M7MBA wrote:At what angle do lines y = Kx + B and y = Bx + K intersect?

(1) B + K = 1

(2) BK = 0

The OA is C.

How can I find the angle? I don't understand how could I solve this DS question. May someone helps me? Please.

We have to find out the angle between the two lines y = Kx + B and y = Bx + K.

Let's see each statement one by one.

(1) B + K = 1

Case 1: Say B = K =1/2

This implies that the lines are y = x/2 + 1/2 and y = x/2 + 1/2. In fact they are the same lines. The angle between them is 0.

Case 2: Say B = 0 and K =1

This implies that the lines are y = x and y = 1. The angle y = x makes with y = 1 is 45 degrees. If you do not know how to calculate it, it is fine. There is no need to know this. All you can deduce from the equations is that the slope of the lines is not the same; thus, they make an angle greater than 0.

No unique answer. Insufficient.

(2) BK = 0

=> At least one of B and K is 0.

If both of them are 0, the equation would be y = 0. The two lines would be the same line, implying that the angle between them is 0. However, If say B = 0 and K =1, then the two lines will have an angle greater than 0.

No unique answer. Insufficient.

(1) and (2) togther

From the two statements, we have either B = 0 and K = 1 OR B = 1 and K = 0. In either case, the equations are y = x and y = 1. Since the slopes of the two lines are know, the angle between them can be calculated. Sufficient.

Computation of angle between the two lines is not within the scope of the GMAT. Since this is a DS question, and one needs to be only sure whether the unqiue value is possible, we need not necessarily calculate it.

The correct answer: C

Hope this helps!

-Jay
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