we need to know that the line is not flat and it's either has negative or positive slope, because flat line also can pass through the origin and have (ab)=0 condition

st(1) this must be Sufficient as we have negative slope condition and a=b=0 we can answer No
st(2) a<b is Not Sufficient, as the line can be flat and pass through the origin; y coordinate can be 0 or positive

a

Spartacus2000 wrote:In the xy-plane, the line k passes through the origin and through the point (a,b), where ab !=0. Is b positive?

(1) The slope of line k is negative

(2) a < b

Thanks,

(1) The slope of line k is negative
A line with negative slope that goes through the origin passes through both Quadrant 2, where b>0, and Quadrant 4, where b<0. Insufficient.

(2) a < b
This is pretty clearly not information to answer the question, since the line could be anything that goes through the origin.

Combined:
In Quadrant 2 a is negative and b is positive, so a < b.
In Quadrant 4 a is positive and b is negative, so a > b.
According to Statement 2 we must be in Quadrant 2, so b must be positive. Sufficient.

@Greg, I have read again into the condition of this DS and would note a*b=0. This is only possible if y=0 and the line is flat or we have positive or negative slopes. So three conditions may be versed. In statement (1) we are suggested that the slope is negative, hence for a*b=0 we need to set a=b=0, agree?
a not c

gmatboost wrote:(1) The slope of line k is negative
A line with negative slope that goes through the origin passes through both Quadrant 2, where b>0, and Quadrant 4, where b<0. Insufficient.

(2) a < b
This is pretty clearly not information to answer the question, since the line could be anything that goes through the origin.

Combined:
In Quadrant 2 a is negative and b is positive, so a < b.
In Quadrant 4 a is positive and b is negative, so a > b.
According to Statement 2 we must be in Quadrant 2, so b must be positive. Sufficient.

It actually says

ab !=0

The exclamation point is a shorthand for NOT equal to. ("!=" means "not equal to" in many programming languages).

i found this a mistype and decided that st(2) is impossible as slope can be 0 and/or undefined there. In case slope is 0 we have b=0 always (non-positive, non-negative). When slope is undefined, b is positive.

anyway, interesting quest

gmatboost wrote:It actually says

ab !=0

The exclamation point is a shorthand for NOT equal to. ("!=" means "not equal to" in many programming languages).