Geometry DS 1- GMAT PREP

[GMATDUD]

Hi All ,

I would appreciate if someone could take a look at this problem. I think I have this figured out but am not confident about the logic used..

[arawamis]

Answer is E.

(1) is not sufficient alone, as well as (2). A line can intercept x at >1 and can intersect circle for infinite number of cases (there are infinite number of lines going through one point). Or slope can be -1/10 and still can instersect for infinite cases (imagine the line moving along x axis with the same slope). NOT SUFFICIENT

(1) and (2) if line intercepts y axis at 1 than it is tangential to the circle and intercepts x at 10. with any x-intercept point between 1 and 10, line intersects circle. if intercept point is greater than 10 then it does not intercept. NOT SUFFICIENT

[GMATDUD]

Arawamis,

I am not clear about the reasoning on 2. Can you please explain in more detail ?

Thanks for responding .

cheers,
T

[arawamis]

Arawamis,

I am not clear about the reasoning on 2. Can you please explain in more detail ?

Thanks for responding .

cheers,
T

Slope information byitslef is not sufficient where the line intercepts x-axis. Line can intercept x at 1,2,3,4,-100,1000 with -1/10 slope. See that when x-intercept changes y-changes too.
Let me put it this way. If line k has a slope of -2 then its equation is
y=-2*x+a. a can be anything. the value of a does not have any effect on the slope. For example. say y = -2x+5 than x-intercept is 5/2. if y = -2x+12 then x-intercept us 6. Back to the question, depending where line intercepts axis, it may or may not intersect Circle C in the question, Does it make sense?