Mathematical reasoning serves as a crucial testbed for evaluating the intelligence of large language models (LLMs), and math word problems (MWPs) represent one of the most widely used formats. Most existing MWP datasets contain only the necessary information, while problems with distracting or excessive conditions are often overlooked. Prior studies have shown that popular LLMs experience a dramatic performance drop when such distracting conditions are introduced. However, available datasets of MWPs with distracting conditions remain limited, and most exhibit low difficulty and out-of-context expressions. These shortcomings make the distracting conditions easy to detect and disregard, thereby reducing the credibility of benchmarking on these datasets. Moreover, when distracting conditions are added, the reasoning process and answers may change, requiring intensive manual effort to check and rewrite solutions. To address these issues, we design an iterative framework that leverages LLMs to generate distracting conditions automatically. We develop a set of prompts to revise MWPs from multiple perspectives and cognitive levels, encouraging the creation of meaningful distracting conditions as well as suggestions for further refinement. A key advantage of our framework is the preservation of shared solutions between the original and revised problems: the LLMs are explicitly guided to generate distractions that do not alter the original solution, thus eliminating the need to produce new answers. This framework is efficient and easy to deploy, substantially reducing the effort required to generate MWPs with distracting conditions while maintaining high data quality.

翻译：数学推理是评估大型语言模型智能的关键测试平台，而数学应用题则是其中应用最广泛的题型之一。现有大多数数学应用题数据集仅包含必要信息，而带有干扰条件或冗余条件的问题常被忽视。先前研究表明，当引入此类干扰条件时，主流大型语言模型的性能会出现显著下降。然而，现有包含干扰条件的数学应用题数据集仍然有限，且多数存在难度偏低和语境脱节的问题。这些缺陷使得干扰条件易于被检测和忽略，从而降低了基于这些数据集进行基准测试的可信度。此外，当添加干扰条件时，推理过程和答案可能发生变化，需要大量人工投入来检查和重写解答。为解决这些问题，我们设计了一个迭代框架，利用大型语言模型自动生成干扰条件。我们开发了一套提示词模板，从多角度和认知层次对数学应用题进行修订，鼓励生成有意义的干扰条件并提供进一步优化的建议。本框架的核心优势在于保持原始问题与修订问题之间的解答一致性：通过明确引导大型语言模型生成不改变原问题解的干扰条件，从而无需生成新的答案。该框架具有高效易部署的特点，在保证数据质量的同时，显著降低了生成含干扰条件的数学应用题所需的工作量。