Arpit is thinking of a 2-digit number where the tens digit is twice the ones digit. How many different numbers can Arpit be thinking of?

To find the number of different numbers Arpit can be thinking of, we need to determine the possible values for both the tens digit and the ones digit.

Let's start with the ones digit. The ones digit can be any digit from 0 to 9. Since the tens digit is twice the ones digit, we can calculate the possible values for the tens digit:

0 --> 2 x 0 = 0
1 --> 2 x 1 = 2
2 --> 2 x 2 = 4
3 --> 2 x 3 = 6
4 --> 2 x 4 = 8
5 --> 2 x 5 = 10 (not a valid tens digit)
6 --> 2 x 6 = 12 (not a valid tens digit)
7 --> 2 x 7 = 14 (not a valid tens digit)
8 --> 2 x 8 = 16 (not a valid tens digit)
9 --> 2 x 9 = 18 (not a valid tens digit)

As we can see, the valid values for the tens digit are 0, 1, 2, 3, 4. For each tens digit, there is only one corresponding ones digit and vice versa. Therefore, there are 5 different numbers Arpit can be thinking of.