coordinate geometry question from powerprep

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shrutib: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Wed May 30, 2012 5:21 am; Thanked: 3 times

by shrutib » Wed May 30, 2012 5:26 am

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

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

Please explain with little background with coordinate geometry. I am little weak in that.

Thank you

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Source: Beat The GMAT — Problem Solving | Wed May 30, 2012 5:26 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed May 30, 2012 6:59 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed May 30, 2012 9:36 pm

shrutib wrote:circle C and line K lie in the XY plane.If Circle C is centered at the origin and has radius 1, does line k intersect circle C?

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

Please explain with little background with coordinate geometry. I am little weak in that.

Thank you

(1) The x-intercept of line K is greater than 1 implies that the x-intercept of line K is towards the right of circle C but this does not imply if line K intersects circle C; NOT sufficient.

(2) The slope of line K is -1/10 implies line K goes down left to right, but again this does not imply if line K intersects circle C; NOT sufficient.

Combining (1) and (2), we do not know the exact intercept of line K, and we cannot find if line K intersects circle C or not; NOT sufficient.

The correct answer is E.

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