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slope of line X is m, and slope of line Y is n. Is line X

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slope of line X is m, and slope of line Y is n. Is line X [#permalink]

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28 Oct 2005, 06:38
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slope of line X is m, and slope of line Y is n. Is line X parellel to line Y ?

1) m+n = -1
2) m*n = 1/4
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28 Oct 2005, 06:43
gamjatang wrote:
slope of line X is m, and slope of line Y is n. Is line X parellel to line Y ?

1) m+n = -1
2) m*n = 1/4

X//Y <===> m=n

1 and 2.
m=-1-n
---> m*n= -n-n^2=1/4----> n^2+n+1/4=0 ----> (n+1/2)^2=0 ---->
n=-1/2 ----> m=-1-(-1/2)= -1/2
So m=n=-1/2 ---> X//Y ----> suff

Last edited by laxieqv on 28 Oct 2005, 07:39, edited 1 time in total.
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28 Oct 2005, 13:44
It's C.

Q: Is X parallel to Y ?
When lines are parallel their slopes are equal.
So is m=n?

1) m+n = -1
Infinite possibilities for m,n:
-1/2, -1/2
0, -1
-1, 0
...
NOT SUFF => BCE

2) m*n = 1/4
Again infinite possibilities for m,n:
-1/2, -1/2
1, 1/4
1/4, 1
...
NOT SUFF => CE

1+2) taken together we have 2 equations and two unknowns
Solving we get (m + 1/2)^2=0 which means one unique val for m = -1/2
therefore -1/2*n=1/4 => n = -1/2 or m=n
SUFF => C
Director
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Location: South Korea
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30 Oct 2005, 06:36
Thanks for the discussion.

There's a possibility that the two lines are actually one same line, and none of the subconditions (1, 2, 1+2) clarify this.
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30 Oct 2005, 06:49
gamjatang wrote:
Thanks for the discussion.

There's a possibility that the two lines are actually one same line, and none of the subconditions (1, 2, 1+2) clarify this.

good trap!
30 Oct 2005, 06:49
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