Advancements in LLMs have largely overlooked low-resource languages (LRLs), creating a gap in evaluation benchmarks. To address this for Georgian, a Kartvelian language, we introduce GeoLogicQA. This novel, manually-curated benchmark assesses LLMs’ logical and inferential reasoning through 100 questions. Questions cover syllogistic deduction, inferential reading comprehension, common-sense reasoning, and arithmetic, adapted from challenging sources (Kangaroo Mathematics Competition) and validated by native Georgian speakers for linguistic nuances. Initial evaluations of state-of-the-art LLMs (Gemini 2.5 Flash, DeepSeek-V3, Grok-3, GPT-4o) show an average accuracy of 64% to 83%, significantly exceeding the human baseline of 47%. While demonstrating strong reasoning potential, error analysis reveals persistent challenges in multi-step combinatorial and highly constrained inferential tasks. GeoLogicQA is a public resource for tracking progress and diagnosing weaknesses in Georgian LLMs. We plan to expand the benchmark and establish a public leader-board to foster continuous improvement.