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# In the figure shown, if the area of the shaded region is 3 times

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Intern
Joined: 25 Feb 2017
Posts: 42
Location: Korea, Republic of
Schools: LBS '19 (A)
GMAT 1: 720 Q50 V38
GPA: 3.67
Re: In the figure shown, if the area of the shaded region is 3 times [#permalink]

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02 May 2017, 20:02
In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

(A) 4
(B) 3
(C) 2
(D) 3√3
(E) 2√2

My 2 cents.
Plug in.

So the area of shaded region needs to be 3 times the area of smaller circular region.
Let's say smaller circular region has r=2, so the area would be 4 pi.
As the area of shaded region needs to be 3 times, then it would be 12 pi.
As the area of shaded region can be found by larger - smaller circles, then we have x - 12pi = 4pi.
Then the x would be 16 pi, which means that its radius is 4.

Therefore, the circumference of big circle is 8 pi and that of smaller circle is 4 pi.
Manager
Joined: 22 Nov 2016
Posts: 238
Location: United States
GPA: 3.4
Re: In the figure shown, if the area of the shaded region is 3 times [#permalink]

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06 Jul 2017, 13:45
Using larger radius as x and smaller one as y, we get : $$πx^{2} - πy^{2} = 3πy^{2}$$ OR $$πx^{2} = 4πy^{2}$$............(1)

We need to find the ratio of the circumference, $$\frac{2πx}{2πy}= ?$$ OR $$\frac{x}{y}= ?$$

From (1); $$\frac{x}{y} =\frac{2}{1}$$

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Senior Manager
Joined: 02 Apr 2014
Posts: 467
Re: In the figure shown, if the area of the shaded region is 3 times [#permalink]

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18 Mar 2018, 23:14
shaded region is 3 three times the area of inner circle.

so, total circle area is 4 times the area of inner circle.

big circle area/small circle area = 4/1

(if two triangles are similiar, if the length of the sides are in ratio, k : 1, the area must be k^2 : 1)
we can extend this concept here, since areas are in ratio 4:1, lengths(radius, diameter, circumference) must be in ratio 2:1

(C)
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Joined: 08 Sep 2016
Posts: 56
In the figure shown, if the area of the shaded region is 3 times [#permalink]

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27 Mar 2018, 11:00
Assume smaller circle has the radius of 4. The shaded region has an area 3 times the smaller circle.
Smaller = 16pi
Total circle area = smaller + shadeded = 64pi

64pi = pi*r^2(area of circle)
r= 8 (radius of total circle

circumference - 2*pi*r

Circumference or bigger circle = 2*pi*8 = 16pi
Circuference of smaller circle = 2*pi*4= 8pi

Larger circle circumference is double smaller circle or 2 times the smaller circle
In the figure shown, if the area of the shaded region is 3 times   [#permalink] 27 Mar 2018, 11:00

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