Large language models (LLMs) have opened new opportunities for automated mobile app exploration, an important and challenging problem that used to suffer from the difficulty of generating meaningful UI interactions. However, existing LLM-based exploration approaches rely heavily on LLMs to generate actions in almost every step, leading to a huge cost of token fees and computational resources. We argue that such extensive usage of LLMs is neither necessary nor effective, since many actions during exploration do not require, or may even be biased by the abilities of LLMs. Further, based on the insight that a precise and compact knowledge plays the central role for effective exploration, we introduce LLM-Explorer, a new exploration agent designed for efficiency and affordability. LLM-Explorer uses LLMs primarily for maintaining the knowledge instead of generating actions, and knowledge is used to guide action generation in a LLM-less manner. Based on a comparison with 5 strong baselines on 20 typical apps, LLM-Explorer was able to achieve the fastest and highest coverage among all automated app explorers, with over 148x lower cost than the state-of-the-art LLM-based approach.