Performing non-aggregate range queries on cloud stored data, while achieving both privacy and efficiency is a challenging problem. This paper proposes constructing a differentially private index to an outsourced encrypted dataset. Efficiency is enabled by using a cleartext index structure to perform range queries. Security relies on both differential privacy (of the index) and semantic security (of the encrypted dataset). Our solution, PINED-RQ develops algorithms for building and updating the differentially private index. Compared to state-of-the-art secure index based range query processing approaches, PINED-RQ executes queries in the order of at least one magnitude faster. The security of PINED-RQ is proved and its efficiency is assessed by an extensive experimental validation.