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# M03 #15

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M03 #15 [#permalink]  09 Jul 2010, 02:37
If two lines have slopes $$m$$ and $$n$$ , respectively, are they perpendicular?

1. $$m*n=-1$$
2. $$m=-n$$

I have an issue in OE when explaining the statement 2. From OE shown below one can still answer the question that whether m & n are perpendicular.

I think in OE there should be two examples. First an example of two lines $$y= x+10$$ & $$y=-x+10$$, here you can see that the lines are parallel as the product of their slope is $$-1$$. In second example we can quote $$y=10x$$ & $$y=-10x$$. Now its make more sense that statement 2 is insufficient.

OE:
Statement (2) by itself is insufficient. We only know that the lines have reciprocal slopes. For example line $$y=10x$$ and $$y=-10x$$ , are mirror reflections of each other on the x axis, but not perpendicular.
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Re: M03 #15 [#permalink]  09 Jul 2010, 20:14
Statement-1:
We know that if two lines are perpendicular to each other, their slopes will be negative reciprocal to each other.
So here m*n= -1 => m = -1/n (Hence SUFFICIENT)

Statement-2:
m=-n
They can be negative reciprocal for some numbes(like 1) but not for others.(Hence NOT SUFFICIENT)

Ans : A

OA?
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Re: M03 #15 [#permalink]  15 Jul 2010, 11:30
1
KUDOS
Shouldn't statement 2 be sufficient because the lines are never going to be perpendicular.??
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Re: M03 #15 [#permalink]  15 Jul 2010, 12:53
flash wrote:
Shouldn't statement 2 be sufficient because the lines are never going to be perpendicular.??

@flash
Nope . see the first reply.
eg: m=1 , n = -1 .
That could be one of the answers. So not sufficient with stmt 2.
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Re: M03 #15 [#permalink]  15 Jul 2010, 13:09
aaah...got ya. tks
Re: M03 #15   [#permalink] 15 Jul 2010, 13:09
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# M03 #15

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