

(1) Area of the total shaded portion is half the area of the circle pi*(r^2)/2

(2) Area below the red line = area of segment BYC of circle + area of shaded semicircle BC
= (30/360)*(pi*r^2) + pi ((r/2)^2)/2
=pi*(r^2)/12+pi*(r^2)/8
=5 * pi * (r^2) / 24

(3) Area above the red line is (1)-(2) above
= [ pi * (r^2)/2 ] - [ 5 * pi* (r^2) / 24 ]
= 7 * pi * (r^2) / 24

Answer is (3) / (2) which is 7/5

Kudos if you like the post :)
Attachments

Circle 1.png
Circle 1.png [ 6.08 KiB | Viewed 632 times ]

Intern
Intern
avatar
Joined: 17 Apr 2013
Posts: 9
Followers: 0

Kudos [?]: 0 [0], given: 51

GMAT ToolKit User
Re: In the diagram, points A, B, and C are on the diameter of [#permalink] New post 25 Jun 2014, 23:20
I Thought that's a nice question for a strategic guess (50/50) since the shaded area above the line seemed bigger therefore the answer should be either 3/4 or 5/6 but they tricked me !! :(
Re: In the diagram, points A, B, and C are on the diameter of   [#permalink] 25 Jun 2014, 23:20
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic In the diagram above, points A, O, and B all lie on a dia saintforlife 6 15 Oct 2013, 07:09
2 Experts publish their posts in the topic If A, B, and C are distinct points metallicafan 12 04 Jul 2012, 16:22
2 In the diagram above, points A, B, C, D, and E represent the boomtangboy 4 28 Apr 2012, 20:31
In the diagram to the right, points A, B, and C are on the sludge 4 18 Sep 2007, 16:34
In the diagram above, points A, B, C, D, and E represent the Avis 1 26 Feb 2006, 09:44
Display posts from previous: Sort by

In the diagram, points A, B, and C are on the diameter of

  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®.