M25-23

Question

https://gmatclub.com/gmat-practice-tests/resources/import/img/m25-23.png 
 
The diagram above shows a circle inscribed in a square. The area of the shaded region is approximately what percent of the area of the square?

A. 14%
B. 18%
C. 22%
D. 28%
E. 30%

Bunuel · Answer

Official Solution:

https://gmatclub.com/gmat-practice-tests/resources/import/img/m25-23.png 
 
The diagram above shows a circle inscribed in a square. The area of the shaded region is approximately what percent of the area of the square?

A. 14%
B. 18%
C. 22%
D. 28%
E. 30%

Consider the side of the square to be 20 centimeters. Notice that the diameter of the circle equals to the side of the square, hence the radius equals to  \frac{20}{2}=10  centimeters.
 
Next, the area of the square is  20^2=400  square centimeters and the area of the circle is  \pi r^2 = 100 \pi \approx 314  square centimeters. Since the area of the shaded region equals to the difference of those areas then it's  400-314=86  square centimeters. So the area of the shaded region is approximately  \frac{86}{400}*100 \approx 22%  of the area of the square.

Answer: C

bsmith37 · Answer

assigning numbers, assume the radius = 2. Therefore the circle area = 4pi. With a radius = 2, each side of the square = 4, so the area is 16. Now, the area of the sq - area of the circle is what you want. 16 - ~12 = ~4, then ~4 / 16 = slightly less than 1/4, so Ans. C

CAMANISHPARMAR · Answer

Lets pick up a smart number.

Let the side of the square to be 1 inch. side of square = diameter of circle.

Area of square is  1^2  = 1 and area of circle is  \pi r^2 = \frac{1}{4} \pi \approx 0.78

Since the area of the shaded region equals to area of square minus the area of the circle we have  1-0.78=0.22  square inch.

So the area of the shaded region is approximately  \frac{0.22}{1}*100 \approx 22 percent  of the area of the square.
 
Correct Answer: C

MsInvBanker · Answer

I did not have to solve it. Looking at the picture (and knowing it is drawn to scale), I could see what percentage it would be.

RefError · Answer

Area of square = s^2
Area of circle = pi * r^2

r = 1/2 s
2r = s

Compare pi*r^2 with 4*r^2...
pi = 3.14
4 = 4.00
4.00-3.14 = 0.86
1/4 = 25% (=1.0)
20% of 4 = 0.8
Answer has to be someplace between 25% and 20%, so pick 22%.

HWPO · Answer

Bunuel , say one wants to solve it without substituting numbers, i.e.:

Area of square s^2; area of circle pie*r^2 , is there anyway of doing so?

Bunuel · Answer

Just substitute 20 with s in the solution,

Consider the side of the square to be s centimeters. Notice that the diameter of the circle equals to the side of the square, hence the radius equals to  \frac{s}{2}  centimeters.
 
Next, the area of the square is  s^2  square centimeters and the area of the circle is  \pi (s/2)^2  square centimeters. Since the area of the shaded region equals to the difference of those areas then it's  s^2-\pi (s/2)^2=(1 - π/4) s^2 \approx 0.21s^2  square centimeters. So the area of the shaded region is approximately  \frac{0.21s^2}{s^2}*100 \approx 21\%  of the area of the square.

Answer: C

Archit3110 · Answer

let each side of square be 4 are of square 16
for circle the radius is 2 and area is 4pi
area of shaded region 16-4pi 
% of area shaded region to that of square ; 16-4pi/16 ; ~ 22%
option C

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