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Three circles with their centers on line segment
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12 May 2021, 06:07
12 May 2021, 06:07
Expert Reply
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Question Stats:
49% (02:04) correct
49% (01:59) wrong based on 28 sessions
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Attachment:
GRE Three circles with their centers .jpg [ 34.1 KiB | Viewed 4997 times ]
Three circles with their centers on line segment 𝐴𝐵 are tangent at points 𝐴, 𝐹, and 𝐵, where point 𝐹 lies on line segment 𝐴𝐵.
Quantity A |
Quantity B |
The area of the shaded region |
The area of the unshaded region |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: Three circles with their centers on line segment
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12 May 2021, 19:28
12 May 2021, 19:28
1
In the stem, we are not given the exact value for the radius for both the small circle.
Let's take the radius of both the circle = 1 :: Area of both the circle= \(2 pi\)
The radius of bigger circle = 2 :: Area = \(4 pi\)
So Qt A = Qt B
BUT
if the radius of both the smaller circle is different, then Qt A < Qt B
Answer D
Let's take the radius of both the circle = 1 :: Area of both the circle= \(2 pi\)
The radius of bigger circle = 2 :: Area = \(4 pi\)
So Qt A = Qt B
BUT
if the radius of both the smaller circle is different, then Qt A < Qt B
Answer D
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Three circles with their centers on line segment
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12 May 2021, 22:56
12 May 2021, 22:56
1
Carcass wrote:
Attachment:
GRE Three circles with their centers .jpg
Three circles with their centers on line segment 𝐴𝐵 are tangent at points 𝐴, 𝐹, and 𝐵, where point 𝐹 lies on line segment 𝐴𝐵.
Quantity A |
Quantity B |
The area of the shaded region |
The area of the unshaded region |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Let the radius of bigger circle be R and smaller circle be r
Therefore, radius of largest circle = R + r
Col. A: \(π(R + r)^2 - πR^2 - πr^2\)
Col. B: \(πR^2 + πr^2\)
Col. A: \(2πRr\)
Col. B: \(πR^2 + πr^2\)
Dividing both sides by \(π\);
Col. A: \(2Rr\)
Col. B: \(R^2 + r^2\)
Subtracting \(2Rr\) from both the sides;
Col. A: \(0\)
Col. B: \((R - r)^2\)
We will always have Col. B > Col. A except when R = r
Since, we have no idea about R and r
Hence, option D
