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Circle C and line K lie in the XY plane. C has its center at

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Circle C and line K lie in the XY plane. C has its center at [#permalink]

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New post 17 Aug 2008, 15:36
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Circle C and line K lie in the XY plane. C has its center at origin and has radius 1. Does k intersect the circle ?

1) x intercept of k is greater than 1.
2) slope of k is -1/10.

Is there a good way to solve this one ? This little pup drained a decent amount of my time and still turned out to be wrong.

OA is E.

My reason involves the concept of tangent as a derivatives. In the neighborhood of 1, the line has to have a slope of nearly infinity to not intersect the circle. Since it is -1/10, and x intercept can be anything greater than 1, you can have k that does and does not intersect the circle.

Kudos [?]: 68 [0], given: 0

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Re: DS problem [#permalink]

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New post 17 Aug 2008, 16:15
bhushangiri wrote:
Circle C and line K lie in the XY plane. C has its center at origin and has radius 1. Does k intersect the circle ?

1) x intercept of k is greater than 1.
2) slope of k is -1/10.

Is there a good way to solve this one ? This little pup drained a decent amount of my time and still turned out to be wrong.

OA is E.

My reason involves the concept of tangent as a derivatives. In the neighborhood of 1, the line has to have a slope of nearly infinity to not intersect the circle. Since it is -1/10, and x intercept can be anything greater than 1, you can have k that does and does not intersect the circle.


You can do this one w/o doing any math. Just visualize a circle in the coordinate plane with center (0,0) and radius 1

(1) Insufficient
If the x intercept is greater than 1, there are lines that don't intersect the circle (e.g., a vertical line). There are lines that do (e.g., lines with very small negative slopes will intercept the top half of the circle)

(2) Slope if -1/10
As long as the x-intercept is sufficiently far away (e.g., at (1000000,0)), this line won't intersect the circle.

(1) and (2)
See explanation for (2)

Kudos [?]: 162 [0], given: 0

Director
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Kudos [?]: 162 [0], given: 0

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Re: DS problem [#permalink]

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New post 17 Aug 2008, 16:18
bhushangiri wrote:
Circle C and line K lie in the XY plane. C has its center at origin and has radius 1. Does k intersect the circle ?

1) x intercept of k is greater than 1.
2) slope of k is -1/10.

Is there a good way to solve this one ? This little pup drained a decent amount of my time and still turned out to be wrong.

OA is E.

My reason involves the concept of tangent as a derivatives. In the neighborhood of 1, the line has to have a slope of nearly infinity to not intersect the circle. Since it is -1/10, and x intercept can be anything greater than 1, you can have k that does and does not intersect the circle.


You're think about it wrong here. In the vicinity of 1, a line of slope -1/10 will intersect, but the problem doesn't say vicinity, it just says greater than.

Kudos [?]: 162 [0], given: 0

Manager
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Re: DS problem [#permalink]

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New post 17 Aug 2008, 16:20
zoinnk wrote:
bhushangiri wrote:
Circle C and line K lie in the XY plane. C has its center at origin and has radius 1. Does k intersect the circle ?

1) x intercept of k is greater than 1.
2) slope of k is -1/10.

Is there a good way to solve this one ? This little pup drained a decent amount of my time and still turned out to be wrong.

OA is E.

My reason involves the concept of tangent as a derivatives. In the neighborhood of 1, the line has to have a slope of nearly infinity to not intersect the circle. Since it is -1/10, and x intercept can be anything greater than 1, you can have k that does and does not intersect the circle.


You can do this one w/o doing any math. Just visualize a circle in the coordinate plane with center (0,0) and radius 1

(1) Insufficient
If the x intercept is greater than 1, there are lines that don't intersect the circle (e.g., a vertical line). There are lines that do (e.g., lines with very small negative slopes will intercept the top half of the circle)

(2) Slope if -1/10
As long as the x-intercept is sufficiently far away (e.g., at (1000000,0)), this line won't intersect the circle.

