Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A financial analyst observes that a company's stock value decreased by 15% in January and then increased by 20% in February. If the stock started at $80 per share, what was its final value per share at the end of February?
- A$82.00
- B$78.00
- C$81.60
- D$84.00
Show answer & explanationAnswer & explanation
Correct answer: C. $81.60
First, calculate the value after the 15% decrease: $80 * (1 - 0.15) = $80 * 0.85 = $68. Then, calculate the value after the 20% increase on the new value: $68 * (1 + 0.20) = $68 * 1.20 = $81.60.
Why the other options are wrong
- A. This could be a result of incorrectly averaging the percentage changes or calculating the increase based on the original value.
- B. This might incorrectly subtract and add percentages from the original value or make an arithmetic error.
- D. This might come from calculating the net change as +5% of the original value, which is incorrect for sequential changes.
Sequential Percentage Change
When a quantity undergoes multiple percentage changes, each subsequent change is applied to the *new* value, not the original value.
- Percentage increases are calculated as (1 + percentage) * current value.
- Percentage decreases are calculated as (1 - percentage) * current value.
- The order of operations matters for sequential changes.
Memory trick: Each step's new sum, for the next change to come!