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Math Expert V
Joined: 02 Sep 2009
Posts: 58427
In the diagram above, B is the center of the larger circle. AB is the  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 71% (01:12) correct 29% (01:07) wrong based on 62 sessions

HideShow timer Statistics In the diagram above, B is the center of the larger circle. AB is the radius of the larger circle and the diameter of the smaller circle. The shaded area is what fraction of the larger circle?

A. 1/8
B. 1/4
C. 1/2
D. 2/3
E. 3/4

Attachment: GRE exam - In the diagram above, B is the center of the larger circle. .jpg [ 12.44 KiB | Viewed 703 times ]

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NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
In the diagram above, B is the center of the larger circle. AB is the  [#permalink]

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AB is the diameter of the smaller circle.
Area = $$\frac{π*AB^2}{4}$$

The radius of bigger circle = AB
Area of the bigger circle = $$π*AB^2$$
Area of the shaded portion = Area of the bigger circle - Area of the smaller circle
$$π*AB^2$$ - $$\frac{π*AB^2}{4}$$
$$\frac{3AB^2}{4}$$ = Shaded area

Now,
$$\frac{3πAB^2}{4}$$/$$πAB^2$$ = 3/4

E is the answer.
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Joined: 18 Aug 2017
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Concentration: Sustainability, Marketing
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Re: In the diagram above, B is the center of the larger circle. AB is the  [#permalink]

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Bunuel wrote: In the diagram above, B is the center of the larger circle. AB is the radius of the larger circle and the diameter of the smaller circle. The shaded area is what fraction of the larger circle?

A. 1/8
B. 1/4
C. 1/2
D. 2/3
E. 3/4

Attachment:
GRE exam - In the diagram above, B is the center of the larger circle. .jpg

let AB = 4
so area of larger circle ; 16pi
and small circle ; 4pi
shaded area = 16-4 = 12 pi
ratio
12pi/16pi ; 3/4
IMO E
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4018
Re: In the diagram above, B is the center of the larger circle. AB is the  [#permalink]

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Top Contributor
Bunuel wrote: In the diagram above, B is the center of the larger circle. AB is the radius of the larger circle and the diameter of the smaller circle. The shaded area is what fraction of the larger circle?

A. 1/8
B. 1/4
C. 1/2
D. 2/3
E. 3/4

Attachment:
GRE exam - In the diagram above, B is the center of the larger circle. .jpg

Let r = radius of SMALLER circle
So, 2r = radius of LARGER circle (since the diameter of the SMALLER circle = radius of LARGER circle)

Area of circle: π(radius)²

Area of SMALLER circle = πr²
Area of LARGER circle = π(2r)² = π4r²

Area of shaded part = area of LARGER circle - area of SMALLER circle
= π4r² - πr²
= π(4r² - r²)
= π3r²

The shaded area is what fraction of the larger circle?
Faction = π3r²/π4r² = 3/4

Cheers,
Brent
_________________ Re: In the diagram above, B is the center of the larger circle. AB is the   [#permalink] 03 May 2019, 06:26
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In the diagram above, B is the center of the larger circle. AB is the

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