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macjas
Joined: 09 May 2012
Last visit: 30 Jul 2015
Posts: 306
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Affiliations: UWC
Location: Canada
Schools: Rotman '15 (A) Schulich '15 (M)
GMAT 1: 620 Q42 V33
GMAT 2: 680 Q44 V38
GPA: 3.43
WE:Engineering (Media/Entertainment)
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27 May 2012, 09:40
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A
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:
78% (01:37) correct
22%
(01:16)
wrong
based on 222
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In a certain playground, a square sand box rests in a circular plot of grass so that the corners of the sandbox just touch the edge of the plot of grass at points W, X, Y and Z, as shown. What is the distance from point W to point Y?
(1) The area of the circular plot is 49π
(2) The ratio of the area of the sand box to the area of the circular plot is 2/π.
28 May 2012, 00:41
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macjas
we need to fond radius of circle as WY=2r
1) we can get radius => πr^2=49π=> r=7
2) We cannot get radius as acc to statement=>
2/π= area of square/area of circle= (diagonal\sqrt{2})^2/πr^2
diagonal = 2r hence r^2 cancels out=> we cannot find r
Hence A is the answer
28 May 2012, 04:41
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In a certain playground, a square sand box rests in a circular plot of grass so that the corners of the sandbox just touch the edge of the plot of grass at points W, X, Y and Z, as shown. What is the distance from point W to point Y?
The distance from W to Y equals to the diameter so to 2r.
(1) The area of the circular plot is 49π --> \(\pi{r^2}=49\pi\) --> \(r=7\). Sufficient.
(2) The ratio of the area of the sand box to the area of the circular plot is 2/π --> the area of a square is \(\frac{diagonal^2}{2}=\frac{4r^2}{2}=2r^2\) and the area of a circle is \(\pi{r^2}\) --> the ratio thus is \(\frac{2}{\pi}\). So, we already knew that ratio from the stem. Not sufficient.
Answer: A.
The distance from W to Y equals to the diameter so to 2r.
(1) The area of the circular plot is 49π --> \(\pi{r^2}=49\pi\) --> \(r=7\). Sufficient.
(2) The ratio of the area of the sand box to the area of the circular plot is 2/π --> the area of a square is \(\frac{diagonal^2}{2}=\frac{4r^2}{2}=2r^2\) and the area of a circle is \(\pi{r^2}\) --> the ratio thus is \(\frac{2}{\pi}\). So, we already knew that ratio from the stem. Not sufficient.
Answer: A.
