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Question Stats:
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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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16 Sep 2014, 01:08
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 45degree angle. Answer: C
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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 45degree angle.
Answer: C 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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Re M2017
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23 Jul 2016, 03:05
I think this is a highquality question and the explanation isn't clear enough, please elaborate. "a line with slope 0 intersects a line with slope 1 at a 45degree angle." . Can you please elaborate on this with some relevant theory as to how to determine the angle with this information?



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Re: M2017
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24 Jul 2016, 02:45
Senthil7 wrote: I think this is a highquality question and the explanation isn't clear enough, please elaborate. "a line with slope 0 intersects a line with slope 1 at a 45degree 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 xaxis, thus with the same 45 degrees with other horizontal lines. Check for more here: mathcoordinategeometry87652.html
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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 = 12030= 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 = y2y1/x2x1 , take two points (5, 3) , (7,3) so m= 33/75 = 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 y2y1= x2x1= 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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Re: M2017
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05 Oct 2017, 06:04
+1 for option C
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Re: M2017
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05 Oct 2017, 06:09
At what angle do lines \(y = Kx + B\) and \(y = Bx + K\) intersect ?
(1) \(B + K = 1\)
(2) \(BK = 0\)
we know tanA = (m1m2)/(1+m1m2) where "A" is the angle between the lines and "M1 and M2" are slopes i) knowing B+ K we cannot find M1M2 or M1M2 :insufficient ii)knowing M1M2 we cannot find M1M2 : insufficient
combining i) and ii) we get KB 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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Re: M2017
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11 Oct 2017, 09:48
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 yaxis line 2: y = Bx + K Here the slope , B = 0 . hence the line is 90° to the yaxis
Therefore the lines intersect at 45°angle. Hence sufficient
K = 0 and B = 1 will also give the same result.



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Re: M2017
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31 Jan 2018, 10:28
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 KxK = BxB K(x1) = B(x1) //divide by x1 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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Re: M2017
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31 Mar 2018, 14:18
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.



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Re: M2017
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31 Mar 2018, 14:47
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 KxK = BxB K(x1) = B(x1) //divide by x1 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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Re: M2017
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20 Apr 2018, 07:31
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
KxK = BxB K(x1) = B(x1) //divide by x1
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?



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Re: M2017
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12 Nov 2018, 05:21
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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Re: M2017
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21 Feb 2019, 13:51
Bunuel wrote: Senthil7 wrote: I think this is a highquality question and the explanation isn't clear enough, please elaborate. "a line with slope 0 intersects a line with slope 1 at a 45degree 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 xaxis, thus with the same 45 degrees with other horizontal lines. Check for more here: http://gmatclub.com/forum/mathcoordina ... 87652.htmlHi Bunuel, Is there a page where you have a compilation of all your quant links combined? Thanks, Sid



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Re: M2017
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21 Feb 2019, 21:56
siddharthsinha123 wrote: Bunuel wrote: Senthil7 wrote: I think this is a highquality question and the explanation isn't clear enough, please elaborate. "a line with slope 0 intersects a line with slope 1 at a 45degree 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 xaxis, thus with the same 45 degrees with other horizontal lines. Check for more here: http://gmatclub.com/forum/mathcoordina ... 87652.htmlHi 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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