GRE General TestQuantitative ReasoningHard
A production manager observes that the average time to assemble a certain product decreases by 10% for every 50 units produced, starting from the 51st unit. If the first 50 units take an average of 12 minutes each, what is the average assembly time (in minutes) for the next 100 units (units 51-150)?
- A9.72
- B12.00
- C11.16
- D10.80
Show answer & explanationAnswer & explanation
Correct answer: A. 9.72
The problem describes a learning curve effect. For units 51-100, the time decreases by 10% from the initial 12 minutes. For units 101-150, the time decreases by another 10% from the previous interval's time. Calculate the average time for each 50-unit block, then find the overall average for the 100 units.
Why the other options are wrong
- B. This is the original average time, ignoring the decrease.
- C. This is a plausible distractor resulting from an incorrect averaging or percentage application.
- D. This is the average time for the first 50 units of the 'next 100' (units 51-100).
Successive Percentage Decrease
A quantity is subjected to multiple percentage decreases, where each subsequent decrease is applied to the already reduced amount.
- To decrease by P percent, multiply by (1 - P/100).
- For successive decreases, multiply by the factor (1 - P/100) repeatedly.
- The order of application for successive percentage changes does not matter.
Memory trick: Reduce and Repeat: Apply the reduction factor multiple times to the current value.