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# What is the circumference of circle C ? (1) The radius of circle C is

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What is the circumference of circle C ? (1) The radius of circle C is  [#permalink]

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22 Jun 2018, 01:49
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What is the circumference of circle C ?

(1) The radius of circle C is 2π.
(2) The center of circle C is located at point (7,8) in the xy-plane.

NEW question from GMAT® Official Guide 2019

(DS06397)

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Re: What is the circumference of circle C ? (1) The radius of circle C is  [#permalink]

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22 Jun 2018, 02:03

Circumference = 2πr
We need only radius of the circle.

Statement 1 tells us the radius so it is sufficient.
Statement 2 only tells us the centre. The radius can have any value.
Insufficient.

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Intern
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Re: What is the circumference of circle C ? (1) The radius of circle C is  [#permalink]

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22 Jun 2018, 02:04
A most be the right answer since:

1. gives radius and therefore we can find the circumference.

2. is a tautological
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Re: What is the circumference of circle C ? (1) The radius of circle C is  [#permalink]

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22 Jun 2018, 04:25
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2

Solution

To find:
• The circumference of the circle C

Approach and Working:
To find out the circumference of the circle C, we need to know
• The length of the radius of the circle

Analysing Statement 1
• As per the information given in statement 1, the radius of circle C is 2π
• As we know the length of the radius, we can find out the circumference of the circle

Hence, statement 1 is sufficient to answer the question

Analysing Statement 2
• As per the information given in statement 2, the center of circle C is at (7,8) in the xy plane
• However, to find the length of the radius of the circle, we need to know the coordinate of at least one point which is on the circumference of the circle

Hence, statement 2 is not sufficient to answer

Hence, the correct answer is option A.

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Re: What is the circumference of circle C ? (1) The radius of circle C is  [#permalink]

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23 Jun 2018, 06:46
From Stmt 1:We have been given directly ,radius of the circle from which we can find the circumference ,it straight forward answer.

From Stmt 2:The center of circle C is located at point (7,8) in the xy-plane,which can be substituted in equation to circle formula (x-a)^2 +(y-b)^2 = r^2.
(x-7)^2+(y-8)^2=r^2
from where we can expand to find the radius of circle,i think answer should be D.
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Re: What is the circumference of circle C ? (1) The radius of circle C is  [#permalink]

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23 Jun 2018, 09:37
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Top Contributor
1
Bunuel wrote:
What is the circumference of circle C ?

(1) The radius of circle C is 2π.
(2) The center of circle C is located at point (7,8) in the xy-plane.

Target question: What is the circumference of circle C ?

Statement 1: The radius of circle C is .
Useful formula: circumference = (2π)(radius)
Now that we know the radius is , the circumference = 2π() = 4π²
In other words, the answer to the target question is the circumference of circle C is 4π²
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The center of circle C is located at point (7,8) in the xy-plane.

Notice that there are infinitely many different circles that can have their center at (7,8)
This means there are infinitely many different answers to the target question
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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Re: What is the circumference of circle C ? (1) The radius of circle C is  [#permalink]

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23 Jun 2018, 10:40
alphastallion wrote:
From Stmt 1:We have been given directly ,radius of the circle from which we can find the circumference ,it straight forward answer.

From Stmt 2:The center of circle C is located at point (7,8) in the xy-plane,which can be substituted in equation to circle formula (x-a)^2 +(y-b)^2 = r^2.
(x-7)^2+(y-8)^2=r^2
from where we can expand to find the radius of circle,i think answer should be D.

u substituted a and b with the given values in statement 2.. there is no further given point on the circle which we can substitute in the place of x and y to find r.. this we have one equation and three variables so we cannot find R using statement 2, thus answer is C

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Re: What is the circumference of circle C ? (1) The radius of circle C is  [#permalink]

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13 Jul 2019, 13:56

to know circumference, we need to know radius :
Case 1 : gives us radius: so Sufficient
Case 2 : tell us point 7,8 it passes through . So if we draw line from 7,8 to x and y axis we know 2 sides of triangle, 3rd side can be joined from center to origin, i.e 0,0 . We can calculate third side by pythagores theorem , but still it is not the radii.

If questions says that it passes through origin, then we have other point i.e 0,0 and we can say that this hypotenuse is radii, or if questions gives us any other point it passes through or it lies on its surface. Thus it is insufficient

A is only solution
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Re: What is the circumference of circle C ? (1) The radius of circle C is  [#permalink]

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03 Sep 2019, 05:02
Hi Brent, is it okay that we dont know the value of 'n' in statement 1 ?

GMATPrepNow wrote:
Bunuel wrote:
What is the circumference of circle C ?

(1) The radius of circle C is 2π.
(2) The center of circle C is located at point (7,8) in the xy-plane.

Target question: What is the circumference of circle C ?

Statement 1: The radius of circle C is .
Useful formula: circumference = (2π)(radius)
Now that we know the radius is , the circumference = 2π() = 4π²
In other words, the answer to the target question is the circumference of circle C is 4π²
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Cheers,
Brent
Re: What is the circumference of circle C ? (1) The radius of circle C is   [#permalink] 03 Sep 2019, 05:02
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