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Does the point of intersection of line y = k*x + b and line

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Director
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Does the point of intersection of line y = k*x + b and line [#permalink] New post 22 Oct 2007, 22:06
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Does the point of intersection of line y = k*x + b and line x = k*y + b have a negative x coordinate?

1) k>0, b>0
2) k>1

Pls. explain.
VP
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Re: DS: Point of Intersection [#permalink] New post 22 Oct 2007, 23:06
GK_Gmat wrote:
Does the point of intersection of line y = k*x + b and line x = k*y + b have a negative x coordinate?

1) k>0, b>0
2) k>1

Pls. explain.


when they intercept y=y or x=x

so
kx+b=(x-b)/k
xk^2+kb=x-b
xk^2-x=-b-kb
x-xk^2=b+kb
x(1-k^2)=b(1+k)
x=b/(1-k)

statement 1
k>0, b>0. x can be negative and positive so insuff.

statement 2
k>1 then x can be negative or positive depeding on the value of b which can be negative and positive as well so insuff.

combined negative. suff.

C

Last edited by Ravshonbek on 22 Oct 2007, 23:09, edited 1 time in total.
Director
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Re: DS: Point of Intersection [#permalink] New post 23 Oct 2007, 05:47
Ravshonbek wrote:
GK_Gmat wrote:
Does the point of intersection of line y = k*x + b and line x = k*y + b have a negative x coordinate?

1) k>0, b>0
2) k>1

Pls. explain.


when they intercept y=y or x=x

so
kx+b=(x-b)/k
xk^2+kb=x-b
xk^2-x=-b-kb
x-xk^2=b+kb
x(1-k^2)=b(1+k)
x=b/(1-k)

statement 1
k>0, b>0. x can be negative and positive so insuff.

statement 2
k>1 then x can be negative or positive depeding on the value of b which can be negative and positive as well so insuff.

combined negative. suff.

C


Great work! Dude, I could never come up with this sh$#!!!! Thanks a lot.
Re: DS: Point of Intersection   [#permalink] 23 Oct 2007, 05:47
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Does the point of intersection of line y = k*x + b and line

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