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555-605 Level|   Geometry|                           
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CrackverbalGMAT
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In the figure shown, if the area of the shaded region is 3 times 26 Aug 2021, 22:08
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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)

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In the figure shown, if the area of the shaded region is 3 times 04 Oct 2021, 04:37
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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In the figure shown, if the area of the shaded region is 3 times 12 Oct 2021, 01:52
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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 ?
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In the figure shown, if the area of the shaded region is 3 times 24 Mar 2022, 19:00
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EMPOWERgmatRichC
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:
Show Spoiler
C

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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In the figure shown, if the area of the shaded region is 3 times 25 Mar 2022, 15:26
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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).

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In the figure shown, if the area of the shaded region is 3 times 25 Mar 2022, 17:32
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EMPOWERgmatRichC
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

Thank you! To confirm, you plugged in 1 to area of a circle=(pie)(r^2) to get it equal to => 1pie?
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In the figure shown, if the area of the shaded region is 3 times 26 Mar 2022, 16:12
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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.

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Rich
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In the figure shown, if the area of the shaded region is 3 times 09 Mar 2023, 17:51
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The equation for this question is:
Area of the bigger circle - Area of the smaller circle = 3*(Area of the smaller circle)
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In the figure shown, if the area of the shaded region is 3 times 15 Oct 2024, 00:22
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