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# This is from GMAT Prep. My coordinate geometry is pretty

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Joined: 20 Jun 2007
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This is from GMAT Prep. My coordinate geometry is pretty [#permalink]

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12 Jan 2008, 06:12
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This is from GMAT Prep. My coordinate geometry is pretty poor. Can anybody help me to understand this? Thanks.

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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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Director
Joined: 12 Jul 2007
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Re: Coordinate Geometry DS - GMAT Prep [#permalink]

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12 Jan 2008, 07:49

Here's our coordinate plane. The question says we have a line that passes through the origin (the read dot at point 0,0).
The line also passes through point (a,b) which is NOT at (0,0) but rather somewhere else.
The A value will slide the point left and right, the B value will slide the point up and down.
They're asking if B is positive. For B to be positive the point would have to be above the x-axis (quadrant I or II)

Statement 1 The slope of line k is negative

This means that the slope starts high and drops as it moves right. In other words, the line passes through quadrants II and IV. This is insufficient however because we don't know where point (a,b) is. It can be in quadrant II or quadrant IV, and B will only be positive if it's in quadrant II now.

INSUFFICIENT

Statement 2 a<b

This is possible in every quadrant except for quadrant IV where all the As are positive and all the Bs are negative. In every other quadrant though there are points where a<b. From this we know that the point is in quadrant I, II or III.

INSUFFICIENT

Now taken together: from statement 1 we know it's in quadrant II or IV. From statement 2 we know it's in I, II or III. Together we know that point (a,b) is in quadrant II where B is always positive.

SUFFICIENT

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Re: Coordinate Geometry DS - GMAT Prep   [#permalink] 12 Jan 2008, 07:49
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