15. A total of 99 people participated in a mathematics competition, which was divided into three sessions, testing the contestants' abilities in geometry, number theory, and combinatorics. Xiao Ming ranked 16th in the number theory exam, 30th in the combinatorics exam, and 23rd in the geometry exam, and he did not tie with anyone in any of the three exams (the full score for each exam is not necessarily 100 points). The final overall ranking is determined by adding up the scores from the three exams and ranking them from highest to lowest. If we use the $\mathrm{A}$th place to represent the best possible overall ranking Xiao Ming could achieve (the smaller the $\mathrm{A}$, the better the overall ranking), and the $\mathrm{B}$th place to represent the worst possible overall ranking, then $100 A+B=(\quad)$.
【Analysis】When $\left\{\begin{array}{l}\text { in the top } 15 \text { in number theory, ranking last in combinatorics and geometry exams } \\ \text { in the top } 22 \text { in geometry, ranking last in number theory and combinatorics exams }\end{array}\right.$
When the top 15 in number theory, the top 29 in combinatorics, and the top 22 in geometry are different individuals, and all rank ahead of Xiao Ming, Xiao Ming's worst rank, i.e., $\mathrm{B}=15+29+22+1=67$;
Therefore, $100 \mathrm{~A}+\mathrm{B}=167$.