Region Q, shown here, is defined by

Question

https://gmatclub.com/forum/download/file.php?id=38844 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 Capture.PNG

chetan2u · Answer

Look at the attached figure..
Ans C

Join the parallel lines as shown..

Vorovski · Answer

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

Bhadri1199 · Answer

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

Bhadri1199 · Answer

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

Vorovski · Answer

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

KarishmaB · Answer

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)

theoryguy · Answer

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

Manfo · Answer

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

Thank you

nick1816 · Answer

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

RAHUL_GMAT · Answer

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)

rocky620 · Answer

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

justin1993 · Answer

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, 	ext{ and } x \geq 0.y≥0, and x≥0.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Region Q, shown here, is defined by

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Region Q, shown here, is defined by

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards