Large Language Models (LLMs) have shown remarkable capabilities in manipulating natural language across multiple applications, but their ability to handle simple reasoning tasks is often questioned. In this work, we aim to provide a comprehensive analysis of LLMs' reasoning competence, specifically focusing on their prompt dependency. In particular, we introduce a new benchmark dataset with a series of simple reasoning questions demanding shallow logical reasoning. Aligned with cognitive psychology standards, the questions are confined to a basic domain revolving around geometric figures, ensuring that responses are independent of any pre-existing intuition about the world and rely solely on deduction. An empirical analysis involving zero-shot and few-shot prompting across 24 LLMs of different sizes reveals that, while LLMs with over 70 billion parameters perform better in the zero-shot setting, there is still a large room for improvement. An additional test with chain-of-thought prompting over 22 LLMs shows that this additional prompt can aid or damage the performance of models, depending on whether the rationale is required before or after the answer.