Caveat: I have been out of school a LONG time and my math memories are rusty. This may or may not be correct. 
To solve this you would need to find the least common multiple of the numbers 8, 10 and 12. That would give you the number of minutes that must elapse before they are in sync again. Then you would add this number to the original time.
Therefore, the LCM (least common multiple) of 8, 10 and 12 is 120. So, add 120 minutes ... two hours ... to 3:00 pm and the answer is 5:00 pm.
I don't think the question is testing real-life problem solving skills. I think it is just a story problem testing basic math skills for a math intensive job.
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