Step 1: Use rough population and area figures.
Asia has about 4.7 billion people on about 31 million square kilometres, giving roughly 150 people per square kilometre on average.
Step 2: Check the other continents against this.
Africa has about 1.4 billion people on about 30 million square kilometres, close in area to Asia but with under a third of the population, so its density works out far lower. Europe and North America have both fewer people and, in North America's case, a much larger area, pulling their densities down further.
Final Answer:
The numbers confirm option (b) Asia as the densest continent.$\boxed{\text{Asia}}$