ISEE Upper Level Quantitative Reasoning Question of the Day

1. 2,531 pages (correct answer)
2. 2,420 pages
3. 2,250 pages
4. 2,700 pages

Explanation: When you encounter rate problems with efficiency changes, you need to work through three key steps: find the original rate, calculate the new rate after the efficiency change, and apply that rate to the new time period. First, find the original printing rate: $\frac{1,500 \text{ pages}}{20 \text{ minutes}} = 75 \text{ pages per minute}$ Next, calculate the reduced rate. At 75% efficiency, the new rate becomes: $75 \times 0.75 = 56.25 \text{ pages per minute}$ Finally, apply this reduced rate to 45 minutes: $56.25 \times 45 = 2,531.25 \text{ pages}$ Since we can't print partial pages, this rounds to 2,531 pages, making A correct. Looking at the wrong answers: B (2,420 pages) likely comes from incorrectly calculating 75% of the original rate or making an arithmetic error in the final multiplication. C (2,250 pages) results from using exactly 50 pages per minute, suggesting someone miscalculated the efficiency reduction. D (2,700 pages) is what you'd get using 60 pages per minute, which represents 80% efficiency rather than 75%. The key trap here is rushing through the efficiency calculation. Many students correctly find the original rate but then make errors when applying the percentage reduction. Always double-check your percentage calculations—75% means multiplying by 0.75, not subtracting 75% from the original rate. Write out each step clearly to avoid computational mistakes in multi-step rate problems.