The Six Sigma methodology:a.is a direct descendant of benchmarking.b.was developed by Deming, Juran, and Feigenbaum.c.was adopted first by British companies and then Japanese companies during the 1980s.d.is a direct descendant of the total quality management philosophy.

The correct answer is d. is a direct descendant of the total quality management philosophy.

Here's the step by step explanation:

1. The question is asking about the origins of the Six Sigma methodology.

2. The options provided are: it is a direct descendant of benchmarking, it was developed by Deming, Juran, and Feigenbaum, it was adopted first by British companies and then Japanese companies during the 1980s, and it is a direct descendant of the total quality management philosophy.

3. Six Sigma is a set of techniques and tools for process improvement. It was introduced by engineer Bill Smith while working at Motorola in 1986.

4. Option a, it is a direct descendant of benchmarking, is incorrect. Benchmarking is a process of comparing one's business processes and performance metrics to industry bests or best practices from other industries, but it is not the precursor to Six Sigma.

5. Option b, it was developed by Deming, Juran, and Feigenbaum, is incorrect. While these individuals were influential in the field of quality management, they did not develop Six Sigma.

6. Option c, it was adopted first by British companies and then Japanese companies during the 1980s, is incorrect. Six Sigma was first introduced by an American company, Motorola.

7. Therefore, the correct answer is d. is a direct descendant of the total quality management philosophy. Total Quality Management (TQM) is a management approach to long-term success through customer satisfaction, and Six Sigma is a methodology that emerged from the TQM philosophy.