In the xy-coordinate plane, line l and linke k intersect...

[sarahmailings]

DS question from MBA.com CAT #2.

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 line k is positive.
(2) The product of the y intercepts of line l and line k is negative.


My approach - I was able to get it down to C or E by picturing possible lines on the graph. However, I got stuck between answer choice C or E. I guessed E (the answer is C). Any thoughts about the right answer is C? I'd love suggestions about quicker ways to work it out.

Thanks in advance!

[mschwrtz]

Check out these many threads and see whether your answer is in there.

http://www.manhattangmat.com/forums/in-the-xy-coordinate-plane-line-l-and-line-k-intersect-t882.html

[atul.prasad]

Let the lines L and K be given by the equation:

L => y=mx + c
K => y=nx + k

since both lines intersect(or pass thru) @ (4,3)
we can evaluate c and k in terms of m and n respectively.

so L => y = mx + 3-4m
K => y = nx + 3-4n

evaluating statement 1:
x intercept for L = (4m-3)/m
x intercept for K = (4n-3)/n

If you multiply them you get a fraction dependent on m and n from which you cannot infer anything about the product of slopes

From 2 we know that (3-4m)(3-4n) is -ve
or (4m-3)(4n-3) is -ve
Even here we cannot establish if the product of mn is -ve

But if we combine the 2 statements
1 says (4m-3)(4n-3)/(mn) is positive
From 2 we know that (4m-3)(4n-3) is negative.
Hence for 1 to be true, mn must be -ve
which is exactly what we need to find out.

[jnelson0612]

Thank you everyone!