Handling long tail corner cases is a major challenge faced by autonomous vehicles (AVs). While large language models (LLMs) hold great potentials to handle the corner cases with excellent generalization and explanation capabilities and received increasing research interest on application to autonomous driving, there are still technical barriers to be tackled, such as strict model performance and huge computing resource requirements of LLMs. In this paper, we investigate a new approach of applying remote or edge LLMs to support autonomous driving. A key issue for such LLM assisted driving system is the assessment of LLMs on their understanding of driving theory and skills, ensuring they are qualified to undertake safety critical driving assistance tasks for CAVs. We design and run driving theory tests for several proprietary LLM models (OpenAI GPT models, Baidu Ernie and Ali QWen) and open-source LLM models (Tsinghua MiniCPM-2B and MiniCPM-Llama3-V2.5) with more than 500 multiple-choices theory test questions. Model accuracy, cost and processing latency are measured from the experiments. Experiment results show that while model GPT-4 passes the test with improved domain knowledge and Ernie has an accuracy of 85% (just below the 86% passing threshold), other LLM models including GPT-3.5 fail the test. For the test questions with images, the multimodal model GPT4-o has an excellent accuracy result of 96%, and the MiniCPM-Llama3-V2.5 achieves an accuracy of 76%. While GPT-4 holds stronger potential for CAV driving assistance applications, the cost of using model GPT4 is much higher, almost 50 times of that of using GPT3.5. The results can help make decision on the use of the existing LLMs for CAV applications and balancing on the model performance and cost.