GMAT Focus EditionQuantitative ReasoningHard
A company's annual revenue increased by 20% in the first year, decreased by 10% in the second year, and then increased by 5% in the third year. If the initial revenue was $1,000,000, what was the revenue at the end of the third year?
- A$1,134,000
- B$1,120,000
- C$1,200,000
- D$1,150,000
Show answer & explanationAnswer & explanation
Correct answer: A. $1,134,000
Initial Revenue = $1,000,000. Year 1: 1,000,000 * (1 + 0.20) = 1,000,000 * 1.20 = $1,200,000. Year 2: 1,200,000 * (1 - 0.10) = 1,200,000 * 0.90 = $1,080,000. Year 3: 1,080,000 * (1 + 0.05) = 1,080,000 * 1.05 = $1,134,000. Alternatively, Final Revenue = Initial Revenue * (1 + r1) * (1 + r2) * (1 + r3) = 1,000,000 * (1.20) * (0.90) * (1.05) = $1,134,000.
Why the other options are wrong
- B. This is incorrect; it might be the revenue after only the first year's increase and second year's decrease.
- C. This is incorrect; this is the revenue after only the first year's increase.
- D. This is incorrect; it might be a result of simply adding/subtracting the percentage changes (20-10+5 = 15% increase) or other miscalculation.
Successive Percentage Change
The cumulative effect on a quantity when it undergoes multiple percentage changes sequentially.
- Each percentage change is applied to the *new* value, not the original value.
- Expressed as multiplying factors: (1 + r1) * (1 + r2) * ...
- Order of changes matters for different types of changes (e.g., discount then markup).
Memory trick: Multiply factors, one by one, until the final value is won.