It's about so much more than amounts. It's about who the sender and recipient are and what red flags might be triggered. It's also about you and your other transactions.
I don't know what "double K" means. If you're talking about 10,000–99,000, I've seen that flow through without questions sometimes and with questions other times. Within this range, it's quite common to be asked once per business relationship and then things run smoothly. If you mean 100,000–999,999, you should definitely prepare to have supporting documents ready and it may be repeated even for the same business relationship.
I've also seen amounts under 10,000 questioned sometimes. Presumably because some parameter in the transaction profile triggered an alert.