A range query applies an aggregation operation over all selected cells of an OLAP data cube where the selection is speci ed by providing ranges of values for numeric dimensions. We present fast algorithms for range queries for two types of aggregation operations: SUM and MAX. These two operations cover techniques required for most popular aggregation operations, such as those supported by SQL. For range-sum queries, the essential idea is to precompute some auxiliary information pre x sums that is used to answer ad hoc queries at run-time. By maintaining auxiliary information which is of the same size as the data cube, all range queries for a given cube can be answered in constant time, irrespective of the size of the sub-cube circumscribed by a query. Alternatively, one can keep auxiliary information which is 1 bd of the size of the d-dimensional data cube. Response to a range query may now require access to some cells of the data cube in addition to the access to the auxiliary info...