# Train Logical Question

A city train travels on double circle rails having a main station and stations 1 – 8 in this order. There are two trains: Train A and train B. Train A travels clockwise and stops only at odd numbered stations and the main station. Train B travels counterclockwise and stops only at even numbered stations and the main station. Only at the main station the travelers can switch one train for another.

Michael travels from station 5 to station 6, Sarah from station 7 to station 4, and Liza from station 2 to station 5. a) How many times do they totally travel between stations 5 to 6? b) Which station of 1 to 8 is passed maximum number of times? How many times? “Passed” means that the train passes a station without stopping or the traveler doesn´t get out of the train even though the train stops

P.S: I am preparing for my entrance exam and I found this question on my sample paper and have no clue how to verify my answer. This is what I have tried and my answers are:

1) four

2) three times on station 8 not 7.

Updated

*Micheal travels: 5-7-Station A-8-6

Sarah: 7-Station A-8-6-4

Liza:2-4-6-8-Station B-1-3-5*

• It would help if you posted what you have tried, not just magic numbers. Then we can check your reasoning. – Graham Kemp Mar 26 '17 at 13:42

Your first answer is correct, but the train passes station $8$ four times, twice for each of the first two passengers and zero times for the last, and $8$ is the only station passed more than $3$ times making it the solution.
If you explain how you arrived at your answers I can tell you where the faulty reasoning is for $b$ and hopefully confirm that your reasoning is correct for $a$.
• @alexbliss I think you misread the question: “Passed” means that the train passes a station without stopping or the traveler doesn´t get out of the train even though the train stops. Therefore the list of stations Michael passes is $5-6-7-8-A-8-7-6$ – Stella Biderman Mar 26 '17 at 14:09
• Liz is $2-1-S-1-2-3-4-5$ because she gets on the even train first and so is going in the opposite direction. Sarah is $7-8-S-8-7-6-5-4$ because they get on the odd train first and so go in the same direction as Michael. – Stella Biderman Mar 26 '17 at 14:24