this looks like a kaplan
Well it's not a Kaplan
question, but I didn't pick prime
numbers (13 and 17) for the prices by accident
In the case of primes, the first match with two possibilities
could come at A*B. In the case above, this would be at
13*17 = 221. It's easy to see that the difference of 57
(278-221) can't be split in k*13+n*17. So (1) is sufficient.
Always pay a bit more attention if you see primes or numbers
with a big prime factor in questions similar to this one.