NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 06:06 It is currently 25 Apr 2024, 06:06
Decision Tracker
My Rewards
New posts
New comers' posts

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

Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu

SORT BY:
Date
Kudos
 1   2   
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
inakihernandez
Intern
Intern
Joined: 30 Aug 2015
Posts: 21
Own Kudos [?]: 1377 [168]
Given Kudos: 8
GMAT 1: 570 Q42 V27
GMAT 2: 680 Q50 V35
Send PM
Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   28 Apr 2016, 11:26
18
Kudos
150
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

76% (02:29) correct 24% (02:41) wrong based on 1440 sessions
Hide Show timer Statistics
Circle 1, Circle 2 and Circle 3 have the same center, and have a radius r1<r2<r3. Let A1 be the area of circle 1, let A2 be the area of the region within Circle 2 and outside Circle 1, and let A3 be the area of the region within Circle 3 and outside Circle 2. What are the values A1/A2 and A2/A3?

(1) A2=A3

(2) A2+A3 = 2 A1
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1777
Own Kudos [?]: 2094 [70]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   Updated on: 14 Jan 2023, 02:45
47
Kudos
23
Bookmarks
Expert Reply
↧↧↧ Video Solution to the Problem ↧↧↧



Explaining the question:
Area of Circle 1 = \(A_1\) = \(Π (r_1)^2\)
Area of Circle 2 = \(A_1\) + \(A_2\) = \(Π (r_2)^2\)
Area of Circlet 3 = \(A_1\) + \(A_2\) + \(A_3\) = \(Π (r_3)^2\)

Solution
To get \(\frac{A_1}{A_2}\) and \(\frac{A_2}{A_3}\) we need to express all of these values in terms of one value (\(A_1\) or \(A_2\) or \(A_3\))
STAT1 \(A_2\) = \(A_3\) alone is not sufficient as I don't know relation of \(A_1\) with \(A_2\) to find \(\frac{A_1}{A_2}\)
STAT2 \(A_2 + A_3\) = 2 \(A_1\) alone is not sufficient as I don't know the individual relationship between \(A_1\),\(A_2\) and \(A_3\)

Combining both of them we have
\(A_2\) = \(A_3\)
\(A_2\)+\(A_3\) = 2 \(A_1\)
=> 2\(A_3\) = 2\(A_1\) or \(A_1\) = \(A_3\) = \(A_2\)
So \(\frac{A_1}{A_2}\) and \(\frac{A_2}{A_3}\) both will be 1 each
So, both together are sufficient.

So, Answer will be C
Hope it helps!


Watch the following video to Learn Basics of Circles


Originally posted by BrushMyQuant on 28 Apr 2016, 12:14.
Last edited by BrushMyQuant on 14 Jan 2023, 02:45, edited 7 times in total.
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29925 [17]
Given Kudos: 799
Location: Canada
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   19 Jun 2019, 08:10
15
Kudos
2
Bookmarks
Expert Reply
Top Contributor
inakihernandez wrote:
Circle 1, Circle 2 and Circle 3 have the same center, and have a radius r1<r2<r3. Let A1 be the area of circle 1, let A2 be the area of the region within Circle 2 and outside Circle 1, and let A3 be the area of the region within Circle 3 and outside Circle 2. What are the values A1/A2 and A2/A3?

(1) A2=A3

(2) A2+A3 = 2 A1


Target question: What are the values A1/A2 and A2/A3?

Statement 1: A2=A3
This will help us determine the value of A2/A3 (it equals 1) but, since we have no information about A1, statement 1 is NOT SUFFICIENT

Statement 2: A2+A3 = 2 A1
This tells us that the COMBINED areas of A2 and A3 are twice the area of A1
So, for example, we COULD have a scenario that looks like this...

..... in which the green area is twice the area of the A1.

Or we COULD have a scenario that looks like this...

Notice that the green area is still twice the area of the A1.

As you can see, the value of A2/A3 is different for each of the above cases.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that A2=A3, so let's let x = the area of each part
Statement 2 tells us that A2+A3 = 2 A1, which means we can now write: x + x = 2(A1)
In other words, 2x = 2(A1), which means A1 = x

So, all 3 regions have area x:


This means A1/A2 = x/x = 1, and A2/A3 = x/x = 1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
General Discussion
User avatar
B
ravisinghal
Intern
Intern
Joined: 12 Aug 2013
Posts: 43
Own Kudos [?]: 22 [1]
Given Kudos: 0
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   19 May 2016, 00:24
1
Kudos
area of circle 2 would be :- 3.14*r2^2 - 3.14 * r1^2
similarly for circle 3 would be :- 3.14*r3^2 - 3.14 * r2^2

however could not establish the relation between A1,A2,A3?

