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# M25-23

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Math Expert
Joined: 02 Sep 2009
Posts: 47012

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16 Sep 2014, 01:23
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Difficulty:

15% (low)

Question Stats:

78% (01:10) correct 22% (01:03) wrong based on 354 sessions

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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%

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Math Expert
Joined: 02 Sep 2009
Posts: 47012

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16 Sep 2014, 01:23
3
1
Official Solution:

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.

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Intern
Joined: 07 Sep 2014
Posts: 18
Location: United States (MA)
Concentration: Finance, Economics

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11 Oct 2014, 06:46
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
Manager
Joined: 04 Oct 2013
Posts: 155
Location: India
GMAT Date: 05-23-2015
GPA: 3.45

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24 Oct 2014, 07:14
1
Bunuel wrote:
Official Solution:

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 square 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.

It appears that there is a typo.(indicated in RED color).
Math Expert
Joined: 02 Sep 2009
Posts: 47012

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24 Oct 2014, 08:15
arunspanda wrote:
Bunuel wrote:
Official Solution:

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 square 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.

It appears that there is a typo.(indicated in RED color).

Edited. Thank you.
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Senior Manager
Joined: 12 Feb 2015
Posts: 319

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28 Jun 2018, 09:28
1
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.

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Manish

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Joined: 23 May 2018
Posts: 32
Location: Pakistan

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29 Jun 2018, 01:46
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.
Intern
Joined: 12 Jan 2017
Posts: 16

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06 Jul 2018, 13:21
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%.
Re: M25-23   [#permalink] 06 Jul 2018, 13:21
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# M25-23

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