Large language models (LLMs) have demonstrated impressive reasoning capabilities when provided with chain-of-thought exemplars, but curating large reasoning datasets remains laborious and resource-intensive. In this work, we introduce Prompting Test-Time Scaling (P-TTS), a simple yet effective inference-time data augmentation strategy for enhancing LLM reasoning through finetuning. Rather than collecting thousands or even millions of examples, P-TTS leverages a small pool of only 90 manually selected reasoning instances and systematically varies exemplar augmentation through principled instruction prompting intensities at test time to synthesize diverse reasoning trajectory contexts. Then we finetune the various sizes of Qwen-2.5 models on P-TTS data. Across a suite of mathematical reasoning AIME2024 & 25, MATH500, and GPQA-Diamond, our P-TTS-7B and 32B models outperform the prior competitive baselines like S1 and S1.1 (1K-shot), achieving absolute accuracy gains of +26.66% and +30.00% on AIME'24 (7B), and +13.34% and +6.67% on AIME'25 (7B); P-TTS-32B yields gains of +23.33% and +16.63% on AIME'24, and +26.63% and +3.33% on AIME'25 (vs. S1 and S1.1, respectively), with comparable or better performance on MATH500 and GPQA-Diamond. We further show that P-TTS enhances zero-shot generalization accuracy on out-of-domain reasoning benchmarks of Gaokao, Kaoyan, OlympiadBench, AMC23, GradeSchoolMath, and Minerva. Our analysis suggests that test-time scaling effectively explores the latent space of reasoning patterns, amplifying LLM problem-solving with minimal annotation overhead, and further unlocking the reasoning potential and capabilities of LLMs. Prompting Test-Time Scaling offers a practical, low-cost way to elicit LLM reasoning in resource-constrained or rapidly evolving domains.

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