Can someone please explain ? Bunnel can u help here

above explanation,according to me has provided a wrong explanation.

Thanks,
User avatar
GinGMAT
Intern
Intern
Joined: 28 Feb 2016
Posts: 14
Own Kudos [?]: 96 [1]
Given Kudos: 26
Schools: Wharton '19 (A)
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   13 Jun 2016, 15:56
1
Kudos
Could someone please help with this one? How do you disprove statement 2 does not fit? I understand why C is correct but seems too obvious and I spent time trying to understand statement 2.
User avatar
G
keats
Director
Director
Joined: 28 Nov 2014
Posts: 754
Own Kudos [?]: 1263 [0]
Given Kudos: 86
Concentration: Strategy
Schools: Fisher '19 (M$)
GPA: 3.71
Send PM
Reviews Badge
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   26 Aug 2016, 10:16
Bunuel: Can you please help us here. Thanks.

PS: I believe I am over analysing statement II
User avatar
L
abhimahna
Board of Directors
Joined: 18 Jul 2015
Status:Emory Goizueta Alum
Posts: 3600
Own Kudos [?]: 5425 [3]
Given Kudos: 346
Send PM
Reviews Badge
Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   27 Aug 2016, 03:10
3
Kudos
Expert Reply
Keats wrote:
Bunuel: Can you please help us here. Thanks.

PS: I believe I am over analysing statement II


Ok. Let me try helping you out.

See, Statement 2 says A3 + A2 = 2A1.

Even if you go with the approach ravisinghal has given above,

you will not get the values of both the fractions asked.

As per him,

A3 = pi r3^2 - pi r2^2

A2 = pi r2^2 - pi r1^2

A1 = pi r1^2

Substitute these values in the equation given in statement 2.

We will have pi r3^2 - pi r2^2 + pi r2^2 - pi r1^2 = 2(pi r1^2)

or pi r3^2 - pi r1^2 = 2(pi r1^2)

or pi r3^2 = 3(pi r1^2)

or r3=3r1 ( radius cannot be negative)

so, now I give the ball to you. Try substituting these values in A1/A2 and A2/A3, you will NEVER get the real values(independent of variables). Hence, B is insufficient.

(Hint : We donot know what is the relation between r2 and r1 or r3 and r1)

Therefore, with the statement 1, we can find a relation between r2 and r3 and then we can get the relation between r2 and r1, and on substituting we will get the value of each fraction =1.

Hence, C.
User avatar
G
keats
Director
Director
Joined: 28 Nov 2014
Posts: 754
Own Kudos [?]: 1263 [0]
Given Kudos: 86
Concentration: Strategy
Schools: Fisher '19 (M$)
GPA: 3.71
Send PM
Reviews Badge
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   11 Oct 2016, 12:50
I have noted the point you made abhimahna Since there is no relation established between r1 and r3 and r2 and r3 it is impossible to find real value for A1/A2 and A2/A3!
User avatar
G
Nevernevergiveup
Retired Moderator
Joined: 18 Sep 2014
Posts: 1015
Own Kudos [?]: 2755 [1]
Given Kudos: 79
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   29 Oct 2016, 02:34
1
Kudos
inakihernandez wrote:
Circle 1, Circle 2 and Circle 3 have the same center, and have a radius r1<r2<r3. Let A1 be the area of circle 1, let A2 be the area of the region within Circle 2 and outside Circle 1, and let A3 be the area of the region within Circle 3 and outside Circle 2. What are the values A1/A2 and A2/A3?

(1) A2=A3

(2) A2+A3 = 2 A1


Please have a look and let me know if I'm wrong.

I understand that after all the math, we get A1 = A3 = A2 after combining both the statements 1 & 2.

In other words, the solution says areas of all three circles are equal.

But

As per the data mentioned in the question, we have Circles having the same center and distinct radii.
In other words we say that circles having common center and radii are called concentric circles.



My point is when radii are different, it is not possible that areas of 3 circles are equal.
Since radius are r1<r2<r3, we get areas of circles must be A1<A2<A3.
The question must be incorrect for sure.
I want some experts to validate my point
avatar
thapliya
Intern
Intern
Joined: 23 Apr 2016
Posts: 15
Own Kudos [?]: 17 [2]
Given Kudos: 39
Location: Finland
Concentration: General Management, International Business
GPA: 3.65
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   07 Nov 2016, 21:56
2
Kudos
>> In other words, the solution says areas of all three circles are equal.
Nevernevergiveup: A2 and A3 are not area of circle with radii r2 and r3.
A2 is area of circle A2 - Area of Circle A1
A3 is area of circle A3 - Area of circle A2
User avatar
G
Nevernevergiveup
Retired Moderator
Joined: 18 Sep 2014
Posts: 1015
Own Kudos [?]: 2755 [0]
Given Kudos: 79
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   07 Nov 2016, 22:17
thapliya wrote:
>> In other words, the solution says areas of all three circles are equal.
Nevernevergiveup: A2 and A3 are not area of circle with radii r2 and r3.
A2 is area of circle A2 - Area of Circle A1
A3 is area of circle A3 - Area of circle A2


