During the first month of sales, a company sold 1,300,000 units of a certain type of smartphone. During the same...

1. TRANSLATE the key information

• Given information:
  • First month: 1,300,000 units sold
  • 15% of units sold were returned each month
  • Same sales and return rate for next 5 months (6 months total)
• What we need: Total units returned during the entire 6-month period

2. TRANSLATE the percentage into a calculation

• 15% of units returned means: \(15\% \times 1,300,000 = 0.15 \times 1,300,000\)
• Monthly returns = \(195,000\) units

3. INFER the total calculation needed

• Since the pattern repeats for 6 months total, we multiply the monthly return by 6
• The phrase "next 5 months" plus the first month = 6 months total
• Total returns = \(195,000 \times 6 = 1,170,000\) units

Answer: C. 1,170,000

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misunderstanding the time period referenced in the problem. Students might think they only need to calculate returns for the "next 5 months" (not including the first month), leading them to calculate \(195,000 \times 5 = 975,000\).

This may lead them to select Choice B (975,000).

Second Most Common Error:

Incomplete INFER reasoning: Students correctly calculate that \(195,000\) units were returned in the first month but stop there, not realizing they need to extend this to the full 6-month period.

This may lead them to select Choice A (195,000).

The Bottom Line:

This problem requires careful attention to the time frame being asked about. The key insight is recognizing that "during this 6-month period" includes both the first month mentioned and the "next 5 months" - making it crucial to multiply the monthly return rate by 6, not 5.