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This work explores a novel data augmentation method based on Large Language Models (LLMs) for predicting item difficulty and response time of retired USMLE Multiple-Choice Questions (MCQs) in the BEA 2024 Shared Task. Our approach is based on augmenting the dataset with answers from zero-shot LLMs (Falcon, Meditron, Mistral) and employing transformer-based models based on six alternative feature combinations. The results suggest that predicting the difficulty of questions is more challenging. Notably, our top performing methods consistently include the question text, and benefit from the variability of LLM answers, highlighting the potential of LLMs for improving automated assessment in medical licensing exams. We make our code available https://github.com/ana-rogoz/BEA-2024.