Bunuel wrote:
Train T leaves town A for town B and travels at a constant rate of speed. At the same time, train S leaves town B for town A and also travels at a constant rate of speed. Town C is between A and B. Which train is traveling faster? Towns A, C, and B lie on a straight line.
(1) Train S arrives at town C before train T.
(2) C is closer to A than to B.
Let the speed of train T be \(u\), time taken to reach C be \(t_1\) and distance between A & C be \(x\)
Let the speed of train S be \(v\), time taken to reach C be \(t_2\) and distance between B & C be \(y\)
we need to find which speed between \(u\) & \(v\) is greatest
Statement 1: implies \(t_2<t_1\) \(=> \frac{y}{v}<\frac{x}{u}\)
or \(u<\frac{x}{y}v\). Now we need to know the ratio of \(\frac{x}{y}\) to determine whether \(u\) or \(v\) is greater. But the value of \(x\) & \(y\) is not given. Hence
InsufficientStatement 2: implies that \(x<y => ut_1<vt_2\). but nothing given about \(u\), \(v\) or \(t_1\) & \(t_2\). Hence
InsufficientCombining 1 & 2 we get \(x<y => \frac{x}{y}<1\), multiply both sides by \(v\) to get \(\frac{x}{y}v<v\)
from statement 1 we get \(u<v\). Hence
sufficientOption
C