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# What is the circumference of circle O?

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Math Expert
Joined: 02 Sep 2009
Posts: 52343
What is the circumference of circle O?  [#permalink]

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23 Jun 2016, 01:06
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Difficulty:

15% (low)

Question Stats:

83% (00:20) correct 17% (00:27) wrong based on 66 sessions

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What is the circumference of circle O?

(1) The circle inscribes a square.
(2) The perimeter of the square is 10.

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Joined: 04 Jun 2016
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GMAT 1: 750 Q49 V43
What is the circumference of circle O?  [#permalink]

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23 Jun 2016, 01:19
(1) No info about circle or square measurements , No sides, no diagonal, no perimeter, No radius, no area, no diameter = Insufficient
(2) Sufficient
4x=10
x=2.5
sides of squares are each 2.5 unit
diagonal will be $$d^2=(2.5)^2+(2.5)^2$$

A square inscribed in a circle has a diagonal = the diameter of the enveloping circle.
Once you get diameter (which is actually square's diagonal) then you can get circumference = $$pi$$D

Bunuel wrote:
What is the circumference of circle O?

(1) The circle inscribes a square.
(2) The perimeter of the square is 10.

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Re: What is the circumference of circle O?  [#permalink]

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23 Jun 2016, 03:20
LogicGuru1 wrote:
(1) No info about circle or square measurements , No sides, no diagonal, no perimeter, No radius, no area, no diameter = Insufficient
(2) Sufficient
4x=10
x=2.5
sides of squares are each 2.5 unit
diagonal will be $$d^2=(2.5)^2+(2.5)^2$$

A square inscribed in a circle has a diagonal = the diameter of the enveloping circle.
Once you get diameter (which is actually square's diagonal) then you can get circumference = $$pi$$D

Bunuel wrote:
What is the circumference of circle O?

(1) The circle inscribes a square.
(2) The perimeter of the square is 10.

I think the answer is C. Reason being that nowhere in statement 2, it is mentioned whether a square is inscribed in a circle.
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Re: What is the circumference of circle O?  [#permalink]

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23 Jun 2016, 03:25
Bunuel wrote:
What is the circumference of circle O?

(1) The circle inscribes a square.
(2) The perimeter of the square is 10.

Statement 1: The circle inscribes a square
INSUFFICIENT

Statement 2: The perimeter of the square is 10
INSUFFICIENT

Combining both Statements:
Perimeter of square inside a circle = 10
Hence side of the square = 2.5. Diagonal =$$\sqrt{2}$$*2.5
Diagonal of the square = diameter of the circle = 2*radius.
We can calculate the circumference if we have the radius.
SUFFICIENT

Correct Option: C
Attachments

square in circle.JPG [ 13 KiB | Viewed 1082 times ]

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Re: What is the circumference of circle O?  [#permalink]

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23 Jun 2016, 03:31
LogicGuru1 wrote:
(1) No info about circle or square measurements , No sides, no diagonal, no perimeter, No radius, no area, no diameter = Insufficient
(2) Sufficient
4x=10
x=2.5
sides of squares are each 2.5 unit
diagonal will be $$d^2=(2.5)^2+(2.5)^2$$

A square inscribed in a circle has a diagonal = the diameter of the enveloping circle.
Once you get diameter (which is actually square's diagonal) then you can get circumference = $$pi$$D

Bunuel wrote:
What is the circumference of circle O?

(1) The circle inscribes a square.
(2) The perimeter of the square is 10.

The classic mistake of taking informatoin from one statement to another
No where is it mentioned in statement 2 that the circle inscribes the square.
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Status: In the realms of Chaos & Night
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Re: What is the circumference of circle O?  [#permalink]

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23 Jun 2016, 04:03
Bunuel wrote:
What is the circumference of circle O?

(1) The circle inscribes a square.
(2) The perimeter of the square is 10.

Statement 1) Circle inscribes a square - tells us that the square is inside the circle .. Insufficient. Rule out Choice A) & D)

Statement 2) Perimeter of square is 10, let 's' be the length of each side of the square => 4s = 10 => s=2.5
But we have no relation of the square with the circle.
Square may be inscribed or the circle inscribes the square. The side 's' as tangent to the circle. Insufficient Rule out Choice B)

Statement 1) & 2) together - Circle inscribes a square and each side of square is 2.5units.
Rule of geometry - when a circle inscribes a square. the diagonals of the square intersect at right angle at the center point of the circle.

Hence using the pythagoras theorem, one can find the radius 'r' of the circle => r^2+r^2=2.5^2
From this we can find 'r' and calculate the circumference = 2 x pie x r.

Choice C) is the answer Statement 1) & 2) together are sufficient to ans the question.

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Re: What is the circumference of circle O?  [#permalink]

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23 Jun 2016, 04:17
Bunuel wrote:
What is the circumference of circle O?

(1) The circle inscribes a square.
(2) The perimeter of the square is 10.

Statement 1 does not help in getting the "what " part. the exact value is not known.

Not sufficient.

Statement 2 : Obviously not sufficient. (No mention of circle)

When we combine the two:

Perimeter of square is known. Then its side is known (4a = perimeter. a is the side.)
Diagonal is known: a$$\sqrt{2}$$
This diagonal will be the dia of the circle so circumference is known.

Director
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GMAT 1: 750 Q49 V43
Re: What is the circumference of circle O?  [#permalink]

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23 Jun 2016, 05:13

p.s:- Not a good idea to Mix Verbal CR and Quant PS after 8 hours of office work
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Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
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Re: What is the circumference of circle O?  [#permalink]

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23 Jun 2016, 10:45
1
Bunuel wrote:
What is the circumference of circle O?

(1) The circle inscribes a square.
(2) The perimeter of the square is 10.

(1) The circle inscribes a square. We don't know the side of square to calculate radius and circumference. Not sufficient.

(2) The perimeter of the square is 10. Is there any relation of circle and square? Not sufficient

Combining both statement, we can get the side of the square--------> radius of circle-------> circumference of circle.

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Re: What is the circumference of circle O?  [#permalink]

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18 Dec 2018, 22:44
Statement 1. Since we don’t know the sides of square we cannot answer the question using statement 1 alone. Hence, Insufficient.
Statement 2. This statement alone doesn’t have any relevance to the radius of circle. Hence, Insufficient.
Statement 1 & 2 together. By statement 2: side of square is 2.5.
By statement 1. Diameter of circle = side of square.
So, radius of circle = 1.25.Hence, Sufficient.
Re: What is the circumference of circle O? &nbs [#permalink] 18 Dec 2018, 22:44
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