This question becomes very easy if we use one-point form of a line.

The equation of a line is y = mx+c, where m is slope and c is y-intercept.

Now, let the equation of line l be y = mx+c and that of k be y=m₁x+c₁.

Therefore,

Line     x-intercept       y-intercept

l                         c/m                 c

k                        c_{1/m1               c1}

The first statement says the product of x-intercept are +ve

i.e.      x -intercept                > 0

=>        c.c₁/(m.m₁) > 0 —–1

This does not give us a concrete answer as the product of slopes can be both positive or negative, depending on product of y-intercepts.

The answer will be either of B, C, E

The second statement tells us that c.c₁<0.

This again is insufficient. B is eliminated.

Now, taking them together we see that if c.c₁<0

then for 1 to be positive m.m1 must also be -ve.

Therefore, both together are sufficient, option C.