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# Is the perimeter of square S greater than the circumference

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Senior Manager
Status: 1,750 Q's attempted and counting
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Is the perimeter of square S greater than the circumference  [#permalink]

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02 Nov 2013, 00:30
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Difficulty:

25% (medium)

Question Stats:

78% (01:53) correct 22% (02:03) wrong based on 181 sessions

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Is the perimeter of square S greater than the circumference of circle C ?

(1) S is inscribed in circle C.

(2) The ratio of the area of S to the area of C is 2:pi.

GH-05.22.13 | OE to follow
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Re: Is the perimeter of square S greater than the circumference  [#permalink]

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02 Nov 2013, 02:15
avohden wrote:
Is the perimeter of square S greater than the circumference of circle C ?

(1) S is inscribed in circle C.

(2) The ratio of the area of S to the area of C is 2:pi.

GH-05.22.13 | OE to follow

Is 4s>2*pi*r
let side of the square S be 's' and radius of the circle C be 'r'
From stmt1) S is inscribed in circle C, then Diameter 2r becomes the diagonal of the square S, then s^2 + s^2=(2r)^2
=>s^2=2r^2
=>s=r sqrt{2}
then 4*r sqrt{2} is not greater than 2*pi*r (pi=3.14 and sqrt{2} =1.414)
Hence stmt 1 alone is sufficient

From stmt 2) s^2/pi*r^2 = 2/pi
=>s^2=2r^2
=>s=r sqrt{2}
then 4*r sqrt{2}is not greater than 2*pi*r (pi=3.14 and sqrt{2} =1.414)
Hence stmt 2 alone is sufficient

Each stmt alone is sufficient
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Re: Is the perimeter of square S greater than the circumference  [#permalink]

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05 Nov 2013, 20:34
1
Official Explanation

Statement (1) is sufficient: a square inscribed in a circle always has the same relationship with the circle. The diagonal of the square is the diameter of the circle, so you can work out the exact relationship and determine the ratio between the sizes of the figures, which allows you to answer the question.

Statement (2) is also sufficient: if you have the ratio of the areas, you can determine the ratio of the side of the square to the radius of the circle, from which you could compare the perimeter and the circumference of the figures. Choice (D) is correct.
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Re: Is the perimeter of square S greater than the circumference  [#permalink]

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26 Nov 2013, 04:11
1
You can also conclude the sufficiency of statement A just by logically reasoning out, without any calculation. When polygon is inscribed in a circle perimeter of the polygon will always be less than that of circle. This can be inferred because, the distance between any two points is shortest along the straight line joining those two points.

length of line segment (AB) < length of arc (AB)
length of line segment (BC) < length of arc (BC)
length of line segment (CD) < length of arc (CD)
length of line segment (DA) < length of arc (DA)

Perimeter of square ABCD < sum of lengths of arcs => Circumference.
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Re: Is the perimeter of square S greater than the circumference  [#permalink]

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04 Jan 2018, 02:30
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Re: Is the perimeter of square S greater than the circumference   [#permalink] 04 Jan 2018, 02:30
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