Coordinate Geometry question

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Spartacus2000: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sun May 01, 2011 2:31 pm

by Spartacus2000 » Thu Aug 11, 2011 3:35 pm

Circle C and line k lie in the xy-plane. If circle C is centered at the origin and the radius 1, does line k intersect circle C?

(1) The x-intercept of the line k is greater than 1

(2) The slope of line k is -1/10

Thanks,

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

e

by pemdas » Thu Aug 11, 2011 11:55 pm

this must be e
st(1) means that the line k can be flat (vertical) or have positive, or negative slope Not Sufficient
st(2) means that the line k is not flat but close to it with the direction from the upper left to the lower right, we need to know the position of line k around the origin though, Not Sufficient
Combined st(1&2) we don't know x-intercept and the angle resulting from the negative slope of line k being set - 1/10 are Not Sufficient

Spartacus2000 wrote:Circle C and line k lie in the xy-plane. If circle C is centered at the origin and the radius 1, does line k intersect circle C?

(1) The x-intercept of the line k is greater than 1

(2) The slope of line k is -1/10

Thanks,

Last edited by pemdas on Fri Aug 12, 2011 1:38 am, edited 2 times in total.

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Fri Aug 12, 2011 12:23 am

Spartacus2000 wrote:Circle C and line k lie in the xy-plane. If circle C is centered at the origin and the radius 1, does line k intersect circle C?

(1) The x-intercept of the line k is greater than 1

(2) The slope of line k is -1/10

Thanks,

Hi, the answer should be E. Pemdas has pretty well described how both stats are individually insuff.
However even taking them together :

1>Draw the circle with radius 1.
2>Take 2 points A(2,0) and B(-8,1).

Draw above in space. Point A satisfies statement 1 and the slope of this line satisfies stat 2. This line intersects the circle.

However, If you take point A(100,0) and B(90,1) this line will Not intersect the circle.

Hence E.

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Fri Aug 12, 2011 12:36 am

bblast wrote:
Spartacus2000 wrote:Circle C and line k lie in the xy-plane. If circle C is centered at the origin and the radius 1, does line k intersect circle C?

(1) The x-intercept of the line k is greater than 1

(2) The slope of line k is -1/10

Thanks,
Hi, the answer should be E. Pemdas has pretty well described how both stats are individually insuff.
However even taking them together :

1>Draw the circle with radius 1.
2>Take 2 points A(2,0) and B(-8,1).

Draw above in space. Point A satisfies statement 1 and the slope of this line satisfies stat 2. This line intersects the circle.

However, If you take point A(100,0) and B(90,1) this line will Not intersect the circle.

Hence E.

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Last edited by pemdas on Fri Aug 12, 2011 1:24 am, edited 1 time in total.

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Fri Aug 12, 2011 12:54 am

Hi,

A Line with a negative slope always passes through quadrants 2 and 4. (top left to bottom right)

From your drawing above it seems as if the line is missing quadrant 2 altogether and in fact has a positive slope. Kindly reconsider my explanation.

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Fri Aug 12, 2011 1:18 am

it's not that line passes through quadr. 2 and 4 (in simplified way, you can say so) - it's the direction as you correctly stated from the upper left to the lower right.

But at the last insight i agree that there can be infinite parallel lines k with the angle/slope -1/10, which i somehow missed while sketching by fixing the x point close to 1 to the RHS

agree it's e

bblast wrote:Hi,

A Line with a negative slope always passes through quadrants 2 and 4. (top left to bottom right)

From your drawing above it seems as if the line is missing quadrant 2 altogether and in fact has a positive slope. Kindly reconsider my explanation.

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