product of the slopes

[gmat009]

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

 

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

2) The product of the y-intercepts of lines L and K is negative

 

Can someone plz. explain this

[supersuj]

good question

 

IMO, C

 

Important to note that (4,3) does not matter, what matters is that they intersect in first quadrant

 

Statement 1-->

 

Product of x-intercepts is +ve, which means x intercepts are both +ve or both -ve

product of slopes could then be +ve or -ve..........INSUFFICIENT

 

Statement 2-->

 

y intercepts have opposite signs

again product of slopes can be +ve or -ve..........INSUFFICIENT

 

Combining(1) and (2),

both x-intercepts must be +ve(CANNOT be -ve since they wont interesect in quad 1) and one line has +ve y-intercept , the other a -ve y-intercept, thus product of slopes is negative.......SUFFICIENT

[genius_in_the_gene]

Let the equations of the lines be

y=mx+c

y=nx+d

 

1)x intercepts will be

-c/m and -d/n

 

Now -c/m * -d/n >0

-(c/m)*-(d/n)>0

(c/m)*(d/n)>0

cd/mn >0

if cd>0 mn>0

and vice versa

 

Not sufficient

 

2) y intercepts are

 

c and d

 

cd

Not suff

 

From 1 and 2, mn

 

ANS C

[spring2009]

C for me too

[e.cartman]

yes, good ds question as explained by supersuj. Combining both equations to get x-intercepts +ve is the part I liked. Thanks!