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M25-23

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M25-23  [#permalink]

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New post 16 Sep 2014, 01:23
1
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A
B
C
D
E

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Question Stats:

79% (01:10) correct 21% (01:03) wrong based on 369 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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M25-23  [#permalink]

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


Image

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
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Re: M25-23  [#permalink]

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New post 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
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M25-23  [#permalink]

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


Image

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.


Answer: C


It appears that there is a typo.(indicated in RED color).
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Re: M25-23  [#permalink]

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


Image

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.


Answer: C


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


Edited. Thank you.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M25-23  [#permalink]

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New post 28 Jun 2018, 09:28
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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
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Re: M25-23  [#permalink]

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New post 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.
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Re: M25-23  [#permalink]

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