Explanation:

To find the number of times the digit 3 appears between 1 and 100 where the number is not divisible by 3:

1. Numbers with the digit 3 include: 3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93.

2. Numbers not divisible by 3 are: 13, 23, 31, 32, 34, 35, 37, 38, 43, 53, 73, 83.

Count these numbers gives us 12.

Option 2: 12 is the correct answer.