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Coordinate Geometry .. If line L passes through points

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Coordinate Geometry .. If line L passes through points

by Yaj » Wed Aug 21, 2013 2:37 am
If line L passes through points (r,-s) and (t,u), is the slope of the line negative?
(1) r>t
(2) u>-s

[spoiler]OA:C[/spoiler]

I was wondering if this data is sufficient the know the signs of the 4 variables?
Eg: If 's' is negative, then -(-s) makes it positive & if 's' is positive then -(s) makes it negative. I might be over-thinking this.
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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Aug 21, 2013 2:56 am
Yaj wrote:If line L passes through points (r,-s) and (t,u), is the slope of the line negative?
(1) r>t
(2) u>-s

[spoiler]OA:C[/spoiler]
Slope = (u-(-s)) / (t-r) = (u+s)/(t-r).

Question rephrased: Is (u+s)/(t-r) < 0?

Statement 1: r>t
Thus:
0 > t-r
t-r < 0.
No information about u+s.
INSUFFICIENT.

Statement 2: u>-s
Thus:
u+s > 0.
No information about t-r.
INSUFFICIENT.

Statements combined:
(u+s)/(t-r) = positive/negatve = negative.
Thus, (u+s)/(t-r) < 0.
SUFFICIENT.

The correct answer is C.
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