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11 Jul 2019, 01:39
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
84% (00:33) correct
16%
(00:52)
wrong
based on 58
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In the figure above, the circle is inscribed in the square. What is the area of the shaded region?
(1) The area of the square is 16 square feet.
(2) The area of the circle is 4π square feet.
Attachment:
2019-07-11_1238.png [ 12.29 KiB | Viewed 5942 times ]
11 Jul 2019, 02:01
Kudos
Bookmarks
Bunuel
In the figure above, the circle is inscribed in the square. What is the area of the shaded region?
(1) The area of the square is 16 square feet.
(2) The area of the circle is 1.21π square feet.
Attachment:
2019-07-11_1238.png
Let radius of circle b r
Then side of square = 2r
Area of shaded region =\(4r^2 - \pi r^2 = (4-\pi)r^2\)
S1:
The area of the square is 16 square feet
4r^2 = 16
r=2 since r=-2 is not feasible
Area of shaded region = \(4r^2 - \pi r^2 = (4-\pi)r^2 = (4-\pi)4\)
SUFFICIENT
S2:
The area of the circle is 1.21π square feet
\pi r^2 = 1.21 \pi
r^2 = 1.21
r = 1.1
Area of shaded region = \(4r^2 - \pi r^2 = (4-\pi)r^2 = (4-\pi)1.21\)
SUFFICIENT
BUT EVEN IF Area of shaded region MAY BE DETERMINED by using EITHER statement, they provide different area of shaded region. Therefore, the statements are inconsistent with each other and the question is flawed.
Statement 2 could have been changed as
(2) The area of the circle is 4π square feet.
or
Statement 1 could have been changed as
(2) The area of the square is 4.84 square feet
So removal of inconsistency is required.
IMO D
11 Jul 2019, 02:12
Kudos
Bookmarks
Kinshook
Bunuel
In the figure above, the circle is inscribed in the square. What is the area of the shaded region?
(1) The area of the square is 16 square feet.
(2) The area of the circle is 1.21π square feet.
Attachment:
2019-07-11_1238.png
Let radius of circle b r
Then side of square = 2r
Area of shaded region =\(4r^2 - \pi r^2 = (4-\pi)r^2\)
S1:
The area of the square is 16 square feet
4r^2 = 16
r=2 since r=-2 is not feasible
Area of shaded region = \(4r^2 - \pi r^2 = (4-\pi)r^2 = (4-\pi)4\)
SUFFICIENT
S2:
The area of the circle is 1.21π square feet
\pi r^2 = 1.21 \pi
r^2 = 1.21
r = 1.1
Area of shaded region = \(4r^2 - \pi r^2 = (4-\pi)r^2 = (4-\pi)1.21\)
SUFFICIENT
BUT EVEN IF Area of shaded region MAY BE DETERMINED by using EITHER statement, they provide different area of shaded region. Therefore, the statements are inconsistent with each other and the question is flawed.
Statement 2 could have been changed as
(2) The area of the circle is 4π square feet.
or
Statement 1 could have been changed as
(2) The area of the square is 4.84 square feet
So removal of inconsistency is required.
IMO D
(2) should read: (2) The area of the circle is 4π square feet.
Edited. Thank you for noticing.
