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GMAT Club Legend
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Affiliations: CrackVerbal
Posts: 4950
Location: India
Re: In the figure shown, if the area of the shaded region is 3 times
[#permalink]
26 Aug 2021, 21:08
26 Aug 2021, 21:08
1
Bookmarks
Top Contributor
Area of the shaded region is 3 times the area of the smaller circular region.
Let the smaller circle have r as radius and larger have R as radius.
pi(R)^2 - pi(r)^2 = 3 x pi r^2
=>4 pi r^2 = pi(R)^2
=> r/R = 1/2
=> R = 2r
Circumference of the larger circle C1= 2 * pi *R
= 2 * pi * 2r
= 4*pi*r
Circumference of the smaller circle C2 = 2 * pi * r
C1/C2 = 4*pi*r / 2*pi*r
= 2:1
(option c)
D.S
GMAT SME
Let the smaller circle have r as radius and larger have R as radius.
pi(R)^2 - pi(r)^2 = 3 x pi r^2
=>4 pi r^2 = pi(R)^2
=> r/R = 1/2
=> R = 2r
Circumference of the larger circle C1= 2 * pi *R
= 2 * pi * 2r
= 4*pi*r
Circumference of the smaller circle C2 = 2 * pi * r
C1/C2 = 4*pi*r / 2*pi*r
= 2:1
(option c)
D.S
GMAT SME
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Joined: 17 Jul 2019
Posts: 1312
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45 
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Re: In the figure shown, if the area of the shaded region is 3 times
[#permalink]
04 Oct 2021, 03:37
04 Oct 2021, 03:37
Expert Reply
Video solution from Quant Reasoning:
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Re: In the figure shown, if the area of the shaded region is 3 times
[#permalink]
12 Oct 2021, 00:52
12 Oct 2021, 00:52
1
Bookmarks
The area of the larger circle = The area of the smaller circle + The area of the shaded region
Given,
The area of the smaller circle = x
The area of the shaded region = 3x
So,
The area of the larger circle = x+3x = 4x
Let,
The radius of the smaller circle = 1
The radius of the larger circle = a
The area of the smaller circle= π (1)^2 = π
The area of the larger circle = 4π
so,
πa^2 = 4π
a^2 = 4
a= 2
Now,
Circumference of the smaller circle = 2π.1 = 2π
Circumference of the larger circle = 2π.2 = 4π
So, (4π/2π)= 2 times.
The Answer is C.
Is this the right approach Bunuel ?
Given,
The area of the smaller circle = x
The area of the shaded region = 3x
So,
The area of the larger circle = x+3x = 4x
Let,
The radius of the smaller circle = 1
The radius of the larger circle = a
The area of the smaller circle= π (1)^2 = π
The area of the larger circle = 4π
so,
πa^2 = 4π
a^2 = 4
a= 2
Now,
Circumference of the smaller circle = 2π.1 = 2π
Circumference of the larger circle = 2π.2 = 4π
So, (4π/2π)= 2 times.
The Answer is C.
Is this the right approach Bunuel ?
In the figure shown, if the area of the shaded region is 3 times
[#permalink]
24 Mar 2022, 18:00
24 Mar 2022, 18:00
1
Kudos
EMPOWERgmatRichC wrote:
Hi All,
This question can be solved by TESTing VALUES.
We're told that the area of the shaded region is 3 TIMES the area of the central circle...
Area of center = 1
Area of shaded region = 3(1) = 3
Area of FULL CIRCLE = 1+3 = 4
With those values....
Radius of center = 1
Radius of FULL CIRCLE = 2
The question asks how many times the circumference of the full circle is to the smaller circle...
Circumference of small circle = 2pi
Circumference of full circle = 4pi
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This question can be solved by TESTing VALUES.
We're told that the area of the shaded region is 3 TIMES the area of the central circle...
Area of center = 1
Area of shaded region = 3(1) = 3
Area of FULL CIRCLE = 1+3 = 4
With those values....
Radius of center = 1
Radius of FULL CIRCLE = 2
The question asks how many times the circumference of the full circle is to the smaller circle...
