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Math Expert V
Joined: 02 Sep 2009
Posts: 58402

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Difficulty:   75% (hard)

Question Stats: 54% (01:38) correct 46% (01:56) wrong based on 149 sessions

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

(1) $$B + K = 1$$

(2) $$BK = 0$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 58402

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3
3
Official Solution:

To answer this question we must know coefficients in front of $$x$$ in the equations of the lines.

Statement (1) by itself is insufficient. We do not know coefficients in front of $$x$$ in the equations of the lines

Statement (2) by itself is insufficient. We do not know coefficients in front of $$x$$ in the equations of the lines

Statements (1) and (2) combined are sufficient. Either $$K = 1$$ and $$B = 0$$ or vice versa. In either case, a line with slope 0 intersects a line with slope 1 at a 45-degree angle.

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Bunuel wrote:
Official Solution:

To answer this question we must know coefficients in front of $$x$$ in the equations of the lines.

Statement (1) by itself is insufficient. We do not know coefficients in front of $$x$$ in the equations of the lines

Statement (2) by itself is insufficient. We do not know coefficients in front of $$x$$ in the equations of the lines

Statements (1) and (2) combined are sufficient. Either $$K = 1$$ and $$B = 0$$ or vice versa. In either case, a line with slope 0 intersects a line with slope 1 at a 45-degree angle.

Hi !
i have a doubt . so, i marked B as according to this formula - "
tan(theta) = m1 - m2/1 + m1*m2"
= ----taking B and K as the slope of either of the equations -----
as per Option B
the denominator in my formula becomes 0 giving not defined solution ,which is the value of only Tan 90.
Kindly correct me if im wrong.
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I think this is a high-quality question and the explanation isn't clear enough, please elaborate. "a line with slope 0 intersects a line with slope 1 at a 45-degree angle."
.
Can you please elaborate on this with some relevant theory as to how to determine the angle with this information?
Math Expert V
Joined: 02 Sep 2009
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Senthil7 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. "a line with slope 0 intersects a line with slope 1 at a 45-degree angle."
.
Can you please elaborate on this with some relevant theory as to how to determine the angle with this information?

A line with the slope of 0 is horizontal and a line with the slope of 1 is 45 degrees with x-axis, thus with the same 45 degrees with other horizontal lines.

Check for more here: math-coordinate-geometry-87652.html
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Joined: 17 Aug 2015
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y= mx+c , where m = tan(@) where @ is angle made with x axis
so if we know two angles made by two lines on the xy plane, do we need to know the intercepts of line on y axis?

we say that two lines are perpendicular when m1*m2 =-1 where m1 and m2 are slopes of two different lines, example tan30 = 1/root 3 , tan120= -root3 = -tan60

so angle between two lines = 120-30= 90

if BK = m1m2= 0 , means either B IS 0 OR K =0, when one of the slope is 0, it means te line is parallel to x axis, example slope m1 = y2-y1/x2-x1 , take two points (5, 3) , (7,3)
so m= 3-3/7-5 = 0 . this line has two points whose cordinates have same y distance from the x axis, means parallel to x axis

same way if line is parallel to y axis slope is infinity

also when slope is 1 , it means y2-y1= x2-x1= so tan45=1 so angle is 45 so combining 1 and 2 we get two lines one with slope 0 and one with slope 45
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+1 for option C
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At what angle do lines $$y = Kx + B$$ and $$y = Bx + K$$ intersect ?

