Question: A faucet fills a tank at a rate of 3 gallons per minute. If the faucet filled 27 gallons...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A faucet fills a tank at a rate of \(\mathrm{3}\) gallons per minute. If the faucet filled \(\mathrm{27}\) gallons into the tank, how many minutes did it take?
1. TRANSLATE the problem information
- Given information:
- Rate of filling: 3 gallons per minute
- Total amount filled: 27 gallons
- Need to find: Time in minutes
2. INFER the mathematical relationship
- When you know the rate and total amount, you can find time using:
\(\mathrm{Time} = \frac{\mathrm{Total\ Amount}}{\mathrm{Rate}}\) - This works because rate tells us "how much per unit of time," so to find how many units of time we need, we divide the total by the rate.
3. Calculate the time
- \(\mathrm{Time} = \frac{27\ \mathrm{gallons}}{3\ \mathrm{gallons\ per\ minute}} = 9\ \mathrm{minutes}\)
Answer: B) 9
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students may not recognize the correct relationship between rate, amount, and time. They might think they need to multiply the rate by something to get 27, leading them to calculate \(27 \div 3 = 9\), but then think "\(9 \times 3 = 27\), so maybe the answer is related to multiplication somehow." This conceptual confusion about rates can lead to selecting an incorrect answer or guessing randomly.
The Bottom Line:
The key challenge is understanding that rate problems require division when you're given the rate and total amount but need to find time. Students who memorize "\(\mathrm{distance} = \mathrm{rate} \times \mathrm{time}\)" without understanding the underlying relationship may struggle to rearrange this to solve for time.