Social media currently plays a significant role in interpersonal interaction and information consumption. However, these platforms have also become spaces where various social issues, such as sexism and gender gaps, are increasingly disseminated. This study evaluates the performance of two large language models, GPT-4o and Mistral 7B, in detecting sexist content on the social media platform X (formerly Twitter), using several prompt combinations on the EXIST 2024 dataset. Our findings show that GPT-4o delivers more consistent results across different prompts and achieves higher f1-scores values. In contrast, Mistral 7B demonstrates greater variability but achieves higher recall in several configurations, allowing it to detect more sexist tweets at the cost of increased false positives. When exploring the impact of prompt design (zero-shot vs. few-shot), we found that including examples in few-shot prompts did not significantly improve performance for GPT-4o and reduced performance for Mistral 7B.