A certain printer can print at an average rate of 24 pages per minute. At this rate, how many minutes...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A certain printer can print at an average rate of \(\mathrm{24}\) pages per minute. At this rate, how many minutes would it take this printer to print \(\mathrm{96}\) pages?
- \(\mathrm{4}\)
- \(\mathrm{24}\)
- \(\mathrm{96}\)
- \(\mathrm{2304}\)
1. TRANSLATE the problem information
- Given information:
- Rate: 24 pages per minute
- Total pages needed: 96 pages
- Find: time in minutes
2. INFER the mathematical relationship
- When you know a rate and total amount, time is found by dividing
- Think about it: if the printer does 24 pages every minute, how many minutes does it need for 96 pages?
- Formula: \(\mathrm{Time = Total\ Amount ÷ Rate}\)
3. SIMPLIFY the calculation
- \(\mathrm{Time = 96\ pages ÷ 24\ pages\ per\ minute}\)
- \(\mathrm{96 ÷ 24 = 4\ minutes}\)
Answer: A (4)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students multiply instead of divide, thinking "more pages means more time, so \(\mathrm{96 × 24}\)"
This backwards reasoning ignores what the rate actually tells us. They see two numbers and assume bigger output means multiply, leading to \(\mathrm{96 × 24 = 2,304}\).
This may lead them to select Choice D (2304)
Second Most Common Error:
Poor TRANSLATE reasoning: Students divide in the wrong order, calculating \(\mathrm{24 ÷ 96 = 0.25}\)
They recognize division is needed but get confused about which number goes where in the division. This gives them a decimal that doesn't match any answer choice.
This leads to confusion and guessing among the available choices.
The Bottom Line:
Rate problems require understanding what the rate means in practical terms - 24 pages per minute tells you how much work gets done in each unit of time, so dividing total work by rate gives you the time needed.