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Circle O is inscribed in square ABCD as shown above. The area of the s

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Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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New post 10 Jan 2016, 08:10
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (01:24) correct 33% (01:10) wrong based on 113 sessions

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Circle O is inscribed in square ABCD as shown above. The area of the shaded region is approximately

A. 10
B. 25
C. 30
D. 50
E. 75

Attachment:
2016-01-10_1908.png
2016-01-10_1908.png [ 4.9 KiB | Viewed 1600 times ]


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Re: Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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New post 10 Jan 2016, 08:29
Bunuel wrote:
Image
Circle O is inscribed in square ABCD as shown above. The area of the shaded region is approximately

A. 10
B. 25
C. 30
D. 50
E. 75

Attachment:
2016-01-10_1908.png



Area of Inscribed Circle = \pi/4 * Area of square
Area of Square = 10*10= 100
Area of circle = \pi/4*100 = 25\pi

Area of parts outside circle but in square = 100-25\pi =100-75 (Approximately)=25

Area of shaded reason = 25/4=6 (Approximately)

The nearest value to 6 is 10. So in test conditions i will opt for A.

Please let me know where am i making mistakes, if i am doing so. I am not sure if the approximate answers can be so further.
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Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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New post 06 Mar 2017, 20:13
Bunuel wrote:
Image
Circle O is inscribed in square ABCD as shown above. The area of the shaded region is approximately

A. 10
B. 25
C. 30
D. 50
E. 75

Attachment:
2016-01-10_1908.png


Area of square = 100
Area of circle = 25π

Area of the shaded region = \(\frac{(100-25π)}{4}\) ~ \(\frac{(100-78.75)}{4}\) ~ \(\frac{21}{4}\)=5.x

Closest is A, which is almost double the calculated value. :S
Can someone help ?
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Re: Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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New post 08 Mar 2017, 14:23
2
This question can be solved logically, in my opinion. Instead of using heavy calculation, we can deduce that the radius is 5- that the radius shown doesn't touch the edge of the square is, again in my opinion, an optical illusion. Actually, if you draw a line from the middle point of any side of the square to the center the radius must be 5. Knowing that the radius must be 5, we can segment a portion of the square- 5 by 5 would be the area of the square that the shaded triangle is contained within; hence, through the process of elimination we can arrive at answer "A." Though this is probably a shoddy method when considering a 700 level question.
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Re: Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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New post 10 Mar 2017, 12:30
Hi Nunuboy1994,

Your approach to this question (and taking advantage of the 'spread' of the answer choices) is a perfectly valid way to approach the question. GMAT prompts are almost always designed so that they can be solved in more than one way (and the math-heavy approach often takes longest), so using every piece of information to your advantage (including the design of the answer choices) can be quite helpful in raising your score and approaching each section in the most efficient way possible. It's not clear what the source of this question actually is, but if something like this were to appear on the Official GMAT, then the answer choices probably wouldn't be as spread out as they are here (meaning that you'd have to do a bit more work to get to the correct answer).

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Re: Circle O is inscribed in square ABCD as shown above. The area of the s  [#permalink]

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New post 08 Jul 2017, 05:35
answer should be around 5.25. n none of the option matches.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


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Re: Circle O is inscribed in square ABCD as shown above. The area of the s   [#permalink] 08 Jul 2017, 05:35
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