A bookstore orders 1,250 copies of a novel. During the first week, 24% of the copies are sold. How many...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A bookstore orders \(\mathrm{1,250}\) copies of a novel. During the first week, \(\mathrm{24\%}\) of the copies are sold. How many copies are sold during the first week?
Enter your answer as an integer.
1. TRANSLATE the problem information
- Given information:
- Total copies ordered: 1,250
- Percentage sold in first week: 24%
- Need to find: Number of copies sold
- What this tells us: We need to find 24% of 1,250 copies
2. INFER the approach
- To find a percentage of a number, we multiply the percentage (as a decimal) by the number
- Strategy: Convert 24% to decimal form, then multiply by 1,250
3. SIMPLIFY the percentage conversion
- Convert 24% to decimal: \(\mathrm{24\% = 24 ÷ 100 = 0.24}\)
4. SIMPLIFY the multiplication
- Calculate: \(\mathrm{0.24 × 1,250 = 300}\)
Answer: 300
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE reasoning: Students incorrectly convert the percentage to decimal, writing \(\mathrm{24\% = 0.024}\) instead of \(\mathrm{0.24}\) (moving the decimal point the wrong direction or forgetting that percent means 'per hundred').
When they calculate \(\mathrm{0.024 × 1,250 = 30}\), they get 30 copies instead of 300. This leads to confusion since 30 seems too small, but they may stick with this answer or guess randomly.
Second Most Common Error:
Poor SIMPLIFY execution: Students correctly identify that they need \(\mathrm{0.24 × 1,250}\) but make arithmetic errors in the multiplication, potentially getting answers like 3,000 (adding an extra zero) or 30 (losing a zero).
This causes them to doubt their approach and either guess or abandon their systematic solution.
The Bottom Line:
The key challenge is remembering that converting a percentage to decimal requires dividing by 100, not 1,000. Students who master this conversion and can multiply decimals confidently will solve this problem successfully.