vidhya16 wrote: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.

I clearly understand concept of +ve / - ve slope and perpendicular/parallel lines. using those information I can say (1) & (2) alone is insufficient.


Now by using y intercept, how we are concluding that product of two lines slope is negative? By the way answer to this DS is "C".

Note:I know we can go by algebric method but that is very time consuming for this kind of question.

Let the equation of line L be y = m1x + c1.
Let the equation of line K be y = m2x + c2.
We need to know whether m1 * m2 is negative or not.

(1) x-intercept of L is -c1/m1.
x-intercept of K is -c2/m2.
So, (c1 * c2)/(m1 * m2) > 0.
But this does not tell us whether m1 * m2 < 0 or not.
So, (1) alone is NOT sufficient.

(2) y-intercept of L is c1.
y-intercept of K is c2.
So, c1 * c2 < 0.
Again this does not tell us whether m1 * m2 < 0 or not.
So, (2) alone is NOT sufficient.

Next, combine both the statements together and check.
On combining we have that (c1 * c2)/(m1 * m2) > 0 and c1 * c2 < 0.
This automatically means that m1 * m2 < 0.
So, both statements together are sufficient to answer the question.

The correct answer is C.