Sorry ...the [spoiler]OA = C[/spoiler] and not A as stated above.

Also, its not the probability sum...its a line - slope sum.

Thanks

Equation for k and l line:
(l): y1 = a1* x1 + b1
(k): y2 = a2* x2 + b2

1. At x interception all y = 0, then
0 = a1*x1 + b1 => x1 = -b1/a1
0 = a2*x2 + b2 => x2 = -b2/a2
As x1*x2 >0 then b1*b2/a1*a2 >0
Can not determine whether a1*a2 >0 as be unable to define the sign of b1*b2 => insuff

2. At y interception all x = 0, then
y1 = b1
y2 = b2
As y1*y2 <0 then b1*b2 <0
This has nothing to do with a1*a2, then insuff.

1&2. We know:
b1*b2/a1*a2>0 and b1*b2 <0
Then a1*a2 <0 => suff.

Pick C.

the best is to visualize the figure...
but before i give u the soln...
there is one concept of line which should be clear to u..

slope is +ve for a line which we can see go upwards in the first quadrant
and slope is -ve for a line which we can see go downwards in the first quadrant

u can check this with values...
so here is the soln...

check the image below...


statement 1)

the product of x intercepts is positive...

that means they can either both be positive or negative...
so even thought we have the x intercepts... we can draw the lines in any fashion... which will result in the product of their slopes being positive and negative.. .

statement 2)
the product of y intercepts is negative...

that means that one can +ve and one can be -ve...
again so even thought we have the y intercepts... we can draw the lines in any fashion... which will result in the product of their slopes being positive and negative.. .


finally... together...
see the figure.. .
there is only 2 possibilities of drawing the lines... whose product of slopes will always give a -ve answer...
thus together the statements are sufficient...


Hope this helps...

In the XY-coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?

1) The product of the x-intercepts of line L and K is positive.

2) The product of the y-intercepts of line L and k is negative.

This is a visualization question. The trick is to see the different ways the lines could be drawn.

Statement 1: The x intercepts must either both be positive or both be negative.
Line L passes through (4,3) and has an x intercept at (1,0). Slope is positive.
Line K passes through (4,3) has an x intercept at (2,0). Slope is positive.
Positive * Positive = Positive

Line L passes through (4,3) and has an x intercept at (1,0). Slope is positive.
Line K passes through (4,3) and has an x intercept at (10,0). Slope is negative.
Positive * Negative = Negative.

Since the product can be both positive and negative, insufficient.

Statement 2: One y intercept must be positive, the other negative.
Line L passes through (4,3) and has a y intercept at (0,1). Slope is positive.
Line K passes through (4,3) and has a y intercept at (0,-1). Slope is positive.
Positive * Positive = Positive

Line L passes through (4,3) and has a y intercept at (0,10). Slope is negative.
Line K passes through (4,3) and has an y intercept at (0,-1). Slope is positive.
Negative * Positive = Negative.

Since the product can be both positive and negative, insufficient.

Statements 1 and 2 together:
For the product of the x intercepts to be positive, either both must be positive or both must be negative.
For the product of the y intercepts to be negative, one must be positive and the other must be negative.

If both x intercepts are negative, we won't be able to satisfy statement 2, because neither line will be able to pass through (4,3) and have a negative y intercept. Thus, both x intercepts must be positive.

So to satisfy both statements, we need 2 positive x intercepts, 1 positive y intercept, and 1 negative y intercept:
A positive x intercept and a positive y intercept will yield a negative slope.
A positive x intercept and a negative y intercept will yield a positive slope.
Negative * Positive = Negative.
Suffficient.

The correct answer is C.