The average annual increase in the number of urbanites in developing…

Concept: an average annual increase is a rate, not a level. It measures how much a quantity grew in a typical year, so it is built only from the growth that happened during the period; whatever already existed at the start of the period was never added during it.

Average annual increase = (value at the end of the period − value at the start of the period) ÷ number of years in the period.

Applying this to the passage:

1. The passage supplies both endpoints: the urban population of developing countries was 300 million in 1950 and 2 billion, that is 2,000 million, in 2000.

2. The period runs from 1950 to 2000, a span the passage itself describes as the last 50 years.

3. Growth during the period = 2,000 million − 300 million = 1,700 million.

4. Average annual increase = 1,700 million ÷ 50 years = 34 million per year.

Cross-check: 34 million a year for 50 years contributes 1,700 million, and adding that to the 300 million already urban in 1950 returns 2,000 million — exactly the 2 billion the passage reports for the year 2000, so this rate reproduces the passage's own figures.

The stem asks which of the offered values the rate was close to. 34 million lies between 30 million and 40 million and is nearer the former, since 34 − 30 = 4 while 40 − 34 = 6. The answer is therefore 30 million.

Contrast: dividing the year-2000 total of 2,000 million by 50 years gives 40 million, but that treats the whole year-2000 urban population as though every one of them had appeared after 1950, ignoring the 300 million who were already city dwellers. Rates of 50 million and 60 million a year would imply 2,500 million and 3,000 million added over the same span, far more growth than the passage describes.