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M08-15

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If lines \(y=mx+b\) and \(x=y+bm\) intersect at \(a\) degrees angle (where \(a \lt 90\)), what is the value of angle \(a\)?


(1) \(m=2\)

(2) \(m=b\)
[Reveal] Spoiler: OA

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Official Solution:


The angle between the two lines depends on their slope (the same way as the angle between a line and x-axis depends on the slope of that line). We have equations of two lines \(y=mx+b\) and \(y=x-bm\), so the slope of the first line is \(m\) and the slope of the second line is 1. Basically all we need to find is the value of \(m\).

(1) \(m=2\). Sufficient.

(2) \(m=b\). Irrelevant information. Not sufficient.


Answer: A
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Re: M08-15 [#permalink]

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New post 01 Jun 2015, 21:02
Dear Bunuel!
I can find the slope of the first line is m and the slope of the second line is 1
But I don’t know How can we find value of a if we know the slope of two lines. You can more detail.
Thanks so much!

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Mrtinhnv wrote:
Dear Bunuel!
I can find the slope of the first line is m and the slope of the second line is 1
But I don’t know How can we find value of a if we know the slope of two lines. You can more detail.
Thanks so much!


Slope of a line is a measure of its inclination with respect to the horizontal.
The more the inclination the more will be the slope, lesser the inclination less will be the slope.
In general, slope of a line is defined as m = tan θ , where θ is the angle between the line and the horizontal axis.
(Even though trigonometry is not involved in GMAT, if you understand the concept of slope it will help you in solving
problems such as these. In fact the formula for slope m = (y2-y1)/(x2-x1) is actually derived from m = tan θ)

So, if you know slope of a line, you know the angle with which its is inclined. [tan^-1 (m)]
Since the given problem is a data sufficiency problem you dont have to solve for anything. You just need to say whether the info given is sufficient to
answer the question.

See attached figure
From the question stem you know the slope of one line which means the angle at which this line is inclined (θ1)
From the statement 1 you know the slope of other line which means the angle at which this line is inclined (θ2)
The difference between these two angles will give you the angle at which they are intersected.
>> !!!

You do not have the required permissions to view the files attached to this post.


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Re: M08-15 [#permalink]

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New post 04 Jun 2015, 03:31
Tks so much, askhere.

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Re: M08-15 [#permalink]

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New post 25 Jun 2015, 17:29
I'm struggling to see how Slope of line two equals 1. Can anyone explain that part with some added detail, thank you!

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Re: M08-15 [#permalink]

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New post 26 Jun 2015, 01:55
atl12688 wrote:
I'm struggling to see how Slope of line two equals 1. Can anyone explain that part with some added detail, thank you!


If the equation of the line is given in the Point-intercept form: y=mx+b, then m is the slope.

Therefore, the slope of y=x−bm, is 1 (coefficient of x).

Check for more here: math-coordinate-geometry-87652.html

Hope it helps.
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Re: M08-15 [#permalink]

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New post 26 Jun 2015, 20:34
The initial post states the second line to be x=y+bm although this post states that the equation of the second line is x=y - bm

could someone please explain why the difference?


Bunuel wrote:
Official Solution:


The angle between the two lines depends on their slope (the same way as the angle between a line and x-axis depends on the slope of that line). We have equations of two lines \(y=mx+b\) and \(y=x-bm\), so the slope of the first line is \(m\) and the slope of the second line is 1. Basically all we need to find is the value of \(m\).

(1) \(m=2\). Sufficient.

(2) \(m=b\). Irrelevant information. Not sufficient.


Answer: A

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Re: M08-15 [#permalink]

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kelvind13 wrote:
The initial post states the second line to be x=y+bm although this post states that the equation of the second line is x=y - bm

could someone please explain why the difference?


Bunuel wrote:
Official Solution:


The angle between the two lines depends on their slope (the same way as the angle between a line and x-axis depends on the slope of that line). We have equations of two lines \(y=mx+b\) and \(y=x-bm\), so the slope of the first line is \(m\) and the slope of the second line is 1. Basically all we need to find is the value of \(m\).

(1) \(m=2\). Sufficient.

(2) \(m=b\). Irrelevant information. Not sufficient.


