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# M08-15

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Math Expert
Joined: 02 Sep 2009
Posts: 54369

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16 Sep 2014, 00:37
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Difficulty:

75% (hard)

Question Stats:

53% (01:05) correct 47% (01:35) wrong based on 133 sessions

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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) $$m=b$$

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Math Expert
Joined: 02 Sep 2009
Posts: 54369

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16 Sep 2014, 00:37
1
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.

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Intern
Joined: 09 Feb 2015
Posts: 20

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01 Jun 2015, 21:02
1
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!
Manager
Joined: 12 Nov 2014
Posts: 63

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01 Jun 2015, 22:36
13
4
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

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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Kindly press Kudos if the explanation is clear.
Thank you
Ambarish
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Joined: 09 Feb 2015
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04 Jun 2015, 03:31
Manager
Joined: 25 Feb 2014
Posts: 56
Concentration: Healthcare, Finance
GMAT 1: 700 Q49 V35
GPA: 3.5

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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!
Math Expert
Joined: 02 Sep 2009
Posts: 54369

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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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Joined: 06 Apr 2015
Posts: 32

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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.

Math Expert
Joined: 02 Sep 2009
Posts: 54369

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27 Jun 2015, 03:40
1
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.

Aren't $$y=x-bm$$ and $$x=y+bm$$ the same? $$x=y+bm$$ was simply rewritten into y = ... form.
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Joined: 06 Apr 2015
Posts: 32

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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.

Aren't $$y=x-bm$$ and $$x=y+bm$$ the same? $$x=y+bm$$ was simply rewritten into y = ... form.
Manager
Joined: 11 Feb 2015
Posts: 97
GMAT 1: 710 Q48 V38

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28 Jul 2015, 09:19
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

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.
Manager
Joined: 12 Jan 2015
Posts: 197

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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.

Thanks and Regards,
Prakhar
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Thanks and Regards,
Prakhar
Manager
Joined: 06 Jan 2015
Posts: 59

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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.

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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"No pain, no gain
Intern
Joined: 02 Feb 2016
Posts: 2

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30 Jun 2016, 01:52
Tan (theta)= m1-m2/1+m1*m2
Intern
Joined: 20 May 2017
Posts: 3

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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!
Math Expert
Joined: 02 Sep 2009
Posts: 54369

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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 ! ! !
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Re: M08-15   [#permalink] 17 Aug 2017, 07:56
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# M08-15

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