Bunuel
Pam gets on an elevator at the 12th floor of a building going up to the 70th floor. Hilary gets on the elevator on the 63rd floor at the same time in the same building going down to the 1st floor. At what floor will their paths cross?
(1) Pam's elevator is moving twice the rate of Hilary's elevator.
(2) Hilary's elevator is moving at a rate of 4 floors per second.
Pam is at 12th floor and Hilary is at 63rd floor. Two people's elevators is moving in 2 opposite directions.
The distance between Pam and Hilary is 63 - 12 = 51 floors.
Let's call Pam's elevator speed is \(x\) floors per time unit.
Hilary's elevator speed is \(y\) floors per time unit.
Since they started moving, they would be at the same floor in: \(\frac{51}{x+y}\) time units.
Their paths would cross at floor: \(12+\frac{51x}{x+y}\).
(1) We have \(x=2y\). The question didn't say that \(x,y>0\).
Hence, if \(x=y=0\), they will never cross each other.
If \(x \neq 0\) and \(y \neq 0\), they will cross each other at floor: \(12+\frac{51 \times 2}{3}=46\).
Insufficient.
(2) Just know that \(y=4 \text{floors/second}\). There is no information about \(x\). Insufficient.
Combine (1) and (2): We have \(x=2y > 0\). Hence they will cross each other at 29th floor. Sufficient.
The answer is C.