Mark can remember only the first 4 digits of his friends phone number. He also knows that the number has 7 digits and that the last digit is not a 0. If mark were to dial all of the possible numbers and if it takes him 21 seconds to try each one, how long it take to try every possibility

To start, let's find how many possibilities there are. If we have a 7 digit phone number, and we know 4 digits, then that means we have 3 left to determine. Two of the digits have 10 possibilities (0-9), while the last digit only has 9 possibilities (1-9) since we know that it isn't a 0. So 10*10*9=900. With 900 possibilities, and 21 seconds per possibility, we get 900*21=18900 seconds, or 315 minutes.