Short Answer 
The age is narrowed down to two candidates, 7 and 8, based on the initial range. Elimination of 8 leads to the conclusion that the age must be 7, demonstrating effective logical reasoning.
Step 1: Understand the Range
The statement indicates that you are a number between 7 and 9. This means the potential candidates for your age are 7 and 8. Recognizing this initial range is crucial to proceeding with the reasoning.
Step 2: Assess the Clue
The clue provided specifically states that you are not 8. This information is critical as it helps narrow down the options. By eliminating 8, you can rule it out clearly from the choices available. This step is fundamental to applying logical reasoning.
Step 3: Conclusion through Elimination
With 8 eliminated as a possibility, the only number left is 7. Thus, after applying the process of elimination, we can confidently conclude that your age must be 7. This reinforces the effectiveness of simple logical reasoning in problem-solving.