A study recently published on PubMed aimed to compare the effectiveness of different types of training for strength increase and body fat loss. In the study. They took 2 groups of men and trained their upper body strength by using either one set of 6 repititions to failure or 3 sets of 6 repititions to failure. They then compared results of strength increases and fat loss between the 2 groups.
The study can be found here: http://www.ncbi.nlm.nih.gov/pubmed/2408323
They trained the men 3 times per week for 8 weeks in both groups to ensure the test was as fair as possible. The results may shock you a little.
The results actually showed that both ways of training were just as effective as one another. Yes, one set of strength training was just as effective in terms of strength increase and body fat loss as 3 sets of strength training. How crazy does that sound!?! Do a third of the work spend a third of the time in the gym but get the same results, excellent!
As this study was carried out on upper body strength of men we can't be sure if the same results would be replicated for lower body strength or for women, but it at least throws some interesting questions out there.
Hopefully this gives you the confidence that even if you don't have time to get a 'full' workout in you can still make progress with just one set per workout. Obviously we wouldn't recommend just completing strength training without the time spent on looking after your joints, balance, coordination etc but in the short term this could really work for some people.
Hopefully this will get your brain thinking a little and start to see that there's more and more evidence coming out all the time that shows our conventional wisdom isn't necessarily all it's cracked up to be, in all aspects of health and fitness. Go with an open mind and research a little more. You'll be amazed at what you will find