A number of well-known multicriteria problems of evaluating alternatives based on pairwise comparisons are considered. In these problems, given matrices containing results of paired comparisons of criteria and alternatives, one needs to find an absolute rating (priority, weight) of each alternative for decision making. Solutions to the problems are presented obtained using the method of analytical hierarchy process, the method of weighted geometric means, and the method of log-Chebyshev approximation of pairwise comparison matrices. The results obtained show that for some problems, solutions found by different methods may significantly differ from each other. In such cases, the decision to choose the best alternative may be based on additional analysis and comparison of the results of the problem solution obtained by all the methods used.