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In the xy-plane, both line K and L intersect with axis-X. Is K’s inter

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In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  23 Jul 2015, 07:19
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In the xy-plane, both line K and L intersect with axis-X. Is K’s intercept with axis-X greater than that of line L?

1). K’s intercept with axis-Y is greater than that of L.
2). K and L have the same slope.

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Re: In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  23 Jul 2015, 07:36
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GMATinsight wrote:
In the xy-plane, both line K and L intersect with axis-X. Is K’s intercept with axis-X greater than that of line L?

1). K’s intercept with axis-Y is greater than that of L.
2). K and L have the same slope.

Good Questions also Require Kudos :)


Interesting question.

Let the equations of the lines be

k=mx+b
l = ny+c

Per the question, -b/m > -c/n ----> b/m < c/n ---> b/m - c/n < 0?

Statement 1, b>c but no information about m or n. Thus not sufficient to answer b/m - c/n < 0?

Statement 2, m =n . Not sufficient (remember that m,n can be <0 or > 0, we still dont know which!!)

Combining,

b>c and m =n

Consider these cases, let m =n=1

Then : b/1-c/1 > 0 as b>c

but

if m=n=-1

then

b/-1 - (-c/1) = -b+c < 0 (with b = 3, c = 2) . Thus we get 2 different answers from the combination of statements and thus E is the correct answer.
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In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  27 Jul 2015, 01:44
So, could we say that in order to answer this question we would need to know x,y and m (so the points and the slope), for both equations? Or at least the relationship between them, eg that they are parallel or vertical, or be able to draw such a conclusion?
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Re: In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  27 Jul 2015, 01:58
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pacifist85 wrote:
So, could we say that in order to answer this question we would need to know x,y and m (so the points and the slope), for both equations? Or at least the relationship between them, eg that they are parallel or vertical, or be able to draw such a conclusion?


I am not too clear about your question but the way I understand it I would answer it "Not necessarily."

The lines with Opposite slopes can answer the question based on comparison of their Y-Intercept
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In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  27 Jul 2015, 02:08
GMATinsight wrote:
pacifist85 wrote:
So, could we say that in order to answer this question we would need to know x,y and m (so the points and the slope), for both equations? Or at least the relationship between them, eg that they are parallel or vertical, or be able to draw such a conclusion?


I am not too clear about your question but the way I understand it I would answer it "Not necessarily."

The lines with Opposite slopes can answer the question based on comparison of their Y-Intercept



I think this is what I mean.. So, the lines with opposite slopes would be perpendicular. So, we would have a relationship between them, which would give us the slope.

BTW, I read this on purple math (https://www.purplemath.com/modules/slope2.htm) a while ago. Makes sense?
"The slope of the perpendicular line is the "negative reciprocal" of the slope of the original line — and two lines with slopes that are negative reciprocals of each other are perpendicular to each other. In numbers, if the one line's slope is m = 4/5, then the perpendicular line's slope will be m = –5/4. If the one line's slope is m = –2, then the perpendicular line's slope will be m = 1/2".
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In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  Updated on: 27 Jul 2015, 05:17
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pacifist85 wrote:
GMATinsight wrote:
pacifist85 wrote:
So, could we say that in order to answer this question we would need to know x,y and m (so the points and the slope), for both equations? Or at least the relationship between them, eg that they are parallel or vertical, or be able to draw such a conclusion?


I am not too clear about your question but the way I understand it I would answer it "Not necessarily."

The lines with Opposite slopes can answer the question based on comparison of their Y-Intercept



I think this is what I mean.. So, the lines with opposite slopes would be perpendicular. So, we would have a relationship between them, which would give us the slope.

BTW, I read this on purple math (https://www.purplemath.com/modules/slope2.htm) a while ago. Makes sense?
"The slope of the perpendicular line is the "negative reciprocal" of the slope of the original line — and two lines with slopes that are negative reciprocals of each other are perpendicular to each other. In numbers, if the one line's slope is m = 4/5, then the perpendicular line's slope will be m = –5/4. If the one line's slope is m = –2, then the perpendicular line's slope will be m = 1/2".


