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# m03 #15

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Manager
Joined: 20 Jul 2011
Posts: 144

Kudos [?]: 83 [0], given: 15

GMAT Date: 10-21-2011

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12 Sep 2011, 10:06
Thanks for this, Bunuel!

Bunuel wrote:
Matt1177 wrote:
Dont seem to find any discussion of this question in the master thread.

If two lines have slopes m and n, respectively, are they perpendicular?

(a) m*n = -1
(b) m = -n

My question is why the OA is not D? Is it correct that based on the second option, we can conclude that the answer is NO?

Am I missing something? Pls help.

For one line to be perpendicular to another, the relationship between their slopes has to be negative reciprocal, so if the slope of one line is $$m$$ then the line prependicular to it will have the slope $$-\frac{1}{m}$$. In other words, the [highlight]two lines are perpendicular if and only the product of their slopes is -1[/highlight].

For more check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

If two lines have slopes m and n, respectively, are they perpendicular?

(1) m*n = -1 --> directly gives an answer YES to the question.

(2) m = -n --> now, if for example m=3=-(-3)=-n then the lines are not perpendicular but if m=1=-(-1)=-n (or m=-1=-1=-n) then as mn would be equal to -1 the lines would be perpendicular. Not sufficient.

Matt1177 you should have spotted that there was something wrong with your solution as on the GMAT, [highlight]two data sufficiency statements always provide TRUE information and these statements never contradict each other[/highlight].

So we can not have answer YES from statement (1) and answer NO from statement (2), as in this case statements would contradict each other.

Hope it helps.

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Kudos [?]: 83 [0], given: 15

Re: m03 #15   [#permalink] 12 Sep 2011, 10:06

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# m03 #15

Moderator: Bunuel

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