The price of an antique increased by in year 1, and then decreased by in year 2. What was the overall percentage change across the two years?
Answer and explanation
Correct answer: A.
- Step 1: Determine the percentage multiplier for each year: a increase has multiplier ; a decrease has multiplier .
- Step 2: Multiply the consecutive multipliers to find the overall multiplier: .
- Step 3: Convert the compound multiplier back to a percentage change: (an overall increase of ).
Answer
.
Why not the others: simply subtracts the percentages directly (), which ignores that the decrease applies to the higher new value; has the incorrect sign; takes an arithmetic average of percentages.
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