Region Q, shown here, is defined by

Look at the attached figure..
Ans C

Join the parallel lines as shown..

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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??

Expert can you post a clear cut solution... image is not that clear?

The shaded region is around 70% of the circle and 70% is around 2/3.

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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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

Interesting question. However can someone please clarify if this kind of question is indeed it in the scope of GMAT exam?

Thank you

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

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)

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

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.