Coordinate Geometry, DS, Need help

[PrashantP398]

Hi, The below mentioned question appeared in today's CAT test. As per me, answer for this DS question should be E, but in the explanation it is mentioned as C.

My analysis was that the circle needs to intersect x-axis at two different positive coordinates and should be to the right of Y-axis. This leads me to two solutions as centre of the circle could lie either above or below the x-axis, resulting in either positive or negative slope.

What am I missing here?

A circle is drawn on a coordinate plane. If a line is drawn through the origin and the center of that circle, is the line’s slope less than 1?

(1) No point on the circle has a negative x-coordinate.

(2) The circle intersects the x-axis at two different positive coordinates.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

[RonPurewal]

...
... resulting in either positive or negative slope.

What am I missing here?

you're missing the question that's actually asked. (the question is NOT "is the slope positive?")