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Lines m and n are perpendicular to one another. Is the product of the

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Bunuel
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Lines m and n are perpendicular to one another. Is the product of the [#permalink] New post   25 Jul 2017, 22:46
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Lines m and n are perpendicular to one another. Is the product of the slopes of the lines less than the product of the Y-intercepts of the two lines?

(1) Only line m passes through the origin.
(2) None of the lines are parallel to either axis



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Re: Lines m and n are perpendicular to one another. Is the product of the [#permalink] New post   26 Jul 2017, 04:44
Bunuel wrote:
Lines m and n are perpendicular to one another. Is the product of the slopes of the lines less than the product of the Y-intercepts of the two lines?

(1) Only line m passes through the origin.
(2) None of the lines are parallel to either axis


Let Line m be y=mx+c and line n be p=qx+d
We know m*q = -1
Question: is mq<cd

(1) only line m passes through origin
c=0 and d is not equal to 0
cd=0 and mq = -1
Sufficient

(2) none of the lines are parallel to either axis

no information about c and d
Hence not sufficient

A
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grantcke
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Re: Lines m and n are perpendicular to one another. Is the product of the [#permalink] New post   14 Aug 2017, 23:59
Bunuel wrote:
Lines m and n are perpendicular to one another. Is the product of the slopes of the lines less than the product of the Y-intercepts of the two lines?

(1) Only line m passes through the origin.
(2) None of the lines are parallel to either axis


Hi Bunuel,

Please explain why statement 1 alone is not sufficient I came up with the same answer as Luckisnoexcuse.
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Re: Lines m and n are perpendicular to one another. Is the product of the [#permalink] New post   15 Aug 2017, 00:25
Bro, that question is not flawed of coordinate geometry..consider 2 scenarios for statement 1:
2 perpendicular lines, 1 line is x axis and the other one is line x=6 . In this case, y intercept of the both the lines will be 0.
Second scenario, what if the perpendicular lines are Y axis and line y=4. In this case y intercept need not be 0 since y axis has x intercept as 0 and can have any value for y including 0. That makes statement 1 insufficient.
Statement 2 is insufficient.
From 1&2, we can definitely answer hence it's C.


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Re: Lines m and n are perpendicular to one another. Is the product of the [#permalink] New post   15 Aug 2017, 00:41
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grantcke wrote:
Bunuel wrote:
Lines m and n are perpendicular to one another. Is the product of the slopes of the lines less than the product of the Y-intercepts of the two lines?

(1) Only line m passes through the origin.
(2) None of the lines are parallel to either axis


Hi Bunuel,

Please explain why statement 1 alone is not sufficient I came up with the same answer as Luckisnoexcuse.


The reason is that m could coincide with y-axis, so vertical and in this case n would be parallel to x-axis, so horizontal. Vertical line has undefined slope, which makes comparison impossible. This is somewhat technical thing, so because of this I don't think that the question is of good quality.



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Thank you for understanding, and happy exploring!
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Re: Lines m and n are perpendicular to one another. Is the product of the [#permalink]
15 Aug 2017, 00:41
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