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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Lines- intersecting angles (m08q15)

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Manager  Joined: 22 May 2007
Posts: 169

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1
At what angle do the lines $$y = Kx + L$$ and $$x = y + KL$$ intersect?

1. $$K = 2$$
2. $$K = L$$

Source: GMAT Club Tests - hardest GMAT questions

REVISED VERSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/lines-interse ... l#p1235093
Manager  Joined: 05 Jul 2008
Posts: 107
GMAT 2: 740 Q51 V38

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1
aaron22197 wrote:
At what angle do the lines $$y = Kx + L$$ and $$x = y + KL$$ intersect?

1. $$K = 2$$
2. $$K = L$$

Is A right?
y=Kx+L
y=x-KL
To determine the angle, we just need the slopes of the lines.
Senior Manager  Joined: 27 May 2008
Posts: 381

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4
line equation y = mx + c

m1 = K
m2 = 1

angle between lines = A
tan(A) = m1*m2

statement 1 : K = 2, we can find m1*m2 = 2 Suff

statement 2: doesnt give us value of K. Not suff

SVP  B
Joined: 30 Apr 2008
Posts: 1565
Location: Oklahoma City
Schools: Hard Knocks

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I agree that the answer is A.

We need to know the slope. The y-intercept doesn't matter (K=L). That tells us nothing because we still don't know what K is, and that's the only way we can know it's relationship to the slope of the other line.

If we know that K = 2 and then x is a slope of 1. The other, all we know if K=L. If we were told the Y intercept for one of the lines, #2 would be sufficient, but as is, it is insuffiicient.
Manager  Joined: 04 Apr 2008
Posts: 149
Location: Pune

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2
By 1st condition we can form the two equations as
Y=2X+L and Y=X-2L so solving the two equations we get the values of X and Y which gives the intersection points of the two lines. So sufficient
By 2nd condition we ket the two equations as

Y=Lx+L and Y=X-Lsqr2 which will not help to solve the two equations so not sufficient

And combinig the two equations we will not get any additional information other than what we gt in the 1st equations so
A is the correct ans

aaron22197 wrote:
At what angle do the lines $$y = Kx + L$$ and $$x = y + KL$$ intersect?

1. $$K = 2$$
2. $$K = L$$
Current Student Joined: 28 Dec 2004
Posts: 2458
Location: New York City
Schools: Wharton'11 HBS'12

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1
i think this should be C?

cause we dont know if these lines intersect if at all??
SVP  B
Joined: 30 Apr 2008
Posts: 1565
Location: Oklahoma City
Schools: Hard Knocks

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2
If you manipulate the equations to make them in the same form as line functions, we see:

$$y = Kx + L$$
and
$$y = x - KL$$

Once we know that K = 2 and not 1, we know the lines are not parallel. The only way we would know that the lines do not intersect is if they are parallel...otherwise, somewhere the lines must intersect.

If $$Kx = x$$, then the slope would be the same and the lines would be parallel.

fresinha12 wrote:
i think this should be C?

cause we dont know if these lines intersect if at all??
Current Student Joined: 28 Dec 2004
Posts: 2458
Location: New York City
Schools: Wharton'11 HBS'12

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1
you are right..

i m having a slow day..its like my Q skills are degrading by the day...grrrr

i should take this sucker before i drop below 49 on Q...if only i can improve my V to 40+

jallenmorris wrote:
If you manipulate the equations to make them in the same form as line functions, we see:

$$y = Kx + L$$
and
$$y = x - KL$$

Once we know that K = 2 and not 1, we know the lines are not parallel. The only way we would know that the lines do not intersect is if they are parallel...otherwise, somewhere the lines must intersect.

If $$Kx = x$$, then the slope would be the same and the lines would be parallel.

fresinha12 wrote:
i think this should be C?

cause we dont know if these lines intersect if at all??
SVP  B
Joined: 30 Apr 2008
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Location: Oklahoma City
Schools: Hard Knocks

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1
You'll be fine. Do you have it scheduled yet? Mine is 7/25. I think I can bring my Q up from 42 to about 45 - 48, that should be what I need. My verbal was 38 when I took it, but have studied a lot on it and that's my strenght, so improving to a 43 - 47 should be possible. My highest goal is a 47-47 split which should put me around a 750. I've been getting 46-48 in my quant and have been focusing on it mainly. I'll be taking the GMATPrep 2 this weekend. I'm looking for a low to mid 700s on the GMATPrep2.

I saw the picture of your NYC meeting with Walker, GMATBlackbelt, uphillclimb, and others...where did you guys meet? Looks like you all had a great time.

