BECAREFUL: Duped by credit card scam upon check in at Hotel

You arrive at your hotel and check in at the front desk. When checking in, you give the front desk your credit card (for all the charges for your room). You get to your room and settle in. Someone calls the front  desk and asked for (example) Room 620 (which happens to be your room).

Your phone rings in your room. You answer and the person on the other end says the following, 'This is the front desk. When checking in, we came across a problem with your charge card information. Please re-read me your credit card number and verify the last 3 digits numbers at the reverse side of your charge card.

Not thinking anything you might give this person your information, since the call seems to come from the front desk. But actually, it is a scam of someone calling from outside the hotel/front desk. They ask for a random room number. Then, ask you for credit card information and address information. Sounding so professional that you do think you are talking to the front desk. 

If you ever encounter this problem on your vacation, tell the caller that you will be down at the front desk to clear up any problems. Then, go to the front desk and ask if there was a problem. If there was none, inform the manager of the hotel that someone called to scam you of your credit card information acting like a front desk employee.