Fill-in-the-blank Question:A factory sets a daily goal of producing 186 gadgets.Before lunch, the team completes 12 gadgets.After lunch, the team...
GMAT Algebra : (Alg) Questions
- A factory sets a daily goal of producing \(\mathrm{186}\) gadgets.
- Before lunch, the team completes \(\mathrm{12}\) gadgets.
- After lunch, the team works at a constant rate of \(\mathrm{6}\) gadgets every \(\mathrm{10}\) minutes until the daily goal is reached.
- How many \(\mathrm{10}\)-minute intervals are needed after lunch to reach the goal?
Answer Format Instructions: Enter your answer as an integer.
1. TRANSLATE the problem information
- Given information:
- Daily goal: 186 gadgets total
- Before lunch: 12 gadgets completed
- After lunch rate: 6 gadgets every 10 minutes
- What we need to find: How many 10-minute intervals after lunch
2. INFER the solution approach
- Key insight: We need to find how much work remains, then divide by the rate
- Strategy: Calculate remaining gadgets needed, then determine how many 10-minute periods it takes
3. SIMPLIFY to find remaining work needed
- Gadgets still needed = Total goal - Already completed
- Gadgets still needed = \(\mathrm{186 - 12 = 174}\) gadgets
4. SIMPLIFY to find number of intervals
- Number of 10-minute intervals = Remaining gadgets ÷ Rate per interval
- Number of intervals = \(\mathrm{174 \div 6 = 29}\)
5. Verify the answer
- Check: \(\mathrm{12}\) (before lunch) + \(\mathrm{29 \times 6}\) (after lunch) = \(\mathrm{12 + 174 = 186}\) ✓
Answer: 29
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misunderstand the rate and think it's 6 gadgets per minute instead of 6 gadgets per 10-minute interval.
They calculate: \(\mathrm{174 \div 6 = 29}\) minutes total, then think they need \(\mathrm{29 \div 10 = 2.9 \approx 3}\) intervals. This leads to confusion and potentially guessing a much smaller number.
Second Most Common Error:
Poor INFER reasoning: Students forget to subtract the 12 gadgets already completed before lunch.
They set up the problem as: \(\mathrm{186 \div 6 = 31}\) intervals, thinking they need to produce all 186 gadgets after lunch. This leads them to an answer that's too large.
The Bottom Line:
This problem requires careful attention to what's already been accomplished versus what still needs to be done, combined with proper interpretation of the given rate. The key breakthrough is recognizing that only the remaining work matters for the after-lunch calculation.