GRE General TestQuantitative ReasoningMedium
A production manager observes that the average time to assemble a certain product decreases by 10% each week for three consecutive weeks. If the initial average assembly time was 50 minutes, what is the assembly time after three weeks?
- A38.5 minutes
- B40.5 minutes
- C35 minutes
- D36.45 minutes
Show answer & explanationAnswer & explanation
Correct answer: D. 36.45 minutes
Initial time = 50 minutes. Week 1: 50 * (1 - 0.10) = 50 * 0.9 = 45 minutes. Week 2: 45 * 0.9 = 40.5 minutes. Week 3: 40.5 * 0.9 = 36.45 minutes. Alternatively, 50 * (0.9)^3 = 50 * 0.729 = 36.45 minutes.
Why the other options are wrong
- A. This is a plausible distractor, perhaps from rounding errors or incorrect calculation.
- B. This is the assembly time after two weeks, not three.
- C. This is 50 - (3 * 5) = 35, incorrectly subtracting 10% of the original amount three times.
Successive Percentage Decrease
Successive percentage decreases involve applying a percentage reduction multiple times, where each subsequent reduction is applied to the *new* decreased value, not the original value.
- A decrease of X% is equivalent to multiplying by (1 - X/100).
- For 'n' successive decreases, multiply the original value by (1 - X/100)^n.
- This is a form of exponential decay.
Memory trick: Multiply by the 'leftover' factor, power of the repeats.