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Another coordinate geometry question

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Source: — Data Sufficiency |
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by pemdas » Thu Aug 11, 2011 11:15 pm
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

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by gmatboost » Fri Aug 12, 2011 8:00 am
(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.
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by pemdas » Mon Oct 03, 2011 11:38 am
@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.
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by gmatboost » Mon Oct 03, 2011 11:43 am
It actually says
ab !=0
The exclamation point is a shorthand for NOT equal to. ("!=" means "not equal to" in many programming languages).
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by pemdas » Mon Oct 03, 2011 11:54 am
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).
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