A 3D printer extrudes filament at a constant rate of 24 grams per minute.A prototype part requires exactly 216 grams...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
- A 3D printer extrudes filament at a constant rate of 24 grams per minute.
- A prototype part requires exactly 216 grams of filament.
- How many minutes will the printer take to produce the part? Enter your answer as an integer.
1. TRANSLATE the problem information
- Given information:
- Rate: 24 grams per minute (constant)
- Amount needed: 216 grams
- Find: time in minutes
2. INFER the mathematical relationship
- This is a rate problem using the relationship: \(\mathrm{rate \times time = amount}\)
- We know rate and amount, need to solve for time
- Set up the equation: \(\mathrm{24\ grams/minute \times t\ minutes = 216\ grams}\)
3. SIMPLIFY to find the answer
- Solve for t: \(\mathrm{t = 216 \div 24}\)
- \(\mathrm{t = 9\ minutes}\)
Answer: 9
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students may confuse which values represent rate, time, and amount, leading to incorrect equation setup like \(\mathrm{216 \times t = 24}\) or \(\mathrm{t \div 24 = 216}\).
This confusion stems from not carefully identifying what each number represents in the problem context, causing them to set up the wrong mathematical relationship and get stuck or guess randomly.
Second Most Common Error:
Poor SIMPLIFY execution: Students correctly set up \(\mathrm{216 \div 24}\) but make arithmetic errors, perhaps calculating \(\mathrm{216 \div 24 = 8}\) or \(\mathrm{216 \div 24 = 10}\).
These calculation mistakes occur when students rush through the division or make simple computational errors, leading them to confidently submit an incorrect answer.
The Bottom Line:
Success on this problem hinges on recognizing the rate relationship and accurately translating the word problem into the correct mathematical setup, followed by careful arithmetic execution.