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# m03 #15

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13 Jul 2011, 08:36
If two lines have slopes m and n , respectively, are they perpendicular?

1) m*n = -1
2) m=-n

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

The explanation says: "Statement (2) by itself is insufficient. We only know that the lines have reciprocal slopes. For example line 10x and -10x , are mirror reflections of each other on the x axis, but not perpendicular."

However since we know they aren't reciprocals we know they aren't perpendicular, thus it is sufficient!
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Re: m03 #15 [#permalink]

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13 Jul 2011, 09:02
yes but remember that in data sufficiency both the statements has to give the same answer.

this is yes/no question.
so for each statement to be sufficient both the statements has to be either yes or no.

statement 1 is saying 'yes'. so its sufficient.

statement 1 is saying 'no' so not sufficient.

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13 Jul 2011, 09:04
Wow - Really? I have never heard of this? Where can I read more about it?
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Re: m03 #15 [#permalink]

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13 Jul 2011, 09:18
DYNAMITE wrote:
Wow - Really? I have never heard of this? Where can I read more about it?

i think this is very first thing we are suppose to know as part of data sufficient questions. Check in Manhattan Math books, they have this clearly stated.

even otherwise, in DS, ex - if one of the choice says answer is 2/3 for a variable, for other choice to be sufficient answer has to be 2/3 & NOT anything else.
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Re: m03 #15 [#permalink]

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23 Jul 2011, 22:40
the statement 2 is not sufficient since, if :

case 1 : if m = 1 , n= -1, which is also -1/m . This satisfies the property for perpendicular lines.

case 2 : if m = 4 , n= -4, which is not -1/m . This does not satisfy the property for perpendicular lines.

Hence , statement 2 does not give us sufficient information.
Re: m03 #15   [#permalink] 23 Jul 2011, 22:40
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# m03 #15

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