Ratios, rates, proportional relationships, and units SAT question

Choice D is correct. The increase in Iceland’s population can be found by multiplying the increase in population density, in people per square kilometer, by the area, in square kilometers. It’s given that the population density of Iceland was 2.5 people per square kilometer in 1990 and 3.3 people per square kilometer in 2014. The increase in population density can be found by subtracting 2.5 from 3.3, which yields 0.8. It’s given that the land area of Iceland was 100,250 square kilometers. Thus, the increase in population is , or 80,200.

Alternate approach: It’s given that the population density of Iceland, in people per square kilometer of land area, in 1990 was 2.5. Since the land area of Iceland was 100,250 square kilometers, it follows that the population of Iceland in 1990 was , or 250,625. Similarly, the population of Iceland in 2014 was , or 330,825. The population increase is the difference in the population from 1990 to 2014, or , which yields 80,200. Therefore, Iceland’s population increased by 80,200 from 1990 to 2014.

Choice A is incorrect. This is the population of Iceland in 2014. Choice B is incorrect and may result from dividing 3.3 by 2.5, instead of subtracting 2.5 from 3.3. Choice C is incorrect and may result from dividing the population of Iceland in 1990 by 2.