Is it A ?

Equation of the line is y = mx + c

1 - sufficient. We know y = -1/6x + c
For values of x < 6x and negative x, we get +ve y. This proves that
the line passes through quadrant II

2 - insufficient. we just get c = -6. We need slope.

That is correct. OA is (A).

Yes,I agree

I think its always useful to attack the concept as the problems are just twisted around the concept.....
When solving any DS or PS questions from OG11 or GMATPrep,its very useful to find the hidden concept and generalize it so that it can be used for other questions.

eg:From this question it is safe to assume that (From co-ordinate Geometry concepts) :

1.If the slope of a line is negative,the line will always intersect the second quadrant.

2.If the slope of a line is positive,the line will always intersect the first quadrant.

3.If the Slope is zero,Line is parallel to X-axis i.e. of the form Y = C

4.If slope is Undefined,Line is parallel to Y - axis i.e. of the form X = C

I hope I am right in assuming these points!

Good point. Expanding on the first two,

1.If the slope of a line is negative, the line will always intersect the second AND FOURTH quadrants.

2.If the slope of a line is positive, the line will always intersect the first AND THIRD quadrants.

Is that correct? Or did I miss anything obvious?