Data Sufficiency

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

(1) B+K=1

(2) BK=0

rakeshd347 wrote:At what angle do lines y=Kx+B and y=Bx+K intersect ?
(1) B+K=1
(2) BK=0

Q: Angle made by the lines

y = Kx + B ... (i)
y = Bx + K ... (ii)

We need the values of K and B both to find the equations of the 2 lines.

St1:
B + K = 1
Many numbers satisfy this equation. B = 0, K = 1; B = 2, K = -1 ... Thus we dont have a definite answer for the Slope and the Intercept of the lines (i) & (ii)
INSUFFICIENT

St2:
BK = 0
We can have three cases here
1) B = 0; (i) becomes y = Kx (ii) becomes y = K (We still need the value of K)
2) K = 0; (i) becomes y = B (ii) becomes y = Bx (We still need the value of B)
3) B = K = 0; The two equations become the X Axis itself.
All the three cases are possible, So the statement is INSUFFICIENT

St1+St2:
Now we know that the sum must be equal to 1; Case 3 of st2 becomes invalid.
1) B = 0; K = 1 (Since B + K = 1); (i) becomes y = x (ii) becomes y = 1
1) K = 0; B = 1 (Since B + K = 1); (i) becomes y = 1 (ii) becomes y = x



The two equations are y = 1 & y = x and the angle made by them is 45.
SUFFICIENT.

Answer C

Regards,
Vivek

lunarpower wrote:I like this problem. What's the source?

Sorry forgot to mention the source. This problem is created by Bunuel from GMATCLUB it was in one of the gmatclub tests. Surely its not from OG or Official source.