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.

Stations Image

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.


*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*

  • $\begingroup$ It would help if you posted what you have tried, not just magic numbers. Then we can check your reasoning. $\endgroup$ – 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.

Checking problems like this is very hard. The best way to do it on your own is to make a chart and count carefully and double check your work. However, this recommendation basically accounts to "do the problem correctly." The best way to check work for a problem like this is for someone else to check your work for you.

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 $a$.

  • $\begingroup$ Thank you so much Stella. Please refer to my explanation above and correct me for question 2) I have updated my answer $\endgroup$ – alex bliss Mar 26 '17 at 14:06
  • $\begingroup$ @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 $5-6-7-8-A-8-7-6$ $\endgroup$ – Stella Biderman Mar 26 '17 at 14:09
  • $\begingroup$ can you please explain for liza and sarah? I am so much grateful to you : ) $\endgroup$ – alex bliss Mar 26 '17 at 14:22
  • $\begingroup$ 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. $\endgroup$ – Stella Biderman Mar 26 '17 at 14:24

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