GMAT Focus EditionQuantitative ReasoningMedium
A company's revenue increased by 10% in the first quarter and then decreased by 5% in the second quarter. If the revenue at the beginning of the first quarter was $200,000, what was the revenue at the end of the second quarter?
- A$214,000
- B$220,000
- C$210,000
- D$209,000
Show answer & explanationAnswer & explanation
Correct answer: D. $209,000
This is a successive percentage change problem. First quarter increase: $200,000 * (1 + 0.10) = $200,000 * 1.10 = $220,000. Second quarter decrease: $220,000 * (1 - 0.05) = $220,000 * 0.95 = $209,000.
Why the other options are wrong
- A. This might result from a calculation error in one of the steps or incorrect application of percentages.
- B. This is the revenue after only the first quarter increase, not accounting for the second quarter decrease.
- C. This would be the result if the 5% decrease was applied to the original $200,000, not the increased amount.
Net Percentage Change
The net percentage change from successive increases and decreases is found by multiplying the original amount by (1 + increase_rate) and (1 - decrease_rate) sequentially.
- Each percentage change is applied to the *current* value, not the original.
- Can be calculated as Original Value * (1 +/- r1) * (1 +/- r2) ...
- Order of application of changes does not affect the final result.
Memory trick: First you grow the pie, then you shrink the new pie, not the old one.