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M23 #14

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M23 #14 [#permalink] New post 12 Aug 2009, 17:06
The question says if (1) y = kx + b is parallel to (2) x = b + ky, what is true about k?

The answer explains that equation (2) can be rearranged to from y = x/k - b/k.
For the lines to be parallel, the slopes must be equal, so k = 1/k, k*k = 1, and k = +1 or -1.

HOWEVER, I understand that two parallel lines must not share any points, i.e. not be coincident. Thus b must NOT equal -b/k; hence k must NOT equal -1.
Thus for the lines to be parallel (same slope and yet distinct lines) k = +1 only. The answer should be B { k=1 }, and not D { |k|-1=0 }.

I am going by the definition that parallel lines never meet. Is this correct for the GMAT?
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Re: M23 #14 [#permalink] New post 12 Aug 2009, 17:37
I agree with you. K should ideally be only 1.
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Re: M23 #14 [#permalink] New post 12 Aug 2009, 17:58
Lines are possible for K= 1 or -1
If K = -1 then lines will be parallel and colinear.
If k = 1 then the lines will be just parallel
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Re: M23 #14 [#permalink] New post 12 Aug 2009, 18:24
As a further note, the answer for M25 #8 says that parallel lines may not be collinear: "for lines to be parallel [when in y=mx+b form], the coefficients in front of x have to be equal and the other coefficients have to differ." Thus in M25 #8 answer D wins out over answer B.
Re: M23 #14   [#permalink] 12 Aug 2009, 18:24
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M23 #14

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