3. (6 points) If the four-digit number $2 \overline{\mathrm{AB}}$ is divisible by 13, then the maximum value of the two-digit number $\overline{\mathrm{AB}}$ is $\qquad$
【Solution】Solution: For the four-digit number $\overline{2 \mathrm{AB} 7}$ to be divisible by 13, the difference $\overline{\mathrm{AB7}}-2=\overline{\mathrm{AB} 5}$ must be divisible by 13. The maximum value of $\overline{A B 5}$ is 995, and $995 \div 13=76 \cdots 7$, so 995 does not meet the requirement,

Then, $985 \div 13=75 \cdots 10$, so 985 does not meet the requirement,
Then, $975 \div 13=75$, which is divisible by 13,
Therefore, $\overline{2 \mathrm{AB} 7}=2975$, so the maximum value of $\overline{\mathrm{AB}}$ is 97.
Answer: The maximum value of $\overline{\mathrm{AB}}$ is 97.
The answer is: 97.