Data Sufficiency

You can see the answer here just by drawing scenarios on a coordinate plane, but in words:

Neither statement alone tells you anything about where the lines cross the y-axis.

Together, we know they share a point with a negative x coordinate. If the slope of R is greater than the slope of S, then R rises more quickly as it moves to the right than S does (or it falls more slowly, if they have negative slopes). So as we move right from their intersection point to the y-axis, R will be higher than S, and thus has a greater y-intercept, and the answer is C.

grandh01 wrote:Lines r and s lie in the xy-plane. Is the y-intercept of line r less
than the y-intercept of line s ?
(1) At the intersection point of r and s, the x-coordinate
and y-coordinate are both negative.
(2) The slope of line r is greater than the slope of line s.

oa is c

Let the equation of line r be y = m1x+c1, where m1 is the slope and c1 is the y intercept.
Let the equation of line s be y = m2x+c2, where m2 is the slope and c2 is the y intercept.
We need to know whether c1 < c2 or not.

Statement 1:
At the intersection point x = (c2 - c1)/(m1-m2), y = (m1c2 - m2c1)/(m1-m2).
Now, x < 0 and y < 0.
Or (c2 - c1)/(m1-m2) < 0 and (m1c2 - m2c1)/(m1-m2) < 0.
But this is not enough to tell us whether c1 < c2 or not.
We need to know about m1 and m2 as well; NOT sufficient.

Statement 2:
It says m1 > m2.
But this does not tell us whether c1 < c2 or not; NOT sufficient.

Combine (1) and (2):
Since m1 > m2, (m1 - m2) > 0.
Also, since (c2 - c1)/(m1-m2) < 0 from (1), c2 - c1 < 0.
Or c1 > c2.
So, the answer to the main question is NO; SUFFICIENT.

The correct answer is C.