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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2941
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The surface of a mirror is composed of a rectangular piece that is 9 f
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26 Jul 2022, 02:06
26 Jul 2022, 02:06
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Question Stats:
25% (01:18) correct
75% (02:02) wrong based on 4 sessions
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The surface of a mirror is composed of a rectangular piece that is 9 feet long and two semicircular pieces whose diameters are equal to the width of the rectangular piece, as shown in figure. If the ratio of the area of the rectangular piece to the total area of the two semicircular pieces is 9/pi , what is the width of the rectangular piece, in feet?
A. 1
B. 2
C. 3
D. 4
E. 5
Re: The surface of a mirror is composed of a rectangular piece that is 9 f
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27 Jul 2022, 14:05
27 Jul 2022, 14:05
Expert Reply
First, observe that the radius of the semi-circle and the combined circle will be half of width of the rectangle. Next, as per the data given in the question and answer choices, the width should be a multiple of 2. Options A, C and E are ruled out.
Let's check with option B.
If width = 2, area of rectangle = 9*2 = 18
Radius of the circle = 1
Area of the circle = pi
Ratio = 18/pi -> ruled out since we want the ration to be 9/pi.
Answer (D).
Validation:
If width = 4, area of rectangle = 9*4 = 36
Radius of the circle = 2
Area of the circle = 4*pi
Ratio = 9/pi -> good!
Let's check with option B.
If width = 2, area of rectangle = 9*2 = 18
Radius of the circle = 1
Area of the circle = pi
Ratio = 18/pi -> ruled out since we want the ration to be 9/pi.
Answer (D).
Validation:
If width = 4, area of rectangle = 9*4 = 36
Radius of the circle = 2
Area of the circle = 4*pi
Ratio = 9/pi -> good!
gmatclubot
Re: The surface of a mirror is composed of a rectangular piece that is 9 f [#permalink]
27 Jul 2022, 14:05
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