The growing complexity of construction management (CM) projects, coupled with challenges such as strict regulatory requirements and labor shortages, requires specialized analytical tools that streamline project workflow and enhance performance. Although large language models (LLMs) have demonstrated exceptional performance in general reasoning tasks, their effectiveness in tackling CM-specific challenges, such as precise quantitative analysis and regulatory interpretation, remains inadequately explored. To bridge this gap, this study introduces CMExamSet, a comprehensive benchmarking dataset comprising 689 authentic multiple-choice questions sourced from four nationally accredited CM certification exams. Our zero-shot evaluation assesses overall accuracy, subject areas (e.g., construction safety), reasoning complexity (single-step and multi-step), and question formats (text-only, figure-referenced, and table-referenced). The results indicate that GPT-4o and Claude 3.7 surpass typical human pass thresholds (70%), with average accuracies of 82% and 83%, respectively. Additionally, both models performed better on single-step tasks, with accuracies of 85.7% (GPT-4o) and 86.7% (Claude 3.7). Multi-step tasks were more challenging, reducing performance to 76.5% and 77.6%, respectively. Furthermore, both LLMs show significant limitations on figure-referenced questions, with accuracies dropping to approximately 40%. Our error pattern analysis further reveals that conceptual misunderstandings are the most common (44.4% and 47.9%), underscoring the need for enhanced domain-specific reasoning models. These findings underscore the potential of LLMs as valuable supplementary analytical tools in CM, while highlighting the need for domain-specific refinements and sustained human oversight in complex decision making.