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Updated on: 27 Jun 2012, 04:09
Originally posted by cyberjadugar on 25 Jun 2012, 09:39.
Last edited by cyberjadugar on 27 Jun 2012, 04:09, edited 2 times in total.
Last edited by cyberjadugar on 27 Jun 2012, 04:09, edited 2 times in total.
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
25% (01:17) correct
75%
(01:18)
wrong
based on 107
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What is the area of circle passing points A, B & C (in the given figure), if the angle ABC is 60?
(1) Angle AOC is 120.
(2) OA is 6 units.
(1) Angle AOC is 120.
(2) OA is 6 units.
Attachment:
File comment: Rough Diagram
Q.jpg [ 18.97 KiB | Viewed 4552 times ]
Q.jpg [ 18.97 KiB | Viewed 4552 times ]
Show SpoilerSolution
As per the below diagram, lets say a circle is passing through AOC.
angle AOC = angle AEC, so, irrespective of the fact that O is center or not, it is possible to have any angle as twice of angle ABC.
Thus, even after combining the two statement we can't figure out whether O is center of the circle.
Remember, the angle subtended by arc at the center is twice of the angle subtended by the arc on rest of the circumference but the converse is not true.
A.jpg [ 15.11 KiB | Viewed 4243 times ]
angle AOC = angle AEC, so, irrespective of the fact that O is center or not, it is possible to have any angle as twice of angle ABC.
Thus, even after combining the two statement we can't figure out whether O is center of the circle.
Remember, the angle subtended by arc at the center is twice of the angle subtended by the arc on rest of the circumference but the converse is not true.
Attachment:
A.jpg [ 15.11 KiB | Viewed 4243 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
25 Jun 2012, 10:36
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Both statements are required.
We need the first to prove that 'O' is the centre of the circle and second one to know the radius.
We need the first to prove that 'O' is the centre of the circle and second one to know the radius.
25 Jun 2012, 19:16
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ankushgrover
Hi,
Think about it some more!
Regards,
25 Jun 2012, 20:53
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cyberjadugar
I was supposed to answer B. But that is wrong, why? Because the sufficiency of answer B is pivoted on the assumption that O is indeed the center of the circle. But, this is not the case. The question doesn't tell us that O is the center of the circle. This is a very good assumption/data sufficiency question. It doesn't necessarily mean that ABC is 60 that AOC is already 120. That'd be a wrong assumption. What is OA is an arc? or OA is a line segment not connected to the center?
Now, as like what the poster said above, we need A to prove that O is the center. Now that we know O is the center and from (2) we know that OA is 6 units, we know that the radius of the circle is 6. From that we can know the area of the circle.
