WASHINGTON — The security guards at a nuclear weapons plant who failed to stop an 82-year-old nun from reaching a bomb fuel storage building earlier this year were also cheating on a recertification exam, according to an internal investigation by the Department of Energy, which owns the weapons plant.

The exam, with answers, was circulated to guards at the Y-12 National Security Complex, near Oak Ridge, Tenn., before they sat down to take it, according to the report, by the department’s inspector general. The report, released on Wednesday, said that the cheating was enabled by the department itself. It was routine practice for the department to involve contractor personnel in preparation of such exams, because the federal government did not know enough about the security arrangements to write the exam without the help of the contractor.