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Lines- intersecting angles (m08q15)

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Manager
Joined: 22 May 2007
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07 Jul 2008, 20:44
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
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Joined: 05 Jul 2008
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07 Jul 2008, 21:21
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
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07 Jul 2008, 21:38
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

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08 Jul 2008, 07:05
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.
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08 Jul 2008, 08:36
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. $$K = L$$
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Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12

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08 Jul 2008, 08:47
1
i think this should be C?

cause we dont know if these lines intersect if at all??
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08 Jul 2008, 08:50
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??
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08 Jul 2008, 08:59
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??
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08 Jul 2008, 09:25
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
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08 Jul 2008, 10:15

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
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08 Jul 2008, 14:02
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
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Re: Lines- intersecting angles (m08q15)  [#permalink]

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14 Nov 2009, 00:09
A for me.

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

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20 Mar 2010, 16:02
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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Re: Lines- intersecting angles (m08q15)  [#permalink]

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04 Jun 2010, 08:12
I think the correct formula for calculating angle is tan@= (m1-m2)/(1+m1m2)
Please correct me if I'm wrong
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Re: Lines- intersecting angles (m08q15)  [#permalink]

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10 Jun 2010, 15:15
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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12 Jun 2012, 12:05
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!!
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Re: Lines- intersecting angles (m08q15)  [#permalink]

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12 Jun 2012, 23:49
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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15 Feb 2013, 02:54
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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12 Jun 2013, 05:05
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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12 Jun 2013, 05:44
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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