Large Language Models (LLMs) have in recent years demonstrated impressive prowess in natural language generation. A common practice to improve generation diversity is to sample multiple outputs from the model. However, partly due to the inaccessibility of LLMs, there lacks a simple and robust way of selecting the best output from these stochastic samples. As a case study framed in the context of question generation, we propose two prompt-based approaches, namely round-trip and prompt-based score, to selecting high-quality questions from a set of LLM-generated candidates. Our method works without the need to modify the underlying model, nor does it rely on human-annotated references — both of which are realistic constraints for real-world deployment of LLMs. With automatic as well as human evaluations, we empirically demonstrate that our approach can effectively select questions of higher qualities than greedy generation.