What is the circumference of circle O?

Question

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

LogicGuru1 · Answer

(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

Balajikarthick1990 · Answer

I think the answer is C. Reason being that nowhere in statement 2, it is mentioned whether a square is inscribed in a circle.

OptimusPrepJanielle · Answer

Statement 1: The circle inscribes a square
No information about the radius.
INSUFFICIENT

Statement 2: The perimeter of the square is 10
No information about the circle.
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

OptimusPrepJanielle · Answer

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.

Nightfury14 · Answer

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.

Good luck
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adiagr · Answer

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.

C is the answer.

LogicGuru1 · Answer

Oops.. My bad

C is the correct answer p.s:- Not a good idea to Mix Verbal CR and Quant PS after 8 hours of office work

Divyadisha · Answer

(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.

C is the answer

Krabhay · Answer

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.

What is the circumference of circle O?

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What is the circumference of circle O?

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