Ofcourse it makes sense. That the basic property of Slopes of two perpendicular lines

Property-1: Slopes of the parallel line will always be equal i.e. \(m_1 = m_2\)

Property-2: Product of Slopes of two Perpendicular lines will always be equal to -1 i.e. \(m_1*m_2 = -1\)

Originally posted by GMATinsight on 27 Jul 2015, 04:32.
Last edited by GMATinsight on 27 Jul 2015, 05:17, edited 1 time in total.
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In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  27 Jul 2015, 04:54
GMATinsight wrote:

Ofcourse it makes sense. That the basic property of Slopes of two perpendicular lines

Property-1: Slopes of the parallel line will always be equal i.e. \(m_1 = m_2\)

Property-2: Product of Slopes of two Perpendicular lines will always be equal i.e. \(m_1*m_2 = -1\)


GMATinsight, I think you meant "negative reciprocal of each other". Product of slopes of 2 mutually perpendicular lines can not be "equal".
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Re: In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  27 Jul 2015, 05:19
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Engr2012 wrote:
GMATinsight wrote:

Ofcourse it makes sense. That the basic property of Slopes of two perpendicular lines

Property-1: Slopes of the parallel line will always be equal i.e. \(m_1 = m_2\)

Property-2: Product of Slopes of two Perpendicular lines will always be equal i.e. \(m_1*m_2 = -1\)


GMATinsight, I think you meant "negative reciprocal of each other". Product of slopes of 2 mutually perpendicular lines can not be "equal".


I was representing the relation in a way \(m_1*m_2 = -1\) so missed the last letters in red "Product of the slopes of two perpendicular lines will be equal to -1"
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Re: In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  07 Mar 2017, 05:52
This question is asking for X intercept. I understand that its asking for absolute value. Please suggest
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Re: In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  07 Mar 2017, 06:01
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ashokjha1986 wrote:
This question is asking for X intercept. I understand that its asking for absolute value. Please suggest


No. x-intercept can be negative, 0 or positive.
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Re: In the xy-plane, both line K and L intersect with axis-X. Is K’s inter [#permalink] New post  07 Mar 2017, 11:42
Engr2012 wrote:
GMATinsight wrote:
In the xy-plane, both line K and L intersect with axis-X. Is K’s intercept with axis-X greater than that of line L?

1). K’s intercept with axis-Y is greater than that of L.
2). K and L have the same slope.

Good Questions also Require Kudos :)


Interesting question.

Let the equations of the lines be

k=mx+b
l = ny+c

Per the question, -b/m > -c/n ----> b/m < c/n ---> b/m - c/n < 0?

Statement 1, b>c but no information about m or n. Thus not sufficient to answer b/m - c/n < 0?

Statement 2, m =n . Not sufficient (remember that m,n can be <0 or > 0, we still dont know which!!)

Combining,

b>c and m =n

Consider these cases, let m =n=1

Then : b/1-c/1 > 0 as b>c

but

if m=n=-1

then

b/-1 - (-c/1) = -b+c < 0 (with b = 3, c = 2) . Thus we get 2 different answers from the combination of statements and thus E is the correct answer.


I did not understand this explanation. Firstly, The equation of a straight line should contain both x and y parameters. But the equations assumed here are different. One equation has x and other one has y.

Secondly, I did not understand this inference that we need to find that whether the below relation is true or not -

b/m - c/n < 0?

As per my opinion, the ans should be C because if two lines are having same slope then they are parallel. So, because Y intercept for the line K is > Y intercept of line L, so X intercept of line K should be > X intercept of line L. Clear and simple. Please let me know if I am missing anything.
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Re: In the xy-plane, both line K and L intersect with axis-X. Is Ks inter [#permalink] New post  07 Jul 2022, 09:17
Bunuel wrote:
ashokjha1986 wrote:
This question is asking for X intercept. I understand that its asking for absolute value. Please suggest


No. x-intercept can be negative, 0 or positive.


Same Doubt, As per common understanding Intercept is regarded as a length,
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Re: In the xy-plane, both line K and L intersect with axis-X. Is Ks inter [#permalink] New post  28 Aug 2023, 09:16
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