Negative slope line

[sanath.kumar.patro]

i got this question in my GMAT prep. exam. i searched for the solution in the forum but was unable to find one. The question is as follows:

In the x-y plane, the line k passes through the origin and through the point (a,b), where a.b is not equal to 0. Is b positive??
1. slope of line k is negative.
2. a<b
how to respond to this question??
OA is c

My approach was-
equation of a line is - y= mx+c where m is the slope. From 1 we get that slope is negative. nothing more so A itself is insufficient.

statement 2 states that a<b. the question says that the line passes through two points-(a,b) & (0,0).So we can find the slope of the line using these two points .The slope will be- (a/b). So statement two itself is insufficient .


combining the two we get that (a/b) is negative and a<b .so a must be negative . So b is positive . Is my approach correct??
or
is there any other way to solve this??

[ambikasrinivas]

I find it is helpful to draw a picture.

If you draw a picture with a line that passes through the origin, and take statement 1, where the slope is negative, you see that the line has to go through only quad 2 and 4.

So you can narrow a,b to being a point in either quad 2 or 4. In quad 2, a is -, and b is +, and in quad 4, a is + and b is -.

Statement 1 is not sufficient by itself as it could be either of those scenarios.

Statement 2 is not sufficient by itself as we do not know anything about the slope of the line (and therefore cannot figure out which quads it passes through)

If you take the statements together you can see that b can only be greater than a if the point is in quad 2 (because a will be - and b will be +). Therefore b is positive

[jnelson0612]

Thank you; that is an excellent explanation. I agree that it is extremely helpful to pictorially represent the scenario as much as possible for all problems.