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01 Aug 2017, 12:44
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (02:03) correct
36%
(01:55)
wrong
based on 242
sessions
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Date
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Is the circumference of the smallest circle that is not depicted above that can contain all four identical circles in the given figure equal to \(16 + 16\sqrt{2}*\pi\)?
(1) The radius of one of the small circles is 8
(2) The area of all four circles is \(256\pi\)
Attachment:
gmat-tip-circles-1.png [ 13.49 KiB | Viewed 4670 times ]
03 Aug 2017, 14:28
Kudos
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The answer is D.
If all the four centres of the four circles are joined , it will form a square, we will have a square of length 16 units, from this the diagonal would be 16 √2 , the diameter of the bigger circle would be 16+16 √2 (adding the addtional radii to formulate the diameter). (Please refer the attached figure). This would give us the circumference of the bigger circle as (16+16 √2) π.
Since both 1 and 2 give the same data, each statement alone is sufficient as we have the radii of each circle and by forming a square we can find the diameter of the larger circle, thereby finding out the circumference of the circle.
If all the four centres of the four circles are joined , it will form a square, we will have a square of length 16 units, from this the diagonal would be 16 √2 , the diameter of the bigger circle would be 16+16 √2 (adding the addtional radii to formulate the diameter). (Please refer the attached figure). This would give us the circumference of the bigger circle as (16+16 √2) π.
Since both 1 and 2 give the same data, each statement alone is sufficient as we have the radii of each circle and by forming a square we can find the diameter of the larger circle, thereby finding out the circumference of the circle.
Attachments
image1.JPG [ 990.9 KiB | Viewed 4162 times ]
General Discussion
01 Aug 2017, 20:11
Kudos
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\(16 + 16\sqrt{2}*\pi\)?
Well (1) and (2) gives the same information. So answer must be D or E.
Working out, I got the diameter of larger circle as \(16 + 16\sqrt{2}\)
Circumference of the circle will be 2*pi*r or pi*d
= \(16\pi + 16\sqrt{2}*\pi\)
Which is not equal to one given in prompt.
Hence D.
Am I correct?
I will elaborate once I get to know this is correct
Bunuel: Your questions with suspense answers kill me
Well (1) and (2) gives the same information. So answer must be D or E.
Working out, I got the diameter of larger circle as \(16 + 16\sqrt{2}\)
Circumference of the circle will be 2*pi*r or pi*d
= \(16\pi + 16\sqrt{2}*\pi\)
Which is not equal to one given in prompt.
Hence D.
Am I correct?
I will elaborate once I get to know this is correct
Bunuel: Your questions with suspense answers kill me
