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Problem-Solving and Data AnalysisHardSuccessive percent changes

Problem-Solving and Data Analysis practice question

A stock's price rises by 20% one month and then falls by 20% the next month. Compared with its price at the start, the price at the end is

  1. A. 4% lower.Correct
  2. B. the same.
  3. C. 4% higher.
  4. D. 20% lower.

Answer: A. 4% lower.

Start at 100. Up 20%: 120. Down 20% of 120 (which is 24): 96. The final price is 96% of the original — 4% lower. The second change is a percent of the larger number, so it takes off more than the first added.

Why the other answers are wrong

B. the same.
A 20% rise and a 20% fall don't cancel, because the fall is 20% of a BIGGER number. 100 → 120 → 96.
C. 4% higher.
The price ends below where it started, not above. 96 is less than 100.
D. 20% lower.
20% lower would be 80. The fall of 20% is applied to 120, giving 96, not to the original 100 twice.

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