NTLancer wrote:

this looks like a

kaplan question

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.