GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 Mar 2020, 08:30

### 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

# In the figure above, points A, B, C, D, and E lie on a line. A is on

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

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 173
In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

Updated on: 05 Feb 2019, 22:15
4
102
00:00

Difficulty:

85% (hard)

Question Stats:

59% (02:11) correct 41% (02:04) wrong based on 2133 sessions

### HideShow timer Statistics

In the figure above, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

(1) AB = 3 and BC = 2
(2) CD = 1 and DE = 4

Attachment:

Two circles.png [ 5.47 KiB | Viewed 38422 times ]

Originally posted by Walkabout on 14 Dec 2012, 02:31.
Last edited by Bunuel on 05 Feb 2019, 22:15, edited 1 time in total.
Renamed the topic.
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 62291
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

14 Dec 2012, 02:38
19
20

In the figure above, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

We need to find the value of $$\pi{R^2}-\pi{r^2}$$, where R is the radius of the larger circle and r is the radius of the smaller circle. So, bascally we need to find R and r.

(1) AB = 3 and BC = 2 --> $$AB=r=3$$ and $$AB+BC=AC=5=R$$. Sufficient.

(2) CD = 1 and DE = 4 --> $$CD+DE=CE=R=5$$. Next, $$AD+DE=AE=DIAMETER=2R=10$$, and since $$AD=2r$$, then $$2r+DE=10$$ --> $$2r+4=10$$ --> $$r=3$$. Sufficient.

Answer: D.
_________________
##### Most Helpful Community Reply
Intern
Joined: 07 Mar 2014
Posts: 16
Location: India
Concentration: Entrepreneurship, International Business
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

Updated on: 26 Oct 2015, 00:23
7
2
From the figure we know that:
B is the center of the smaller circle
C is the center of the larger circle
We have to find out area of region i.e area obtained when area of the smaller circle removed from area of the larger circle.

Statement 1

AB=3 and BC= 2

from this statement we know radius of the smaller circle i.e 3(AB) and radius of the larger circle as well $$3+2=5 (AB+BC)$$
using radius of both the circle we can find the area of each circle and hence the required area.
Sufficient

Statement 2

CD=1 and DE=4

from this statement we know that radius of the larger circle is $$1+4=5 (CD+DE)$$
now for the smaller circle,we know that AE=10 and we know DE=4. therefore diameter of the smaller circle is $$10(AE)-4(DE)=6 (AC)$$
therefore radius of the smaller circle $$= 3 (\frac{AC}{2})$$. using radius of both the circle we can find the area of each circle and hence the required area.
Sufficient

Answer D

Originally posted by AayushGMAT on 18 Sep 2014, 13:11.
Last edited by AayushGMAT on 26 Oct 2015, 00:23, edited 1 time in total.
##### General Discussion
Intern
Joined: 06 Jun 2009
Posts: 4
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

14 May 2014, 17:29
Kudos for the solution. I tried to solve the problem twice, but could not get it. I am hoping to start getting solutions to such problems with more practice
Manager
Joined: 12 Feb 2011
Posts: 76
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

01 Jul 2014, 21:55
Bunuel - As we know CE=AC=5 so AD=2r=AC+CD=6, can this be an alternative way to confirm that statement#2 is sufficient?
Math Expert
Joined: 02 Sep 2009
Posts: 62291
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

05 Jul 2014, 06:35
Dienekes wrote:
Bunuel - As we know CE=AC=5 so AD=2r=AC+CD=6, can this be an alternative way to confirm that statement#2 is sufficient?

______________
Yes, that's correct.
_________________
Director
Joined: 19 Apr 2013
Posts: 508
Concentration: Strategy, Healthcare
Schools: Sloan '18 (A)
GMAT 1: 730 Q48 V41
GPA: 4
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

03 Aug 2014, 06:05
Bunuel, are there any similar problems to this one?
Math Expert
Joined: 02 Sep 2009
Posts: 62291
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

12 Aug 2014, 01:49
Ergenekon wrote:
Bunuel, are there any similar problems to this one?

We can consider this question as shaded region problem. Check other Shaded Region Problems in our Special Questions Directory.
_________________
Intern
Joined: 21 Oct 2013
Posts: 2
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

13 Sep 2014, 11:35
In this question Why are we considering C towards left of D its not stated in the question that its in left of D its shown but not stated. C is given that its lie on the same line and its center of larger circle, But what if the C is towards right of D. Then we can not solve this question using only statement 2.

Should the diagram be considered as concrete not flexible?
Math Expert
Joined: 02 Sep 2009
Posts: 62291
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

14 Sep 2014, 16:22
1
Parth Monga wrote:
In this question Why are we considering C towards left of D its not stated in the question that its in left of D its shown but not stated. C is given that its lie on the same line and its center of larger circle, But what if the C is towards right of D. Then we can not solve this question using only statement 2.

Should the diagram be considered as concrete not flexible?

OG13, page 272:
A figure accompanying a data sufficiency problem will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, and so forth exist in the order shown and that angle measures are greater than zero degrees.
All figures lie in a plane unless otherwise indicated.

OG13, page 150:
Figures: A figure accompanying a problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Hope it helps.
_________________
Intern
Joined: 21 Oct 2013
Posts: 2
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

18 Sep 2014, 01:29
Bunuel wrote:
Parth Monga wrote:
In this question Why are we considering C towards left of D its not stated in the question that its in left of D its shown but not stated. C is given that its lie on the same line and its center of larger circle, But what if the C is towards right of D. Then we can not solve this question using only statement 2.

Should the diagram be considered as concrete not flexible?

OG13, page 272:
A figure accompanying a data sufficiency problem will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, and so forth exist in the order shown and that angle measures are greater than zero degrees.
All figures lie in a plane unless otherwise indicated.

