GMAT Focus EditionQuantitative ReasoningMedium
A financial analyst is evaluating an investment. The investment's value increased by 25% in the first year. In the second year, its value decreased by 20% from the end of the first year. If the initial investment was $10,000, what is its value at the end of the second year?
- A$9,500
- B$10,500
- C$10,000
- D$11,000
Show answer & explanationAnswer & explanation
Correct answer: C. $10,000
First, calculate the value after the 25% increase. Then, calculate the 20% decrease based on that new value. The final value will be the initial investment multiplied by (1 + 0.25) and then by (1 - 0.20).
Why the other options are wrong
- A. This would be incorrect, as the net change is not a simple subtraction of percentages.
- B. This could result from miscalculating the second year's decrease or applying it incorrectly.
- D. This would imply a net gain, which is not the case for these successive percentage changes.
Successive Percentage Change
When a quantity changes by a percentage, and then changes again by another percentage, the changes are applied sequentially to the current value, not the original value.
- New Value = Original Value × (1 + %change1) × (1 + %change2) ...
- A decrease is represented by (1 - %change).
- Order of changes matters if the base for the second change is not the result of the first.
Memory trick: Remember, percentages are always based on the 'current' amount, not the start!