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# m03 q 115

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Intern
Joined: 15 Oct 2011
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12 Jan 2012, 06:36
If two lines have slopes m and n, respectively, are they perpendicular?

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

Wouldn't the answer be D? Each alone is sufficient?

1. Sufficient - we know that whenever slopes are negative reciprocals of each other, the lines are perpendicular (OK).
2. Sufficient - we know that the slopes are NOT negative reciprocals.. wouldn't this mean that we KNOW for a fact that the lines are NOT perpendicular?

The answer given is A, what am I missing. Can lines whose slopes are just reciprocals be perpendicular?

Thanks!
M
Math Expert
Joined: 02 Sep 2009
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12 Jan 2012, 06:46
getzonator wrote:
If two lines have slopes m and n, respectively, are they perpendicular?

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

Wouldn't the answer be D? Each alone is sufficient?

1. Sufficient - we know that whenever slopes are negative reciprocals of each other, the lines are perpendicular (OK).
2. Sufficient - we know that the slopes are NOT negative reciprocals.. wouldn't this mean that we KNOW for a fact that the lines are NOT perpendicular?

The answer given is A, what am I missing. Can lines whose slopes are just reciprocals be perpendicular?

Thanks!
M

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 two lines are perpendicular if and only the product of their slopes is -1.

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, so if m=1 and n=-1 (or m=-1=-1=-n) then as mn would be equal to -1 the lines would be perpendicular. Not sufficient.

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

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.
_________________
Re: m03 q 115   [#permalink] 12 Jan 2012, 06:46
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# m03 q 115

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