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by awilhelm » Fri Jan 23, 2009 1:23 pm
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 line k is greater than 1
2) The slope of line k is -1/10
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Source: — Data Sufficiency |
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by awesomeusername » Fri Jan 23, 2009 3:13 pm
I believe that knowing both facts is sufficient to answer the question, but both alone are not sufficient.

If we know the slope, that doesn't imply that it will intersect the circle because we don't know where it will cross the x axis.
If we know the x intercept, we don't know what the slope is so we can't say if it intersects the cirlce or not.
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by aroon7 » Fri Jan 23, 2009 6:18 pm
Ans is E

1) implies the line cuts x axis at a point x>1
Insuff because we can draw a line intersecting the circle or not intersecting the circle with this info

2) slope is given. we cant tell the position of the line only with slope - insuff

combining both, still we can draw a line with slope -1/10 which intersects the circle => when x intercept is near 1

also we can shift the line well above parallely such that x intercept is >1 and it doesnt touch the circle
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by chintudave » Sat Jan 24, 2009 11:11 am
IMO - E

Had the x intercept been > 10 the two statements taken together would have solved the problem.
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by gaggleofgirls » Sun Jan 25, 2009 8:44 pm
I also get answer E with the same logic as Aroon.

-Carrie
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