(1) and (2)
See explanation for (2)



Ya, but how do you make sure that in the neighbour hood of 1, you can get them to intersect when slope is -1/10?
If you can't prove intersection in the neighborhood of 1, then you can have c.

Kudos [?]: 68 [0], given: 0

Director
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Re: DS problem [#permalink]

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New post 17 Aug 2008, 16:27
bhushangiri wrote:
zoinnk wrote:
bhushangiri wrote:
Circle C and line K lie in the XY plane. C has its center at origin and has radius 1. Does k intersect the circle ?

1) x intercept of k is greater than 1.
2) slope of k is -1/10.

Is there a good way to solve this one ? This little pup drained a decent amount of my time and still turned out to be wrong.

OA is E.

My reason involves the concept of tangent as a derivatives. In the neighborhood of 1, the line has to have a slope of nearly infinity to not intersect the circle. Since it is -1/10, and x intercept can be anything greater than 1, you can have k that does and does not intersect the circle.


You can do this one w/o doing any math. Just visualize a circle in the coordinate plane with center (0,0) and radius 1

(1) Insufficient
If the x intercept is greater than 1, there are lines that don't intersect the circle (e.g., a vertical line). There are lines that do (e.g., lines with very small negative slopes will intercept the top half of the circle)

(2) Slope if -1/10
As long as the x-intercept is sufficiently far away (e.g., at (1000000,0)), this line won't intersect the circle.

(1) and (2)
See explanation for (2)



Ya, but how do you make sure that in the neighbour hood of 1, you can get them to intersect when slope is -1/10?
If you can't prove intersection in the neighborhood of 1, then you can have c.


The question is asking you whether you know the line intersects the circle. Because 1+2 has cases where it does and where it doesn't, you don't know. It's only C if the line intersects the circle 100% of the time.

You're not having trouble with the math here. You're having trouble understanding what the data sufficiency section is asking you to decide.

Kudos [?]: 162 [0], given: 0

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Re: DS problem [#permalink]

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New post 17 Aug 2008, 16:35
bhushangiri wrote:
zoinnk wrote:
Ya, but how do you make sure that in the neighbour hood of 1, you can get them to intersect when slope is -1/10?
If you can't prove intersection in the neighborhood of 1, then you can have c.

The question is asking you whether you know the line intersects the circle. Because 1+2 has cases where it does and where it doesn't, you don't know. It's only C if the line intersects the circle 100% of the time.
What if the line does not intersect 100% of the time. It will still be C.
And that is where i had trouble, ascertaining if that was the case.




The question asks: Does k intersect the circle ?

C says: 1 and 2 are sufficient to decide whether k intersects the circle 100% of the time.
E says: 1 and 2 are not sufficient to decide whether k intersects the circle 100% of the time.

Kudos [?]: 162 [0], given: 0

Director
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Re: DS problem [#permalink]

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New post 17 Aug 2008, 16:45
bhushangiri wrote:
I disagree. The question asks "Can you decide whether k intersects the circle or not ? " If it does 100% pf the time, then C. If it never intersects, then also the answer would be C.


Right, and in this case, the line doesn't intersect 100% of the time. A line with slope -1/10 and x intercept at 100000 will not intercept the circle.

Kudos [?]: 162 [0], given: 0

Manager
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Re: DS problem [#permalink]

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New post 17 Aug 2008, 16:52
zoinnk wrote:
bhushangiri wrote:
I disagree. The question asks "Can you decide whether k intersects the circle or not ? " If it does 100% pf the time, then C. If it never intersects, then also the answer would be C.


Right, and in this case, the line doesn't intersect 100% of the time. A line with slope -1/10 and x intercept at 100000 will not intercept the circle.


Thats fine. We are in agreement. But how do u make sure that at x intercept 1.000000000001, k "does" hit the circle.

In the current case, it is intuitive. But if i reduce the slope to something like -10000, then how do you verify ? Now i am digressing from the "GMAT level" issue, but it does pique my curiosity.

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Re: DS problem   [#permalink] 17 Aug 2008, 16:52
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Circle C and line K lie in the XY plane. C has its center at

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