Line K - is b positive?

[queenisabella]

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

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

OA is C
Source: GMATPrep

[Bill@VeritasPrep]

1) Since K goes through the origin and has a negative slope, (a,b) can fall in quadrant 4 (which would mean a > 0 and b < 0) or quadrant 2 (which would mean a < 0 and b > 0). We can see that b could be positive or negative. Insufficient.

2) Knowing that a is less than b leaves a lot of possibilities. (2, 4) means b is positive, while (-4, -2) means b is negative.

When combined, Statement 2 rules out quadrant 4 (where a > b), leaving us with only quadrant 2 (where b > a). Thus, we know that b must be positive.

[Anurag@Gurome]

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

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

OA is C
Source: GMATPrep

(1) The slope of line K is negative implies b can be positive or negative.
No definite answer; NOT sufficient.

(2) a < b
If (a, b) = (2, 4), then b = positive
If (a, b) = (-4, -2), then b = negative.
No definite answer; NOT sufficient.

Combining (1) and (2), we know that either a = negative, b = positive OR a = positive, b = negative
Now a < b implies a = negative, b = positive, which implies certainly that b = positive; SUFFICIENT.

The correct answer is C.