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Gnpth
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

50% (02:31) correct 50% (02:46) wrong based on 300 sessions

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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


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Attachment:
Capture.PNG
Capture.PNG [ 25.12 KiB | Viewed 13065 times ]
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C
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chetan2u
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GMAT Focus 1: 735 Q90 V89 DI81
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Region Q, shown here, is defined by 26 Nov 2017, 02:44
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Gnpth
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
Show more

Look at the attached figure..
Ans C

Join the parallel lines as shown..
Attachments

IMG_20171126_151118.jpg
IMG_20171126_151118.jpg [ 1.48 MiB | Viewed 12768 times ]

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Region Q, shown here, is defined by 26 Nov 2017, 04:01
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Gnpth
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
Show more


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 =\(\pi * r^2\) \(= 100 *\pi\) = 300

The shaded region is around \(\frac{2}{3}\) of the circle area => \(\frac{2}{3} * 300 = 200\)

Hence, the answer is C
Attachments

circle1.jpg
circle1.jpg [ 20.07 KiB | Viewed 12527 times ]

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Region Q, shown here, is defined by 29 Nov 2017, 00:44
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Vorovski
Gnpth
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 =\(\pi * r^2\) \(= 100 *\pi\) = 300

The shaded region is around \(\frac{2}{3}\) of the circle area => \(\frac{2}{3} * 300 = 200\)

Hence, the answer is C
Show more

Can you eloborate how you arrived at 2/3??
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Region Q, shown here, is defined by 29 Nov 2017, 00:45
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chetan2u
Gnpth
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..
Show more

Expert can you post a clear cut solution... image is not that clear?
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Region Q, shown here, is defined by 29 Nov 2017, 01:57
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Vorovski
Gnpth
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 =\(\pi * r^2\) \(= 100 *\pi\) = 300

The shaded region is around \(\frac{2}{3}\) of the circle area => \(\frac{2}{3} * 300 = 200\)

Hence, the answer is C

Can you eloborate how you arrived at 2/3??
Show more

The shaded region is around 70% of the circle and 70% is around 2/3.
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Region Q, shown here, is defined by 29 Nov 2017, 03:20
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Gnpth
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
Show more

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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Region Q, shown here, is defined by 26 Oct 2018, 20:41
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A simpler approach- I drew a square around the entire shaded region, the length is 16 and the height is 14, 16x14 = 224, the shaded region would slightly be less than 224, giving you an answer of C
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Interesting question. However can someone please clarify if this kind of question is indeed it in the scope of GMAT exam?

Thank you
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Subtract the black highlighted area from rectangle ABDC

Approximate area = (16*14)- (1/2*2*4)-(1/2*2*4)- (100-25pi)=224-4-4-21.5= 194.5
Option C

Gnpth
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
Show more

Attachments

l.png
l.png [ 26.35 KiB | Viewed 9924 times ]

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Region Q, shown here, is defined by 07 Jun 2020, 13:47
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So basically i did this question in less than 1 min

I saw the square which encompases the Pink area is 14x 16 = 224

So the are should be less than 224

D and E are too big
A and B are too small

i marked C

you can argue that B can be a potential answer, however the approach is still gives you a 50 % chance on a very hard question. (save time take your chance and move ahead)
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Area of the shaded region = Area of Region (1+2+3).........(Kindly refer the image)

Max. Area Of Region-1 => \(\frac{1}{4}\) * Area of circle =>\(\frac{100*\pi}{4}\)=>\(\frac{314}{4}\) =>78.5

Area Of Region-2
As per the image, Region-3 is a trapezium, so, area = \(\frac{1}{2}\) * (14+12)*6 => 78

Area Of Region-3
As per the image, Region-2 is a Rectangle, so, area = 10*4 =>40

Area of the shaded region ~ 78.5 + 78 + 40 =>206.5

Option C
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Then why did the question also include this equation?? Is it to derail the test taker..it's as if the gmat exam curators or "scholars" are trying to make you feel like killing yourself.

Region Q, which is the shaded area shown here, is defined by

(x-6)^2+(y-4)^2 \leq 100 ,(x−6)
​2
​​ +(y−4)
​2
​​ ≤100,

y \geq 0, \text{ and } x \geq 0.y≥0, and x≥0.
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