Circumference of small circle = 2pi
Circumference of full circle = 4pi
Final Answer:
GMAT assassins aren't born, they're made,
Rich
EMPOWERgmatRichC
How do you get to the radius of the center being 1 and the radius of the full circle being 2? What is the math there? I am confused because if I solve for the radius for the circle that has an area of 1... I set 1=pier^2 which gives you the squareroot of (1/pie) which is not 1. Thank you
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Status:GMAT Assassin/Co-Founder
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Posts: 21846
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GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In the figure shown, if the area of the shaded region is 3 times
[#permalink]
25 Mar 2022, 14:26
25 Mar 2022, 14:26
1
Kudos
Expert Reply
Hi woohoo921,
Thanks for pointing out the missing references to pi in my original post (I've edited the post to correct the issue). The three areas should be represented as:
Area of center = 1pi
Area of shaded region = 3(1pi) = 3pi
Area of FULL CIRCLE = 1pi + 3pi = 4pi
These values would make the radius of the smaller circle equal to 1 and the radius of the larger circle equal to 2 (and the corresponding circumferences would be 2pi and 4pi).
GMAT assassins aren't born, they're made,
Rich
Thanks for pointing out the missing references to pi in my original post (I've edited the post to correct the issue). The three areas should be represented as:
Area of center = 1pi
Area of shaded region = 3(1pi) = 3pi
Area of FULL CIRCLE = 1pi + 3pi = 4pi
These values would make the radius of the smaller circle equal to 1 and the radius of the larger circle equal to 2 (and the corresponding circumferences would be 2pi and 4pi).
GMAT assassins aren't born, they're made,
Rich
Re: In the figure shown, if the area of the shaded region is 3 times
[#permalink]
25 Mar 2022, 16:32
25 Mar 2022, 16:32
1
Kudos
EMPOWERgmatRichC wrote:
Hi woohoo921,
Thanks for pointing out the missing references to pi in my original post (I've edited the post to correct the issue). The three areas should be represented as:
Area of center = 1pi
Area of shaded region = 3(1pi) = 3pi
Area of FULL CIRCLE = 1pi + 3pi = 4pi
These values would make the radius of the smaller circle equal to 1 and the radius of the larger circle equal to 2 (and the corresponding circumferences would be 2pi and 4pi).
GMAT assassins aren't born, they're made,
Rich
Thanks for pointing out the missing references to pi in my original post (I've edited the post to correct the issue). The three areas should be represented as:
Area of center = 1pi
Area of shaded region = 3(1pi) = 3pi
Area of FULL CIRCLE = 1pi + 3pi = 4pi
These values would make the radius of the smaller circle equal to 1 and the radius of the larger circle equal to 2 (and the corresponding circumferences would be 2pi and 4pi).
GMAT assassins aren't born, they're made,
Rich
Thank you! To confirm, you plugged in 1 to area of a circle=(pie)(r^2) to get it equal to => 1pie?
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In the figure shown, if the area of the shaded region is 3 times
[#permalink]
26 Mar 2022, 15:12
26 Mar 2022, 15:12
1
Kudos
Expert Reply
Hi woohoo921,
Yes - by setting the area of the inner circle equal to 1pi (meaning that the radius would equal 1), then all of the other calculations (and additional values) proceed from there.
GMAT assassins aren't born, they're made,
Rich
Yes - by setting the area of the inner circle equal to 1pi (meaning that the radius would equal 1), then all of the other calculations (and additional values) proceed from there.
GMAT assassins aren't born, they're made,
Rich
Re: In the figure shown, if the area of the shaded region is 3 times
[#permalink]
09 Mar 2023, 16:51
09 Mar 2023, 16:51
1
Kudos
The equation for this question is:
Area of the bigger circle - Area of the smaller circle = 3*(Area of the smaller circle)
Area of the bigger circle - Area of the smaller circle = 3*(Area of the smaller circle)
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gmatclubot
Re: In the figure shown, if the area of the shaded region is 3 times [#permalink]
09 Mar 2023, 16:51
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