Allen

fresinha12 wrote:
you are right..

i m having a slow day..its like my Q skills are degrading by the day...grrrr

i should take this sucker before i drop below 49 on Q...if only i can improve my V to 40+

jallenmorris wrote:
If you manipulate the equations to make them in the same form as line functions, we see:

$$y = Kx + L$$
and
$$y = x - KL$$

Once we know that K = 2 and not 1, we know the lines are not parallel. The only way we would know that the lines do not intersect is if they are parallel...otherwise, somewhere the lines must intersect.

If $$Kx = x$$, then the slope would be the same and the lines would be parallel.

fresinha12 wrote:
i think this should be C?

cause we dont know if these lines intersect if at all??
Manager  Joined: 27 May 2008
Posts: 107

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intersecting angle can be found by tan@ = (m1-m2)/(1-m1m2)
(experts please guide me if anybody can find angle b/w two intersecting lines with out using tan@ even though gmat does not support trignometry)

so considering first line

y=kx +L --- m1 = k
x = y+KL --- m2 = 1

so tan@ = k-1/k+1

so we need K value here, tan@ = 1/3 -- which can be some angle.. so we can find angle with A SUFFICIENT

For B,
K=L,
it doesn't make big difference so INSUFFICIENT
Director  Joined: 03 Apr 2007
Posts: 780

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aaron22197 wrote:
At what angle do the lines $$y = Kx + L$$ and $$x = y + KL$$ intersect?

1. $$K = 2$$
2. $$K = L$$

Slope of line 1 = K
slope of line 2 = 1

We need to find K

(1) suff
(2) insuff

A
Manager  Joined: 11 Sep 2009
Posts: 50
Re: Lines- intersecting angles (m08q15)  [#permalink]

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A for me.

For the same slope, it does not matter what L is. The two lines always intersect at the same angle
Manager  Joined: 16 Apr 2009
Posts: 176
Re: Lines- intersecting angles (m08q15)  [#permalink]

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Few things :-

Is the correct formula to find the angle is tan@ = (m1-m2)/(1-m1m2)

and is there another way to find the angle ?
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Intern  Joined: 27 May 2010
Posts: 3
Re: Lines- intersecting angles (m08q15)  [#permalink]

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I think the correct formula for calculating angle is tan@= (m1-m2)/(1+m1m2)
Please correct me if I'm wrong
Senior Manager  Joined: 21 Dec 2009
Posts: 451
Concentration: Entrepreneurship, Finance
Re: Lines- intersecting angles (m08q15)  [#permalink]

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Irrespective of the formula, the intersecting angle requires a knowledge of the two slopes (gradients) -
M1 and M2
Intern  Joined: 11 Jan 2010
Posts: 35
Re: Lines- intersecting angles (m08q15)  [#permalink]

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1
Given: y = Kx + L => Slope m1 = K
And y = x - KL => Slope m2 = 1
In order to find the angle between two lines, we must know the values of the two slopes m1 and m2.
Rephrase the question: What is K?
S1: K = 2 Sufficient
S2: K = L => What is L? Unknown => Not sufficient.

Please click on Kudos+1 if you like the post! Cheers!! Manager  Joined: 10 Jan 2011
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Location: India
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Re: Lines- intersecting angles (m08q15)  [#permalink]

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The question is asking about the angle of two intersecting lines. first we need to find out whether two lines are parallel. second we need to know the slopes of two lines to find the angle. The formula for angle between two lines is tan @ = m1-m2/1+m1m2.
Given
equation 1 Y= Kx + L and equation 2 Y= X-KL. form equation 2 slope m2 = 1.
statement 1 K =2. Slope of first equation is 2. m1<>m2. means lines are not parallel. Also we know m1 and m2 so angle can be calculated. suff.
statement 2 K=L slope m2 unknown .... not suff.
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Re: Lines- intersecting angles (m08q15)  [#permalink]

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bunuel,
How do you calculate the angle between the 2 lines when you know their slopes ?
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Re: Lines- intersecting angles (m08q15)  [#permalink]

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aaron22197 wrote:
At what angle do the lines $$y = Kx + L$$ and $$x = y + KL$$ intersect?

1. $$K = 2$$
2. $$K = L$$

Spoiler: :: OA
A

Source: GMAT Club Tests - hardest GMAT questions

BELOW IS REVISED VERSION OF THIS QUESTION:

m08 q15

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

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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Re: Lines- intersecting angles (m08q15)  [#permalink]

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NOTE: If the lines are parallel then the angle of intersection between them is 0. Re: Lines- intersecting angles (m08q15)   [#permalink] 12 Jun 2013, 05:44

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# Lines- intersecting angles (m08q15)

Moderator: Bunuel  