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05 Mar 2015, 10:57
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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:
5%
(low)
Question Stats:
95% (01:04) correct
5%
(02:14)
wrong
based on 152
sessions
History
Date
Time
Result
Not Attempted Yet
Attachment:
chord.png [ 11.26 KiB | Viewed 5096 times ]
A 3π
B 5π
C 6π
D 8π
E 10π
05 Mar 2015, 11:00
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The official solution by Veritas is this one:
"The key to solving this problem is recognizing that to find the circumference you have to know the radius. And since the problem provides you with the center (0, 0) and tells you that the chord intersects the circle at the x-axis, it gives you a roadmap to find exactly that radius: if you can find the second coordinate of that point where the chord intersects the circle (you know that it intersects at the x-axis, which is where y = 0) you have the radius.
Since at that point y = 0, then plug that into the equation for the chord. That wipes out the √3y term, making the equation just x = 5. So that point is (5, 0), meaning that the radius of the circle is 5, and the circumference is then 10π".
Evrything sounds good, but I need to ask about one thing. Why are we assuming that the x in the equation of the line for the chord is the same x as in the point (0,0)? Is this a rule I don't know?
"The key to solving this problem is recognizing that to find the circumference you have to know the radius. And since the problem provides you with the center (0, 0) and tells you that the chord intersects the circle at the x-axis, it gives you a roadmap to find exactly that radius: if you can find the second coordinate of that point where the chord intersects the circle (you know that it intersects at the x-axis, which is where y = 0) you have the radius.
Since at that point y = 0, then plug that into the equation for the chord. That wipes out the √3y term, making the equation just x = 5. So that point is (5, 0), meaning that the radius of the circle is 5, and the circumference is then 10π".
Evrything sounds good, but I need to ask about one thing. Why are we assuming that the x in the equation of the line for the chord is the same x as in the point (0,0)? Is this a rule I don't know?
05 Mar 2015, 13:13
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Hi pacifist85,
Since the prompt opens by telling us that the circle is "centered at the Origin", we're meant to infer that both the circle and the line are on a graph (the phrase "the equation of the chord...." also implies that the X and Y variables represent the various points on that line). The Official GMAT tends to be a bit more 'obvious' about these types of details.
On Test Day, you would likely see the phrase "In the XY co-ordinate plane, the circle is centered at the Origin...." (or some equivalent); that establishes that the question is a graphing question and that you should be thinking in those terms.
GMAT assassins aren't born, they're made,
Rich
Since the prompt opens by telling us that the circle is "centered at the Origin", we're meant to infer that both the circle and the line are on a graph (the phrase "the equation of the chord...." also implies that the X and Y variables represent the various points on that line). The Official GMAT tends to be a bit more 'obvious' about these types of details.
On Test Day, you would likely see the phrase "In the XY co-ordinate plane, the circle is centered at the Origin...." (or some equivalent); that establishes that the question is a graphing question and that you should be thinking in those terms.
GMAT assassins aren't born, they're made,
Rich