(1) $$B + K = 1$$

(2) $$BK = 0$$

we know tanA = (m1-m2)/(1+m1m2) where "A" is the angle between the lines and "M1 and M2" are slopes
i) knowing B+ K we cannot find M1-M2 or M1M2 :insufficient
ii)knowing M1M2 we cannot find M1-M2 : insufficient

combining i) and ii) we get K-B as 1 or -1 ,as
case1: B=0 and K=1
case2: B=-1 and K=0
but inverse tan of 1 and -1 will give you a 45 degree between: them so combining is sufficient
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B + K = 1
=> B = 1 - K

B*K = 0
=> K* ( 1 - K) = 0
Hence K = 0 or K = 1
for K = 0 , B = 1
and for K = 1 , B = 0

Let K = 1 and B = 0
line 1: y = Kx + B
Here slope , K = 1 . hence the line is 45° to the y-axis
line 2: y = Bx + K
Here the slope , B = 0 . hence the line is 90° to the y-axis

Therefore the lines intersect at 45°angle. Hence sufficient

K = 0 and B = 1 will also give the same result.
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Joined: 16 Jan 2017
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Hi Bunuel,

before I approached each statement, I tried to simplify the expression, letting both lines interesect, to check if both do intersect at all or are just parallel.

Kx+B = Bx+K

Kx-K = Bx-B
K(x-1) = B(x-1)
//divide by x-1

K= B ...so the statement tells me that K=B? And each answer choice is not sufficient and E should have been the correct answer choice?
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hi @bunnel,

I came to the same ans as 45 degrees, but intersection of lines make 45 deg and 135 deg both, so opted for E option, can you clarify why only 45 degree is taken into consideration.
Intern  B
Joined: 29 Mar 2017
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Kontaxis wrote:
Hi Bunuel,

before I approached each statement, I tried to simplify the expression, letting both lines interesect, to check if both do intersect at all or are just parallel.

Kx+B = Bx+K

Kx-K = Bx-B
K(x-1) = B(x-1)
//divide by x-1

K= B ...so the statement tells me that K=B? And each answer choice is not sufficient and E should have been the correct answer choice?
Even I approached in he same manner...Bunuel please clarify.

Sent from my Moto G (4) using GMAT Club Forum mobile app
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Joined: 07 Apr 2018
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Puja priya wrote:
Kontaxis wrote:
Hi

before I approached each statement, I tried to simplify the expression, letting both lines interesect, to check if both do intersect at all or are just parallel.

Kx+B = Bx+K

Kx-K = Bx-B
K(x-1) = B(x-1)
//divide by x-1

K= B ...so the statement tells me that K=B? And each answer choice is not sufficient and E should have been the correct answer choice?
Even I approached in he same manner...

Sent from my Moto G (4) using

me too. does it even make sense to simplify the equations?
Intern  B
Joined: 02 Feb 2018
Posts: 31

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nitsrj wrote:
hi @bunnel,

I came to the same ans as 45 degrees, but intersection of lines make 45 deg and 135 deg both, so opted for E option, can you clarify why only 45 degree is taken into consideration.

Good question
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Joined: 10 Jul 2016
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Bunuel wrote:
Senthil7 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. "a line with slope 0 intersects a line with slope 1 at a 45-degree angle."
.
Can you please elaborate on this with some relevant theory as to how to determine the angle with this information?

A line with the slope of 0 is horizontal and a line with the slope of 1 is 45 degrees with x-axis, thus with the same 45 degrees with other horizontal lines.

Check for more here: http://gmatclub.com/forum/math-coordina ... 87652.html

Hi Bunuel,

Is there a page where you have a compilation of all your quant links combined?

Thanks,
Sid
Math Expert V
Joined: 02 Sep 2009
Posts: 58402

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siddharthsinha123 wrote:
Bunuel wrote:
Senthil7 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. "a line with slope 0 intersects a line with slope 1 at a 45-degree angle."
.
Can you please elaborate on this with some relevant theory as to how to determine the angle with this information?

A line with the slope of 0 is horizontal and a line with the slope of 1 is 45 degrees with x-axis, thus with the same 45 degrees with other horizontal lines.

Check for more here: http://gmatclub.com/forum/math-coordina ... 87652.html

Hi Bunuel,

Is there a page where you have a compilation of all your quant links combined?

Thanks,
Sid

Check below:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
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