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# M20#17

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Senior Manager
Joined: 29 Sep 2009
Posts: 396
GMAT 1: 690 Q47 V38
Followers: 2

Kudos [?]: 31 [0], given: 5

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14 Oct 2010, 22:34
At what angle do lines $$y = Kx + B$$ and $$y = Bx + K$$ intersect ?

(1) $$B + K = 1$$
(2) $$BK = 0$$

(C) 2008 GMAT Club - m20#17

[Reveal] Spoiler:
1: B + k = 1 N.S : 1/2,1/2, 0/1 etc.
2. BK = 0 N.S : 1/0, 0/1, etc.
Angle between two lines with slopes m1 and m2 is :
tan(q) = (m1-m2)/(1+m1.m2)
Now if m1m2 = 0 and m1+m2 = 0 this implies: 1,0 or 0,1
arctan(1) = 45 and arctan(-1)=-45. Eventhough relative angle between the lines will be 45. Probably the question can be rephrased as "angle between the lines"
Retired Moderator
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 101

Kudos [?]: 858 [0], given: 25

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15 Oct 2010, 00:57
vicksikand wrote:
At what angle do lines $$y = Kx + B$$ and $$y = Bx + K$$ intersect ?

1. $$B + K = 1$$
2. $$BK = 0$$

(C) 2008 GMAT Club - m20#17

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient
1: B + k = 1 N.S : 1/2,1/2, 0/1 etc.
2. BK = 0 N.S : 1/0, 0/1, etc.
Angle between two lines with slopes m1 and m2 is :
tan(q) = (m1-m2)/(1+m1.m2)
Now if m1m2 = 0 and m1+m2 = 0 this implies: 1,0 or 0,1
arctan(1) = 45 and arctan(-1)=-45. Eventhough relative angle between the lines will be 45. Probably the question can be rephrased as "angle between the lines"

Angle between two lines is $$arctan(\frac{m_1-m_2}{1+m_1m_2})$$
(1) Not sufficient
(2) All this says is that one of the lines is horizontal
(1+2) One of the lines is horizontal hence the other has a slope of 45 degrees. Sufficient to say angle is 45 degrees

Now wether it is -45 or 45 ...when you talk of angle of itnersection it is the same thing. The angles formed by the two lines will be 45 degrees and 135 degrees.
_________________
Senior Manager
Joined: 29 Sep 2009
Posts: 396
GMAT 1: 690 Q47 V38
Followers: 2

Kudos [?]: 31 [0], given: 5

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15 Oct 2010, 04:31
shrouded1 wrote:
vicksikand wrote:
At what angle do lines $$y = Kx + B$$ and $$y = Bx + K$$ intersect ?

1. $$B + K = 1$$
2. $$BK = 0$$

(C) 2008 GMAT Club - m20#17

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient
1: B + k = 1 N.S : 1/2,1/2, 0/1 etc.
2. BK = 0 N.S : 1/0, 0/1, etc.
Angle between two lines with slopes m1 and m2 is :
tan(q) = (m1-m2)/(1+m1.m2)
Now if m1m2 = 0 and m1+m2 = 0 this implies: 1,0 or 0,1
arctan(1) = 45 and arctan(-1)=-45. Eventhough relative angle between the lines will be 45. Probably the question can be rephrased as "angle between the lines"

Angle between two lines is $$arctan(\frac{m_1-m_2}{1+m_1m_2})$$
(1) Not sufficient
(2) All this says is that one of the lines is horizontal
(1+2) One of the lines is horizontal hence the other has a slope of 45 degrees. Sufficient to say angle is 45 degrees

Now wether it is -45 or 45 ...when you talk of angle of itnersection it is the same thing. The angles formed by the two lines will be 45 degrees and 135 degrees.

At what angle do lines y = Kx + B and y = Bx + K intersect ?

I dont think I wrote anything different from what you have written.

At what angle do the lines intersect can be interpreted as : at what angle from the X axis/ Y axis. To formulate a more "closed" question it would have been better if the statement read : angle between the lines.
Senior Manager
Joined: 06 Aug 2011
Posts: 405
Followers: 2

Kudos [?]: 166 [0], given: 82

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04 Mar 2014, 00:26
can anyone draw a figure for me How can we say its C?

Thank u
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Math Expert
Joined: 02 Sep 2009
Posts: 34456
Followers: 6277

Kudos [?]: 79639 [1] , given: 10022

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04 Mar 2014, 00:44
1
KUDOS
Expert's post
sanjoo wrote:
At what angle do lines $$y = Kx + B$$ and $$y = Bx + K$$ intersect ?

(1) $$B + K = 1$$
(2) $$BK = 0$$

can anyone draw a figure for me How can we say its C?

Thank u

From $$B + K = 1$$ and $$BK = 0$$ we have that b=0 and k=1 OR b=1 and k=0. In either cases the two lines are y=x and y=1:
Attachment:

graph.png [ 6.6 KiB | Viewed 648 times ]
Angle = 45 degrees.

Hope it helps.
_________________
Re: M20#17   [#permalink] 04 Mar 2014, 00:44
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# M20#17

Moderator: Bunuel

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