geet_ge wrote:In the xy co ordinate plane, line l and line k intersect at the point (4,3). Is the product of their slopes negative?

1)The product of x intercept of lines l and k is positive
2)The product of y intercept of lines l and k is negative

1)A Alone sufficient
2)B Alone sufficient
3)Together sufficient
4) Either
5) Neither

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; 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; NOT sufficient.

Combining (1) and (2), (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.

mankey wrote:Thanks Anurag. But what do you do with the information that the two lines intersect at (4,3)? How do you make out it is the extraneous information?

Thanks.

We got the answer C, without using the info about the intersection point of the lines. So this is the extraneous information.