Thanks for the clarification. thapliya.
I really got mistaken.
Possibly a bit overconfident. 8-)
avatar
B
GMATsamurai
Intern
Intern
Joined: 29 Apr 2015
Posts: 4
Own Kudos [?]: 15 [4]
Given Kudos: 0
Location: Canada
Schools: INSEAD Jan'18 (D) IMD Jan'18
GMAT 1: 690 Q49 V35
WE:Corporate Finance (Manufacturing)
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   17 Mar 2017, 08:22
3
Kudos
1
Bookmarks
inakihernandez wrote:
Circle 1, Circle 2 and Circle 3 have the same center, and have a radius r1<r2<r3. Let A1 be the area of circle 1, let A2 be the area of the region within Circle 2 and outside Circle 1, and let A3 be the area of the region within Circle 3 and outside Circle 2. What are the values A1/A2 and A2/A3?

(1) A2=A3

(2) A2+A3 = 2 A1


**************

1) A2 = A3
A1/A2 = ? (we do not have any information about A1)
A2/A3 = A3/A3 = 1
--> INSUFFICIENT

2) A2+A3 = 2*A1
A1 = (A2+A3)/2
Substitute in A1/A2: (A2+A3)/2/A2 = (A2+A3)/(2*A2) = A2/(2*A2) + A3/(2*A2) = 1/2 + A3/(2*A2)
We could try to get A2/A3 but considering A1/A2 did not give a definite answer we can stop and test 1) and 2) simultaneously
--> INSUFFICIENT

1)+2) A2 = A3 AND A2+A3 = 2*A1
A2/A3 = 1 (from 1))
A1/A2 = 1/2 + A3/(2*A2) (from 2))
A2 = A3 so substitution gives us A1/A2 = 1/2 + A3/(2*A3) = 1/2 + 1/2 = 1
--> SUFFICIENT

ANSWER C
User avatar
D
Nikkb
Current Student
Joined: 02 Jul 2017
Posts: 235
Own Kudos [?]: 291 [3]
Given Kudos: 70
Concentration: Entrepreneurship, Technology
Schools: Tepper '20 (M$) McCombs '20 (A) Darden '20 (D) Haas '20 (D) Anderson '20 (D)
GMAT 1: 730 Q50 V38
Send PM
GMAT ToolKit User
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   30 Aug 2017, 11:05
1
Kudos
2
Bookmarks
Given : r1<r2<r3

Also: pi*r1^2 =A1
pi*r2^2 -pi*r1^2 =A2
pi*r3^2 - pi*r2^2 =A3

Find Part 1: A1/A2 and Part 2: A2/A3

1) A2=A3

So A2/A3 = 1 . We got answer of 2nd part

Now A1/A2 =? We dont have any additional information to solve this. So No we are not able to find 1st part.

So option 1 not Sufficient


2) A2+A3=2A1

substitute equations here:

A2+A3=2A1
(pi*r2^2 -pi*r1^2) + (pi*r3^2 - pi*r2^2) =2*pi*r1^2
pi*r3^2 - pi*r1^2 = 2*pi*r1^2

pi*r3^2 = 3*pi*r1^2

No information we got from here

so option 2 is Not sufficient


1+2
So we already have answer for 2nd part. We have to find 1st part A1/A2

so as A2+A3=2A1 and A2=A3

A2+A2=2A1 => 2A2=2A1

So A1/A2 =1 . Got answer for 1st Part

So sufficient


Answer : C
avatar
strongcat
Intern
Intern
Joined: 10 Jul 2017
Posts: 2
Own Kudos [?]: 3 [3]
Given Kudos: 0
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   17 Sep 2017, 08:23
3
Kudos
Can this one not be simplified as follows?

Just call A1 = X; A2 = Y; A3 = Z

We are looking for 2 ratios.
X / Y and Y / Z

1) Y = Z
Obviously this gives us one of the ratios, but tells us nothing about X. INSUFF

2) Y + Z = 2X
I don't see anyway to get the ratios with that. INSUFF

1 + 2)
We have the Y / Z ratio, but need the X / Y ratio.

