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.

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

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 :