A mechanical device in a workshop produces items at a constant rate of 60 items per hour. At this rate,...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A mechanical device in a workshop produces items at a constant rate of \(60\) items per hour. At this rate, how many items will the mechanical device produce in \(3\) hours?
Solution
- Rate of production = \(60\) items per hour
- Time = \(3\) hours
- Total items produced = \(60 \times 3\)
- Total items produced = \(180\) items
Therefore, the mechanical device will produce \(180\) items in \(3\) hours.
1. TRANSLATE the problem information
- Given information:
- Production rate: 60 items per hour (constant)
- Time period: 3 hours
- Need to find: Total items produced
- What this tells us: The device makes the same number of items each hour.
2. INFER the approach
- Since we have a constant rate, we can use: \(\mathrm{Total = Rate \times Time}\)
- The rate stays the same for each hour, so we multiply the hourly production by the number of hours
3. SIMPLIFY the calculation
- \(\mathrm{Total\,items = 60\,items/hour \times 3\,hours}\)
- \(\mathrm{Total\,items = 180\,items}\)
Answer: 180
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE reasoning: Students may not clearly understand what 'rate' means or how to set up the calculation.
Some students might think they need to add instead of multiply \(\mathrm{(60 + 3 = 63)}\) or might get confused about which operation to use. This leads to confusion and guessing among the available answer choices.
The Bottom Line:
This problem tests whether students understand that a constant rate means 'same amount per unit time,' making it a straightforward multiplication problem once properly translated.