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M20-17

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M20-17 [#permalink]

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New post 16 Sep 2014, 01:08
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Difficulty:

  55% (hard)

Question Stats:

48% (01:12) correct 52% (00:48) wrong based on 130 sessions

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Re M20-17 [#permalink]

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New post 16 Sep 2014, 01:08
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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.


Answer: C
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M20-17 [#permalink]

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New post 23 Jun 2016, 04:09
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.


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 M20-17 [#permalink]

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New post 23 Jul 2016, 03:05
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?

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Re: M20-17 [#permalink]

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New post 24 Jul 2016, 02:45
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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M20-17 [#permalink]

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New post 09 Sep 2016, 19:56
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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Re: M20-17 [#permalink]

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New post 05 Oct 2017, 06:04
+1 for option C
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Re: M20-17 [#permalink]

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New post 05 Oct 2017, 06:09
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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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Re: M20-17 [#permalink]

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New post 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 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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Re: M20-17   [#permalink] 11 Oct 2017, 09:48
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