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Intern  B
Joined: 30 Aug 2015
Posts: 24
GMAT 1: 570 Q47 V23 GMAT 2: 570 Q42 V27 GMAT 3: 680 Q50 V35 Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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7
51 00:00

Difficulty:   35% (medium)

Question Stats: 72% (02:21) correct 28% (02:33) wrong based on 456 sessions

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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
##### Most Helpful Expert Reply
GMAT Tutor G
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Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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17
10
Explaining the question:
Area of Circle 1 = A1 = Π (r1)^2
Area of Circle 2 = A1 + A2 = Π (r2)^2
Area of Circlet 3 = A1 + A2 + A3 = Π (r3)^2

Solution
To get A1/A2 and A2/A3 we need to express all of these values in terms of one value (A1 or A2 or A3)
STAT1 A2 = A3 alone is not sufficient as i don't know relation of A1 with A2 to find A1/A2
STAT2 A2+A3 = 2 A1 alone is not sufficient as i don't know the individual relationship between A1,A2 and A3

Combining both of them together we have
A2 = A3
A2+A3 = 2 A1
=> 2A3 = 2A1 or A1 = A3 = A2
So A1/A2 and A2/A3 both will be 1 each
So, both together are sufficient => Answer C

Hope it helps!

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

_________________
##### General Discussion
Intern  B
Joined: 12 Aug 2013
Posts: 46
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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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,
Current Student Joined: 28 Feb 2016
Posts: 16
Schools: Wharton '19 (A)
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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1
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.
Current Student G
Joined: 28 Nov 2014
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Schools: Fisher '19 (M\$)
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Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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Bunuel: Can you please help us here. Thanks.

PS: I believe I am over analysing statement II
Board of Directors V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
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Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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1
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.
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Current Student G
Joined: 28 Nov 2014
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Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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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!
Retired Moderator S
Joined: 18 Sep 2014
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Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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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
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Location: Finland
Concentration: General Management, International Business
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Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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1
>> 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
Retired Moderator S
Joined: 18 Sep 2014
Posts: 1104
Location: India
Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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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. Intern  B
Joined: 29 Apr 2015
Posts: 7
Location: Canada
GMAT 1: 690 Q47 V38 GMAT 2: 690 Q49 V35 WE: Corporate Finance (Manufacturing)
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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1
1
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
Current Student P
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GMAT 1: 730 Q50 V38 Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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2
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
Intern  Joined: 10 Jul 2017
Posts: 2
Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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1
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?
Current Student B
Joined: 14 Sep 2015
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GMAT 1: 720 Q49 V39 Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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2
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.
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Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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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.
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Migatte no Gokui
Intern  B
Joined: 09 Apr 2018
Posts: 20
Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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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.
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Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu  [#permalink]

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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... Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu   [#permalink] 14 Apr 2019, 18:03
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# Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu

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