To answer this question, we need to understand the concept of concatenating partitioned data sets.

In IBM Mainframe systems, partitioned data sets (PDS) are a type of dataset that can contain multiple members. Each member within a PDS is an independent data set with its own name and attributes.

When concatenating PDSs, the maximum number of members that can be concatenated together is determined by the system's maximum number of available concatenation slots.

In the case of this question, the correct answer is A) 16. This means that a maximum of 16 PDSs can be concatenated together.

Options B) 32, C) 31, and D) 64 are incorrect. These options do not represent the correct maximum number of partitioned data sets that can be concatenated together.