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

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

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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
[Reveal] Spoiler: OA

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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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New post 28 Apr 2016, 12:14
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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

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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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New post 19 May 2016, 00:24
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,

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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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New post 13 Jun 2016, 15:56
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.

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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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New post 26 Aug 2016, 10:16
Bunuel: Can you please help us here. Thanks.

PS: I believe I am over analysing statement II

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

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New post 27 Aug 2016, 03:10
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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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Re: Circle 1, Circle 2 and Circle 3 have the same center, and have a radiu [#permalink]

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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!

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

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New post 29 Oct 2016, 02:34
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.

Image

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

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>> 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

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

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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-)
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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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New post 17 Mar 2017, 08:22
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

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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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New post 30 Aug 2017, 11:05
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

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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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New post 17 Sep 2017, 08:23
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?

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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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New post 21 Oct 2017, 02:57
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] 21 Oct 2017, 02:57
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