Problem-Solving and Data AnalysisHardPercent increase versus percent decrease between the same two numbers
Problem-Solving and Data Analysis practice question
A town's population grew from 12,000 to 15,000 over a decade. Which of the following statements is true?
- A. The population increased by 25%, and a fall from 15,000 back to 12,000 would be a 20% decrease.Correct
- B. The population increased by 20%.
- C. The population increased by 25%, and a fall back to 12,000 would also be a 25% decrease.
- D. The population increased by 3%.
Answer: A. The population increased by 25%, and a fall from 15,000 back to 12,000 would be a 20% decrease.
Increase: 3,000/12,000 = 25%. A fall of 3,000 from 15,000 is 3,000/15,000 = 20%. Percent change depends on the starting value.
Why the other answers are wrong
- B. The population increased by 20%.
- 20% divides the change by the NEW population; increases are measured from the start.
- C. The population increased by 25%, and a fall back to 12,000 would also be a 25% decrease.
- The same 3,000 is a smaller share of 15,000 than of 12,000, so the decrease is 20%, not 25%.
- D. The population increased by 3%.
- 3% confuses the change of 3,000 with a percentage.
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