Large Language Models (LLMs) pretrained on massive corpora exhibit remarkable capabilities across a wide range of tasks, however, the attention given to non-English languages has been limited in this field of research. To address this gap and assess the proficiency of language models in the Korean language and culture, we present HAE-RAE Bench, covering 6 tasks including vocabulary, history, and general knowledge. Our evaluation of language models on this benchmark highlights the potential advantages of employing Large Language-Specific Models(LLSMs) over a comprehensive, universal model like GPT-3.5. Remarkably, our study reveals that models approximately 13 times smaller than GPT-3.5 can exhibit similar performance levels in terms of language-specific knowledge retrieval. This observation underscores the importance of homogeneous corpora for training professional-level language-specific models. On the contrary, we also observe a perplexing performance dip in these smaller LMs when they are tasked to generate structured answers.