We present a controlled study of multi-hop contextual reasoning in large language models, providing a clean demonstration of the task-method dissociation: rule-based pattern matching achieves 100% success on structured information retrieval but only 6.7% on tasks requiring cross-document reasoning, while LLM-based multi-agent systems show the inverse pattern, achieving up to 80% on reasoning tasks where rule-based methods fail. Using a synthetic evaluation framework with 120 trials across four models (LLaMA-3 8B, LLaMA-2 13B, Mixtral 8x7B, DeepSeek-V2 16B), we report three key findings: (1) Multi-agent amplification depends on base capability: statistically significant gains occur only for models with sufficient reasoning ability (p < 0.001 for LLaMA-3 8B, p = 0.014 for Mixtral), with improvements of up to 46.7 percentage points, while weaker models show no benefit, suggesting amplification rather than compensation; (2) Active parameters predict reasoning performance: Mixtral's performance aligns with its ~12B active parameters rather than 47B total, consistent with the hypothesis that inference-time compute drives reasoning capability in MoE architectures; (3) Architecture quality matters: LLaMA-3 8B outperforms LLaMA-2 13B despite fewer parameters, consistent with known training improvements. Our results provide controlled quantitative evidence for intuitions about multi-agent coordination and MoE scaling, while highlighting the dependence of multi-agent benefits on base model capability. We release our evaluation framework to support reproducible research on reasoning in mid-scale models.