The MedHopQA challenge presents a critical test for Large Language Models (LLMs): complex, multi-hop reasoning in the high-stakes biomedical domain. This paper details our direct API-based evaluation of Google's Gemini Flash models, focusing on the impact of advanced prompt engineering. We designed a sophisticated, multi-component prompt for Gemini 2.0 Flash that combined role-playing, explicit multi-shot Chain-of-Thought (CoT) examples, and detailed formatting rules. Our best run, using this complex prompt, achieved a Concept Level Score of 0.720. This result dramatically outperformed a baseline prompt which scored only 0.565. Remarkably, this performance on the efficient Gemini 2.0 Flash was almost identical to the result from the next-generation Gemini 2.5 Flash. Our findings demonstrate that sophisticated prompt design is a critical factor for unlocking the full reasoning capabilities of modern LLMs.