OG13, page 150:
Figures: A figure accompanying a problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Hope it helps.

This a lot Bunuel that solves my concern with this question. Thanks a lot for your help.
P.S. the content provided in your signature is quite good and helpful. Really appreciate your work and effort.
NUS School Moderator
Affiliations: Oracle certified java programmer , adobe certified developer
Joined: 14 Jul 2013
Posts: 51
GMAT Date: 02-12-2015
GPA: 3.87
WE: Programming (Telecommunications)
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

27 Sep 2014, 00:08
Walkabout wrote:
Attachment:
Two circles.png
In the figure above, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

(1) AB = 3 and BC = 2
(2) CD = 1 and DE = 4

A - clearly sufficient
B- cd+de= radius so smaller circle can also be found if you use it in opposite direcetion - sufficient
OA:D
_________________
IF IT IS TO BE , IT IS UP TO ME
Manager
Joined: 13 Jun 2012
Posts: 195
Location: United States
WE: Supply Chain Management (Computer Hardware)
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

07 Nov 2014, 01:47
I have one question, how do we know CE is the diameter. The problem never says it is?
Math Expert
Joined: 02 Sep 2009
Posts: 62291
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

07 Nov 2014, 03:47
Turkish wrote:
I have one question, how do we know CE is the diameter. The problem never says it is?

CE is the radius of the large circle because C is its center and E is on its circumference.
_________________
Manager
Joined: 13 Jun 2012
Posts: 195
Location: United States
WE: Supply Chain Management (Computer Hardware)
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

07 Nov 2014, 06:50
Bunuel wrote:
Turkish wrote:
I have one question, how do we know CE is the diameter. The problem never says it is?

CE is the radius of the large circle because C is its center and E is on its circumference.

Sorry Bunuel may be I am not getting this. In the problem it never say E is one the circumference, It says E is on larger circle. Should we believe in what we see,even if its not mentioned?
Math Expert
Joined: 02 Sep 2009
Posts: 62291
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

07 Nov 2014, 07:06
1
Turkish wrote:
Bunuel wrote:
Turkish wrote:
I have one question, how do we know CE is the diameter. The problem never says it is?

CE is the radius of the large circle because C is its center and E is on its circumference.

Sorry Bunuel may be I am not getting this. In the problem it never say E is one the circumference, It says E is on larger circle. Should we believe in what we see,even if its not mentioned?

E is on the larger circle means that E is on the circumference.
_________________
Current Student
Joined: 10 Mar 2013
Posts: 454
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A\$)
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

14 Jul 2015, 04:57
2
1
We need to find AREA (BIG)-(SMALL) --> P*R^2 - P*R^2
1) AB=3, BC=2, R(big)=3+2=5, R(small)=3 Sufficient
2) CD=1, DE=4, Diameter of the big circle = CD+DE=5, Diameter of the small circle = AC+CD=5+1=6, Radius =3 Sufficient
Intern
Joined: 11 Aug 2013
Posts: 24
Location: India
Concentration: Finance, General Management
GMAT 1: 620 Q47 V28
GPA: 3.23
WE: Information Technology (Investment Banking)
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

18 Jul 2015, 09:36
In this question what we need to decide is that area of both the circles can be calculated or not
Area of circle = π r^2
from (1):radius of inner circle = AB=3(given);Radius of outer circle = AC=AB+BC=3+2=5 Both area can be calculated. Hence Sufficient
from(2): radius of outer circle => AC=CE=CD+DE=1+4=5=>AD=AC+CD=5+1=6
radius of inner circle=>AB=BD(since b is the center and D is a point on inner circle)=AD/2=6/2=3. Both area can be calculated. Hence Sufficient

Answer: D
VP
Joined: 09 Mar 2016
Posts: 1220
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

23 Aug 2018, 11:23
Bunuel wrote:

In the figure above, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, 0 is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

We need to find the value of $$\pi{R^2}-\pi{r^2}$$, where R is the radius of the larger circle and r is the radius of the smaller circle. So, bascally we need to find R and r.

(1) AB = 3 and BC = 2 --> $$AB=r=3$$ and $$AB+BC=AC=5=R$$. Sufficient.

(2) CD = 1 and DE = 4 --> $$CD+DE=CE=R=5$$. Next, $$AD+DE=AE=DIAMETER=2R=10$$, and since $$AD=2r$$, then $$2r+DE=10$$ --> $$2r+4=10$$ --> $$r=3$$. Sufficient.

Answer: D.

i dont get is D in the center ?
Math Expert
Joined: 02 Sep 2009
Posts: 62291
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on  [#permalink]

### Show Tags

23 Aug 2018, 19:51
1
dave13 wrote:
Bunuel wrote:

In the figure above, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

We need to find the value of $$\pi{R^2}-\pi{r^2}$$, where R is the radius of the larger circle and r is the radius of the smaller circle. So, bascally we need to find R and r.

(1) AB = 3 and BC = 2 --> $$AB=r=3$$ and $$AB+BC=AC=5=R$$. Sufficient.

(2) CD = 1 and DE = 4 --> $$CD+DE=CE=R=5$$. Next, $$AD+DE=AE=DIAMETER=2R=10$$, and since $$AD=2r$$, then $$2r+DE=10$$ --> $$2r+4=10$$ --> $$r=3$$. Sufficient.

Answer: D.

i dont get is D in the center ?

No, D is not the centre of any circle in the image. Check the highlighted parts.
_________________
Re: In the figure above, points A, B, C, D, and E lie on a line. A is on   [#permalink] 23 Aug 2018, 19:51

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by

# In the figure above, points A, B, C, D, and E lie on a line. A is on

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne