GMAT Prep2?? (Slope)

[dferm]

In the xy-plane, the line k passes through the origin and through the point (a,b), where ab does not = 0. Is b positive?

(1) The slope of line k is negative
(2) a<b


Please Help...

How can I attack these types of questions?

[akshatsingh]

from 1) b can lie in II or IV quadrant. Not Sufficient
from 1) and 2) (a,b) will lie in second quadrant only. since in IV a will always be greater than b.

Answer should be C

[codesnooker]

Another approach to solve this question:-

We know that line passes through two points: O (0, 0) and P (a, b).

Now, by the equation of line,

(x - x1)/(y-y1) = (x2 - x1)/(y2-y1)

x/y = a/b
ay = bx
y = bx/a

Now by condition 1: Slope is negative.

Any equation line could be: y = mx + c (where c is constant)

and our line equation is y = bx/a

This means c = 0 and m = b/a

Now as m is negative, therefore b/a < 0

Now if b is negative then b < a otherwise a < b

It yields two different results, hence Condition 1 is not alone sufficient,

Condition (2) also alone INSUFFICIENT, as it said a < b, but doesn't give any clues of their signs.

Now when we take both statements together, we have already proved that
of a < b then b is positive.

So both statements together are SUFFICIENT.