Substituting the information in 1 (Y = Z) into the 2nd equation, we get:

Y + Y = 2X
Or 2Y = 2X

So now we can find the other ratio

Forget about the circles. Any flaws here?
avatar
B
neeleshravi
Intern
Intern
Joined: 14 Sep 2015
Posts: 8
Own Kudos [?]: 20 [3]
Given Kudos: 36
Location: India
Schools: HEC Jan 2018 Intake (M)
GMAT 1: 720 Q49 V39
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   21 Oct 2017, 02:57
3
Kudos
I really think this question is trying to distract the test taker and overcomplicate things with all the details about the circles and radii. That information is unnecessary.

Let me know if anything is wrong in my approach here. Admittedly, I got this one wrong while taking the test because I got caught up in all the additional details about circles and areas. After analysing for a bit here's how I would do it instead:

Question asks us to find values of A1/A2 and A2/A3.

Jump to answer choices.

Statement 1. No info about A1. Insuff

Statement 2. Gives us 3 variables, one equation. No further info. Insuff

Combined. Plug in info from St 1 into St 2. We should finally get A1=A2+A3

Now we can find A1/A2 and A2/A3.
User avatar
S
oasis90
Manager
Manager
Joined: 20 Jan 2016
Posts: 56
Own Kudos [?]: 61 [0]
Given Kudos: 68
Location: Canada
Schools: HBS '18
WE:Consulting (Other)
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   10 Jun 2018, 12:37
neeleshravi wrote:
I really think this question is trying to distract the test taker and overcomplicate things with all the details about the circles and radii. That information is unnecessary.

Let me know if anything is wrong in my approach here. Admittedly, I got this one wrong while taking the test because I got caught up in all the additional details about circles and areas. After analysing for a bit here's how I would do it instead:

Question asks us to find values of A1/A2 and A2/A3.

Jump to answer choices.

Statement 1. No info about A1. Insuff

Statement 2. Gives us 3 variables, one equation. No further info. Insuff

Combined. Plug in info from St 1 into St 2. We should finally get A1=A2+A3

Now we can find A1/A2 and A2/A3.


Ya I agree. The same thing happened to me. I was trying to link Radiis with areas and make all sorts of connections. After 3 min, I ended up guessing and moving on.
User avatar
B
tann412
Intern
Intern
Joined: 09 Apr 2018
Posts: 16
Own Kudos [?]: 18 [0]
Given Kudos: 35
Send PM
Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   27 Sep 2018, 03:25
I did write on the test, A1 = pie r1^2...
Then I saw A2=A3 and simply got ok, we know one of the ratios is 1. What about 2nd?

Looking at B, it also looked clearly insufficient.

Combining both, its simply 2A1=2A2, Hence the second Ratio is also 1.

This particular questions is nothing but 2 equations in 2 variables. And NO INFO from the questions stem, on radii and stuff is required to solve it. Sometimes, we do complicate things unnecessarily, this is an example. Have noticed more of this happening in IR though.
avatar
B
sumert
Intern
Intern
Joined: 30 Nov 2015
Posts: 27
Own Kudos [?]: 18 [1]
Given Kudos: 92
Location: United States (CO)
WE:Information Technology (Consumer Products)
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   14 Apr 2019, 18:03
1
Bookmarks
This question got me!
Just like others here, I kept banging my head against the wall with the areas (pi (r1 square)) etc.
All you have to do is look at A1/A2 and A2/A3. See if the values given in the options makes it true. Had I done that, I would've got this one right. Alas...
avatar
B
amandesai17
Intern
Intern
Joined: 16 Apr 2018
Posts: 16
Own Kudos [?]: 2 [0]
Given Kudos: 74
Schools: LBS MiM "21 (A)
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   19 Jun 2019, 03:08
GMATPrepNow Can you help me out with this question please?

-Aman
User avatar
P
energetics
Senior Manager
Senior Manager
Joined: 05 Feb 2018
Posts: 312
Own Kudos [?]: 794 [0]
Given Kudos: 325
Send PM
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink] New post   02 Nov 2019, 10:54
inakihernandez wrote:
Circle 1, Circle 2 and Circle 3 have the same center, and have a radius r1<r2<r3. Let A1 be the area of circle 1, let A2 be the area of the region within Circle 2 and outside Circle 1, and let A3 be the area of the region within Circle 3 and outside Circle 2. What are the values A1/A2 and A2/A3?


(1) A2=A3
We are asked for values, so we need to know the definite ratios of A1,A2,A3
From (1) we know that A2/A3 = 1, but no info is given about A1, not sufficient

(2) A2+A3 = 2 A1
We can't determine a value for either A1/A2 or A2/A3 from this

Together:
We know A2=A3 and A2+A3=2A1
A2/A3 = 1 as above
Substitute A2 for A3 --> 2A2 = 2A1
So A1/A2 = 1
Sufficient
GMAT Club Bot
gmatclubot
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink]
02 Nov 2019, 10:54
 1   2   
Moderator:
Bunuel
Math Expert
92912 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions