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Twice the area of the shaded region

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Carcass
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Twice the area of the shaded region [#permalink] New post   21 Dec 2020, 13:27
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Attachment:
GRE Twice the area of the shaded region.jpg
GRE Twice the area of the shaded region.jpg [ 14.61 KiB | Viewed 2000 times ]


\(O\) is the center of the circle.


Quantity A
Quantity B
Twice the area of the shaded region
The area of the triangle \(AOB\)



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.

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A
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Re: Twice the area of the shaded region [#permalink] New post   21 Dec 2020, 16:35
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Carcass wrote:
Attachment:
GRE Twice the area of the shaded region.jpg


\(O\) is the center of the circle.


Quantity A
Quantity B
Twice the area of the shaded region
The area of the triangle \(AOB\)



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


Area of a triangle \(= \frac{(base)(height)}{2}\)

Area of triangle AOB\(= \frac{(2)(2)}{2}=2\)

QUANTITY B = 2

-----------------------------
Area of a sector \(= (\frac{central angle}{360})\pi r^2\)

Area of sector OAB \(= (\frac{90}{360})(\pi)(2^2)= (\frac{1}{4})(\pi)(4) = \pi\)

So, the area of the shaded region \(= \pi - 2 ≈ 3.14 - 2≈ 1.14\)

QUANTITY A = (2)(1.14) = 2.28

Answer: A
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gmatclubot
Re: Twice the area of the shaded region [#permalink]
21 Dec 2020, 16:35
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