PSAT Math Multiple-Choice Question 372: Answer and Explanation

Question: 372

Over the past decade, the population of a certain town increased by 20 percent. If the population of the town increases 15 percent over the next decade, by what percent will the population have increased over the entire two-decade period?

• A. 33%
• B. 35%
• C. 38%
• D. 43%

Correct Answer: C

Explanation:

C

Difficulty: Medium

Getting to the Answer: One key piece of information not given is the initial population of the town. Since this is a percent change question, pick 100 for the initial population. (Your number doesn't have to be realistic, only easy to work with.) Over the last decade, the population increased by 20%, so that is an increase from 100 to 120. Over the next decade, if the population increases by 15%, the total population would become 120 + (0.15)120 = 120 + 18 = 138. Therefore, the total increase in actual population over the two decades is 138 - 100 = 38. Now, apply the percent change formula:

Choice (C) is correct.