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In the xy-coordinate plane, line L and line K intersect at

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VP
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In the xy-coordinate plane, line L and line K intersect at [#permalink] New post 10 Mar 2008, 10:52
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In the xy-coordinate plane, line L and line K intersect at point (4,3). Is the
product of their slopes negative?

(1) The product of the x-intercepts of lines L and K is positive.
(2) The product of the y-intercepts of lines L and K is negative.
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Re: gmatprep coordinate geo [#permalink] New post 10 Mar 2008, 17:53
C

Say the two lines are

L: x/a + y/b = 1 and K: x/c + x/d = 1

Slope of L = -b/a
Slope of K = -d/c

Product of slopes = bd/ac

Statement 1: ac>0 - Insufficient
Statement 2: bd<0 - Insufficient

Combined - bd/ac is negative.
VP
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Re: gmatprep coordinate geo [#permalink] New post 15 Mar 2008, 01:18
sreehari wrote:
C

Say the two lines are

L: x/a + y/b = 1 and K: x/c + x/d = 1

Slope of L = -b/a
Slope of K = -d/c

Product of slopes = bd/ac

Statement 1: ac>0 - Insufficient
Statement 2: bd<0 - Insufficient

Combined - bd/ac is negative.


I reasoned in this way:

we must show whether be/ad<0
1. y=c/a and y1=k/d; ck/ad>0 where c and k are the constants. it doesn't say much
2. ck/be<0 alone insuff

together it's clear that ad and be have different signs so c is suff

anyway, it took me far more than 2 minutes to solve this one and would like to know if there is any shortcut. moreover, why does the argument tell us that the intersection point is 4,3?
thanks
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Re: gmatprep coordinate geo [#permalink] New post 15 Mar 2008, 21:21
Expert's post
marcodonzelli wrote:
moreover, why does the argument tell us that the intersection point is 4,3?
thanks


I think to help solve the problem with drawing.
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Re: gmatprep coordinate geo [#permalink] New post 15 Mar 2008, 23:50
walker wrote:
marcodonzelli wrote:
moreover, why does the argument tell us that the intersection point is 4,3?
thanks


I think to help solve the problem with drawing.


yes, drawing would help solve this problem in 1 minute.
Re: gmatprep coordinate geo   [#permalink] 15 Mar 2008, 23:50
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