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Twice the area of the shaded region
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21 Dec 2020, 13:27
21 Dec 2020, 13:27
Expert Reply
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Question Stats:
74% (01:24) correct
24% (01:16) wrong based on 28 sessions
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Attachment:
GRE Twice the area of the shaded region.jpg [ 14.61 KiB | Viewed 2304 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.
Kudos for the right answer and explanation
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Given Kudos: 136
Re: Twice the area of the shaded region
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21 Dec 2020, 16:35
21 Dec 2020, 16:35
1
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
gmatclubot
Re: Twice the area of the shaded region [#permalink]
21 Dec 2020, 16:35
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