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GMATPrep: coordinate plane

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GMATPrep: coordinate plane [#permalink] New post 17 Jun 2006, 12:46
Could you please explain how do we get the right answer (marked in blue box)

Thanks
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 [#permalink] New post 17 Jun 2006, 13:25
I got C

C1. product of the two x-intercepts is positive

two cases:

line k = b/m = +ve
line l = b/m = +ve

line k = b/m = -ve
line l = b/m = -ve

so m can be either +ve for both m or -ve or one and +ve for the other

INSUFFICIENT

C2. product of the y-intercept is -ve

2 cases

line k -> b = +ve,
line l -> b = -ve

line k -> b = -ve
line l-> b = +ve

tells you nothing about the respective slopers

combined:

if line k's b/m = +ve and b = +ve then m = -ve
then line l ->b/m = +ve and b = -ve then m = +ve

product is negative

if line k's b/m = -ve and b = -ve then m = +ve
then line l -> b/m = +ve and b = +ve then m= -ve

product is -ve.
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 [#permalink] New post 18 Jun 2006, 13:28
Mrmikec, could you please explain the basic equations involved here?

I guess I am having trouble understanding how you ascertain slope from x and y intercepts?

b/m = x intercept? where b is y intercept and m is slope?

Any help is much appreciated.
Thanks
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 [#permalink] New post 18 Jun 2006, 16:28
tapan22 wrote:
Mrmikec, could you please explain the basic equations involved here?

I guess I am having trouble understanding how you ascertain slope from x and y intercepts?

b/m = x intercept? where b is y intercept and m is slope?

Any help is much appreciated.
Thanks


right m is slope and b is the y-intercept

the x-intercept formula is -b/m

hope this helps.
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 [#permalink] New post 19 Jun 2006, 05:03
Going with C...
Let line l intersect a point (x1, y1) other than (4,3) and k intersect (x2, y2) other than (4,3)

Stmt1: x1 * x2 = +ve
We could have :
x1= +ve => y1 => -ve or +ve
x2 =+ve => y2 => -ve or +ve

OR
x1 = -ve => y1 => +ve
x2 = -ve => y2 => +ve

Either case, prod of slopes in +ve/-ve
Not sufficient.

Stmt2: y1*y2 = -ve
Following the same logic above this is not sufficient.

Together:
Prod of slopes = (-y2/x2) x (-y1/x1)
= y2*y1/x2*x1 = -ve/+ve

Sufficient.
Therefore C
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 [#permalink] New post 19 Jun 2006, 13:20
It would also be easier to take examples and scribble few lines to counter the argument .. (C) makes sense as it would always yield descending and ascending lines, resultingin product of the slopes -ve.
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 [#permalink] New post 19 Jun 2006, 14:19
C.

Draw a rough sketch. A line that makes an acute angle with the x-axis has a positive slope, and one that makes an obtuse angle with the x-axis has a negative slope.
  [#permalink] 19 Jun 2006, 14:19
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