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Region Q, shown here, is defined by [#permalink]
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 25 Nov 2017, 12:11
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Region Q, shown here, is defined by \((x−6)^{2} +(y−4)^{2} \leq 100\), \(y\geq{0}\), and \(x\geq{0}\). What is the approximate area of Region Q in square units? A.between 75 and 125 B.between 125 and 175 C.between 175 and 225 D.between 225 and 275 E.between 275 and 325 Attachment: 
Capture.PNG [ 25.12 KiB | Viewed 803 times ]
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Joined: 02 Aug 2009
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Re: Region Q, shown here, is defined by [#permalink]
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26 Nov 2017, 02:44
Gnpth wrote: Region Q, shown here, is defined by \((x−6)^{2} +(y−4)^{2} \leq 100\), \(y\geq{0}\), and \(x\geq{0}\). What is the approximate area of Region Q in square units? A.between 75 and 125 B.between 125 and 175 C.between 175 and 225 D.between 225 and 275 E.between 275 and 325 Attachment: The attachment Capture.PNG is no longer available Look at the attached figure.. Ans C Join the parallel lines as shown..
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IMG_20171126_151118.jpg [ 1.48 MiB | Viewed 740 times ]
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Joined: 16 Oct 2017
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Concentration: Healthcare, Finance
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Re: Region Q, shown here, is defined by [#permalink]
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26 Nov 2017, 04:01
Gnpth wrote: Region Q, shown here, is defined by \((x−6)^{2} +(y−4)^{2} \leq 100\), \(y\geq{0}\), and \(x\geq{0}\). What is the approximate area of Region Q in square units? A.between 75 and 125 B.between 125 and 175 C.between 175 and 225 D.between 225 and 275 E.between 275 and 325 Attachment: The attachment Capture.PNG is no longer available As we can see the point (6,4) is a centre of the circle. The dash line is a radius wchich is 10. Circle area =\(\pi * r^2\) \(= 100 *\pi\) = 300The shaded region is around \(\frac{2}{3}\) of the circle area => \(\frac{2}{3} * 300 = 200\) Hence, the answer is C
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circle1.jpg [ 20.07 KiB | Viewed 719 times ]
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Joined: 24 Jun 2017
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Re: Region Q, shown here, is defined by [#permalink]
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29 Nov 2017, 00:44
Vorovski wrote: Gnpth wrote: Region Q, shown here, is defined by \((x−6)^{2} +(y−4)^{2} \leq 100\), \(y\geq{0}\), and \(x\geq{0}\). What is the approximate area of Region Q in square units? A.between 75 and 125 B.between 125 and 175 C.between 175 and 225 D.between 225 and 275 E.between 275 and 325 Attachment: Capture.PNG As we can see the point (6,4) is a centre of the circle. The dash line is a radius wchich is 10. Circle area =\(\pi * r^2\) \(= 100 *\pi\) = 300The shaded region is around \(\frac{2}{3}\) of the circle area => \(\frac{2}{3} * 300 = 200\) Hence, the answer is CCan you eloborate how you arrived at 2/3??
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Re: Region Q, shown here, is defined by [#permalink]
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29 Nov 2017, 00:45
chetan2u wrote: Gnpth wrote: Region Q, shown here, is defined by \((x−6)^{2} +(y−4)^{2} \leq 100\), \(y\geq{0}\), and \(x\geq{0}\). What is the approximate area of Region Q in square units? A.between 75 and 125 B.between 125 and 175 C.between 175 and 225 D.between 225 and 275 E.between 275 and 325 Attachment: Capture.PNG Look at the attached figure.. Ans C Join the parallel lines as shown.. Expert can you post a clear cut solution... image is not that clear?
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Concentration: Healthcare, Finance
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Re: Region Q, shown here, is defined by [#permalink]
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29 Nov 2017, 01:57
Bhadri1199 wrote: Vorovski wrote: Gnpth wrote: Region Q, shown here, is defined by \((x−6)^{2} +(y−4)^{2} \leq 100\), \(y\geq{0}\), and \(x\geq{0}\). What is the approximate area of Region Q in square units? A.between 75 and 125 B.between 125 and 175 C.between 175 and 225 D.between 225 and 275 E.between 275 and 325 Attachment: Capture.PNG As we can see the point (6,4) is a centre of the circle. The dash line is a radius wchich is 10. Circle area =\(\pi * r^2\) \(= 100 *\pi\) = 300The shaded region is around \(\frac{2}{3}\) of the circle area => \(\frac{2}{3} * 300 = 200\) Hence, the answer is CCan you eloborate how you arrived at 2/3?? The shaded region is around 70% of the circle and 70% is around 2/3.
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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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Location: Pune, India
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Re: Region Q, shown here, is defined by [#permalink]
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29 Nov 2017, 03:20
Gnpth wrote: Region Q, shown here, is defined by \((x−6)^{2} +(y−4)^{2} \leq 100\), \(y\geq{0}\), and \(x\geq{0}\). What is the approximate area of Region Q in square units? A.between 75 and 125 B.between 125 and 175 C.between 175 and 225 D.between 225 and 275 E.between 275 and 325 Attachment: Capture.PNG The shaded region could be seen as sum of three areas: a quarter of a circle and two rectangles (the shaded region is a bit less) Area of quarter of a circle \(= (\pi * r^2)/4 = (3.14 * 10^2)/4 = 314/4 = 75\) approx Area of each rectangle \(= 16*4 + 6*10 = 124\) So total shaded area will be a bit less than 75 + 124 = 199 The reduced area at the top of the top rectangle is less than 6*2/2 = 6 The reduced area at the right of the lower triangle will be even less. Answer (C)
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Re: Region Q, shown here, is defined by
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