Detecting and aggregating sentiments toward people, organizations, and events expressed in unstructured social media have become critical text mining operations. Early systems detected sentiments over whole passages, whereas more recently, target-specific sentiments have been of greater interest. In this paper, we present MTTDSC, a multi-task target-dependent sentiment classification system that is informed by feature representation learnt for the related auxiliary task of passage-level sentiment classification. The auxiliary task uses a gated recurrent unit (GRU) and pools GRU states, followed by an auxiliary fully-connected layer that outputs passage-level predictions. In the main task, these GRUs contribute auxiliary per-token representations over and above word embeddings. The main task has its own, separate GRUs. The auxiliary and main GRUs send their states to a different fully connected layer, trained for the main task. Extensive experiments using two auxiliary datasets and three benchmark datasets (of which one is new, introduced by us) for the main task demonstrate that MTTDSC outperforms state-of-the-art baselines. Using word-level sensitivity analysis, we present anecdotal evidence that prior systems can make incorrect target-specific predictions because they miss sentiments expressed by words independent of target.