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Retired Moderator
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In the floor plan of an executive's beach house above, the north and
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31 Aug 2021, 03:11
31 Aug 2021, 03:11
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Question Stats:
60% (02:49) correct
40% (02:45) wrong based on 25 sessions
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In the floor plan of an executive's beach house.png [ 26.05 KiB | Viewed 3809 times ]
In the floor plan of an executive's beach house above, the north and south walls of the living room are parallel.
Quantity A |
Quantity B |
Floor area, in square feet, of the bedroom |
350 |
A. Quantity A is greater
B. Quantity 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
Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) Edition
GRE - Math Book
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
In the floor plan of an executive's beach house above, the north and
[#permalink]
02 Sep 2021, 05:22
02 Sep 2021, 05:22
1
Explanation:
(Refer to th efigure below)
Since the N and S walls are parallel, we can say △DFB and △DEC are SIMILAR triangles.
i.e. \(\frac{DE}{DF} = \frac{DC}{DB}\)
\(\frac{30}{60} = \frac{DC}{DC + 15}\)
\(DC + 15 = 2DC\)
\(DC = 15\)
This makes △ABD as an Equilateral triangle with each side \(30ft\)
Area of an Equilateral triangle = \(\frac{\sqrt{3}}{4}(side^2) = \frac{\sqrt{3}}{4}(30^2) = \frac{900\sqrt{3}}{4} = 225\sqrt{3}\) \(ft^2\)
Col. A: \(225\sqrt{3} ≈ 390\)
Col. B: \(350\)
Hence, option A
(Refer to th efigure below)
Since the N and S walls are parallel, we can say △DFB and △DEC are SIMILAR triangles.
i.e. \(\frac{DE}{DF} = \frac{DC}{DB}\)
\(\frac{30}{60} = \frac{DC}{DC + 15}\)
\(DC + 15 = 2DC\)
\(DC = 15\)
This makes △ABD as an Equilateral triangle with each side \(30ft\)
Area of an Equilateral triangle = \(\frac{\sqrt{3}}{4}(side^2) = \frac{\sqrt{3}}{4}(30^2) = \frac{900\sqrt{3}}{4} = 225\sqrt{3}\) \(ft^2\)
Col. A: \(225\sqrt{3} ≈ 390\)
Col. B: \(350\)
Hence, option A
Attachments
In the floor plan of an executive's beach house.png [ 28.12 KiB | Viewed 3701 times ]
General Discussion
Re: In the floor plan of an executive's beach house above, the north and
[#permalink]
02 Sep 2021, 01:02
02 Sep 2021, 01:02
Does Anyone have a solution to this question?
