GRE General TestQuantitative ReasoningHard
A production line produces 2,400 items per day. Due to an efficiency improvement, the production increases by 15%. However, 5% of the new production is found to be defective. What is the number of non-defective items produced per day after the improvement?
- A2,760
- B2,508
- C2,622
- D2,460
Show answer & explanationAnswer & explanation
Correct answer: C. 2,622
Initial production = 2400. Production increase by 15%: 2400 * 1.15 = 2760 items. Defective items = 5% of new production. Non-defective items = 95% of new production. Non-defective = 2760 * 0.95 = 2622 items.
Why the other options are wrong
- A. This is the total production after the 15% increase, before accounting for defective items.
- B. This is 2400 * (1 + 0.15 - 0.05) = 2400 * 1.10 = 2640, then 2640 * 0.95, which is an incorrect application of percentages.
- D. This is 2400 + (2400 * 0.05 / 2), a miscalculation.
Multi-Step Percentage Problems
Multi-step percentage problems involve applying several percentage changes or calculations sequentially. Each percentage is applied to the result of the previous step.
- An increase of X% means multiplying by (1 + X/100).
- A decrease of X% (or 'not defective' if X% are defective) means multiplying by (1 - X/100).
- Carry out operations in the order they occur in the problem.
Memory trick: First increase, then filter out the bad.