Answer: A


Aren't \(y=x-bm\) and \(x=y+bm\) the same? \(x=y+bm\) was simply rewritten into y = ... form.
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Collection of Questions:
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Re: M08-15 [#permalink]

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New post 27 Jun 2015, 10:04
you're right, I misread that post.. I've got to stop making these silly mistakes

Bunuel wrote:
kelvind13 wrote:
The initial post states the second line to be x=y+bm although this post states that the equation of the second line is x=y - bm

could someone please explain why the difference?


Bunuel wrote:
Official Solution:


The angle between the two lines depends on their slope (the same way as the angle between a line and x-axis depends on the slope of that line). We have equations of two lines \(y=mx+b\) and \(y=x-bm\), so the slope of the first line is \(m\) and the slope of the second line is 1. Basically all we need to find is the value of \(m\).

(1) \(m=2\). Sufficient.

(2) \(m=b\). Irrelevant information. Not sufficient.


Answer: A


Aren't \(y=x-bm\) and \(x=y+bm\) the same? \(x=y+bm\) was simply rewritten into y = ... form.

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Re: M08-15 [#permalink]

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New post 28 Jul 2015, 09:19
askhere wrote:
Mrtinhnv wrote:
Dear Bunuel!
I can find the slope of the first line is m and the slope of the second line is 1
But I don’t know How can we find value of a if we know the slope of two lines. You can more detail.
Thanks so much!


Slope of a line is a measure of its inclination with respect to the horizontal.
The more the inclination the more will be the slope, lesser the inclination less will be the slope.
In general, slope of a line is defined as m = tan θ , where θ is the angle between the line and the horizontal axis.
(Even though trigonometry is not involved in GMAT, if you understand the concept of slope it will help you in solving
problems such as these. In fact the formula for slope m = (y2-y1)/(x2-x1) is actually derived from m = tan θ)

So, if you know slope of a line, you know the angle with which its is inclined. [tan^-1 (m)]
Since the given problem is a data sufficiency problem you dont have to solve for anything. You just need to say whether the info given is sufficient to
answer the question.

See attached figure
From the question stem you know the slope of one line which means the angle at which this line is inclined (θ1)
From the statement 1 you know the slope of other line which means the angle at which this line is inclined (θ2)
The difference between these two angles will give you the angle at which they are intersected.

Thanks for this explanation. Clear now.

Thanks Brunel for this amazing question. seems simple noe but it was tricky to get in CAT.

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Re: M08-15 [#permalink]

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New post 22 Jan 2016, 02:06
Hi Bunuel,

Can you please tell, how could we find the angle between two lines if we know the slopes of both lines..??

To get the angle between two lines by using the above-mentioned method we should the Tan Table. Additionally, this method will only work with standard angles.

As GMAT does not deal with trigonometry, I am sure there must be another method to get the angle.

Please assist.

Thanks and Regards,
Prakhar
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Re: M08-15 [#permalink]

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New post 25 Jan 2016, 11:37
RAHKARP27071989 wrote:
Hi Bunuel,

Can you please tell, how could we find the angle between two lines if we know the slopes of both lines..??

To get the angle between two lines by using the above-mentioned method we should the Tan Table. Additionally, this method will only work with standard angles.

As GMAT does not deal with trigonometry, I am sure there must be another method to get the angle.

Please assist.

Thanks and Regards,
Prakhar


Prakhar: This is a DS question, just "knowing" that the two slopes would get you to the answer its sufficient, you don't need to know the trigonometry behind the question.
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New post 30 Jun 2016, 01:52
Tan (theta)= m1-m2/1+m1*m2

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Re: M08-15 [#permalink]

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New post 17 Aug 2017, 07:53
Hi Bunuel,

I am not from Maths background, hence I'm finding difficulty in understanding the solution.

Can you please explain how we can arrive at angle based on the slopes of 2 lines?

Thanks!

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New post 17 Aug 2017, 07:56
anirudhasopa wrote:
Hi Bunuel,

I am not from Maths background, hence I'm finding difficulty in understanding the solution.

Can you please explain how we can arrive at angle based on the slopes of 2 lines?

Thanks!


Sure. Check the posts below:

24. Coordinate Geometry



For more check:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
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Re: M08-15   [#permalink] 17 Aug 2017, 07:56
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