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# m03 #15

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31 Jul 2009, 00:21
if two lines have slopes m and n , respectively, are they perpendicular?
1. m*n= -1
2. m=-n
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31 Jul 2009, 00:39
IMO A

Its the property of perpendicular lines that m*n= -1

Note:
-> Parallel lines have equal slopes, i.e. m = n
-> Perpendicual lines have slopes reciprocal of each other, i.e. m = -1/n
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31 Jul 2009, 11:07
[EDIT - REMOVED BY USER]

Last edited by nplaneta on 17 Jun 2012, 06:02, edited 1 time in total.
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31 Jul 2009, 13:12
Thanks for the responses.

But using S2 we can clearly say that the lines are not perpendicular. So why not the ans is D?-
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31 Jul 2009, 13:36
vaivish1723 wrote:
Thanks for the responses.

But using S2 we can clearly say that the lines are not perpendicular. So why not the ans is D?-

Not necessarily true. m=1, n=-1. The slope are perpendicular. OA => A
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31 Jul 2009, 13:39
Plug in 1 and statement 2 will yield a perpendicular answer anything else it will not be perpendicular.
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02 Aug 2009, 22:05
1) is sufficient.

For 2) if m = 1 and n = -1 then the lines are perpendicular. but for any other value of m,n they will not be.

hence A
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28 Aug 2009, 21:22
If two lines have slopes $$m$$ and $$n$$ , respectively, are they perpendicular?

1. $$m * n = -1$$
2. $$m = - n$$
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28 Aug 2009, 22:14
I selected D because stmt2 is also sufficient to say that lines are not perpendicular !!

Because as per stmt2, slope1 and slope2 are NOT reciprocals, it only says that they have opposite signs. So we can safely say that lines are not perpendicular..any comments or counter example?
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28 Aug 2009, 23:48
Economist wrote:
I selected D because stmt2 is also sufficient to say that lines are not perpendicular !!

Because as per stmt2, slope1 and slope2 are NOT reciprocals, it only says that they have opposite signs. So we can safely say that lines are not perpendicular..any comments or counter example?

If m = 1 ans n = -1, the lines are perpendicular but if m is none other than 1 or -1, then n is also other than 1 or -1. In that case, lines m and n are not perpendicular.

m = -n = 0 is also one option. Are lines m and n perpendicular in that case?
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29 Aug 2009, 18:29
GMAT TIGER wrote:
Economist wrote:
I selected D because stmt2 is also sufficient to say that lines are not perpendicular !!

Because as per stmt2, slope1 and slope2 are NOT reciprocals, it only says that they have opposite signs. So we can safely say that lines are not perpendicular..any comments or counter example?

If m = 1 ans n = -1, the lines are perpendicular but if m is none other than 1 or -1, then n is also other than 1 or -1. In that case, lines m and n are not perpendicular.

m = -n = 0 is also one option. Are lines m and n perpendicular in that case?

No, when m=-n=0 they will be paralel to each other (assuming they are not the same line) and paralel to the x axis. Consider lines y=7 , y=3, y=0, y=-3, y=-7...they all have slope zero and they are paralel to each other and the x axis
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15 Sep 2009, 15:47
Can someone clarify why stmt 2 is not sufficient? Tx.

If two lines have slopes m and n , respectively, are they perpendicular?
1. m * n = -1
2. m = -n
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15 Sep 2009, 19:10
Well statement 2 says m/n = 1 and for two lines to be perpendicular m*n should be -1
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16 Sep 2009, 19:02
as per your clarification - and my understanding too - it appears that we have a definitive NO for the question. Hence sufficient, correct?
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19 Sep 2009, 06:20
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crackgmat007 wrote:
Can someone clarify why stmt 2 is not sufficient? Tx.

If two lines have slopes m and n , respectively, are they perpendicular?
1. m * n = -1
2. m = -n

n= 1; then m=-1; then m*n = -1 [perpendicular]
or
n=4; then m=-4; then m*m = -16 [not perpendicular]
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21 Nov 2010, 13:10
The official explanation for this question says:
"Statement (2) by itself is insufficient. We only know that the lines have reciprocal slopes."

I do not understand why, if m=-n, lines have reciprocal slopes?
I think they just have opposite signes. Reciprocal would be n=1/m

Is it just a typo in the explanation or I am missing something?
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15 Feb 2011, 05:07
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.
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15 Feb 2011, 06:38
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 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 (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, 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.
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15 Feb 2011, 06:46
Bunuel wrote:
[.

(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, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Yes, I definately remember that the statements in DS shall not be in confllict, this is why I was confused. Totally forgot that 1 and -1 will satisfy the condition. Sorry about that.

Thank you, Bunuel. As always, you are a great help.
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10 May 2011, 11:07
If two lines have slopes m and n, respectively, are they perpendicular?
1. m*n = -1
2. m=-n
A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
C.BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D.EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient

According to me Answer is D but its wrong. My explanation is
Statement (1) by itself is sufficient. Lines and are perpendicular and the product of their slopes is is always equal to -1 . Answer is Yes.

Statement (2) by itself is sufficient. Its states that lines are mirror reflections of each other, but not perpendicular. So asnwer to question is No. Since there is an answer. this is sufficent.

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