Large language models (LLMs) are increasingly relied upon to solve complex mathematical word problems. However, being susceptible to hallucination, they may generate inaccurate results when presented with unanswerable questions, raising concerns about their potential harm. While GPT models are now widely used and trusted, the exploration of how they can effectively abstain from answering unanswerable math problems and the enhancement of their abstention capabilities has not been rigorously investigated. In this paper, we investigate whether GPTs can appropriately respond to unanswerable math word problems by applying prompts typically used in solvable mathematical scenarios. Our experiments utilize the Unanswerable Word Math Problem (UWMP) dataset, directly leveraging GPT model APIs. Evaluation metrics are introduced, which integrate three key factors: abstention, correctness and confidence. Our findings reveal critical gaps in GPT models and the hallucination it suffers from for unsolvable problems, highlighting the need for improved models capable of better managing uncertainty and complex reasoning in math word problem-solving contexts.