Problem Solving

Drawing the lines as neha24 described is the easiest method to solve this problem. But if you are having problem with that approach then you can follow this mathematical approach but this is way more time consuming.

Let us assume the equations of L1 and L2 are y = ax + b and y = px + q, respectively.
Hence, slopes of the lines are a and p and y-intercept of the lines are b and q, respectively.

As the lines are non-parallel, we know that a ≠ b.
We need to determine whether, a < p or not.

Statement 1: Let us assume that the intersection point is (X, Y), where X > 0 and Y > 0.
Hence, Y = aX + b and Y = pX + q
Solving these two equations, X = (q - b)/(a - p) and Y = (aq - bp)/(a - p)

Hence, (q - b)/(a - p) > 0 and (aq - bp)/(a - p) > 0
In other words, (q - b), (a - p) and (aq - bp) are of same sign.

Clearly this is not enough to conclude whether a < p or not.

Not sufficient

Statement 2: b < q
Clearly this is not enough to conclude whether a < p or not.

Not sufficient

1 & 2 Together: Now we know that, (q - b) > 0
Hence, (a - p) is positive too.
Hence, a > p

Sufficient

The correct answer is C.

i received a message about this thread. just a follow-up comment:

Anju@Gurome wrote:Drawing the lines as neha24 described is the easiest method to solve this problem. But if you are having problem with that approach then you can follow this mathematical approach but this is way more time consuming.
...

while anju's solution is clearly correct, i would give different advice in case of trouble. my advice would be, "if you have trouble with that approach, then try to develop a better visual understanding".

see, the deal is this:
the vast majority of coordinate geometry problems on the exam -- especially in DS -- are specifically designed to test your ability to visualize the concepts.
most of them are much easier (and much faster) to solve if you approach them by trying to visualize the situation. you should only use y = mx + b type stuff as a last resort, in cases when you just can't use visualization (either because it's impossible, or because you just can't imagine what the situation would look like).