The manager of an online news service received the report above on the number of subscriptions sold by the service....

1. TRANSLATE the problem information

• Given information:
  • 2012: 5,600 subscriptions
  • 2013: 5,880 subscriptions
  • Manager's estimate: percent increase from 2012 to 2013 = 2 × percent increase from 2013 to 2014
• What we need to find: Expected subscriptions in 2014

2. SIMPLIFY to find the actual 2012-2013 percent increase

• Using percent increase formula: \(\frac{\mathrm{new - old}}{\mathrm{old}}\)
• \(\frac{5,880 - 5,600}{5,600} = \frac{280}{5,600} = 0.05 = 5\%\)

3. INFER the 2013-2014 percent increase from the manager's relationship

• If 2012-2013 increase = 2 × (2013-2014 increase)
• Then: \(5\% = 2 \times \mathrm{(2013-2014\ increase)}\)
• So: \(\mathrm{2013-2014\ increase} = 5\% \div 2 = 2.5\%\)

4. SIMPLIFY to calculate the expected 2014 subscriptions

• Apply 2.5% increase to 2013 baseline: \(5,880 \times (1 + 0.025)\)
• \(5,880 \times 1.025 = 6,027\) (use calculator)

Answer: B. 6,027

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misinterpreting the direction of the "double" relationship

Students often think the problem means the 2013-2014 increase should be double the 2012-2013 increase, rather than half of it. This leads them to calculate: \(\mathrm{2013-2014\ increase} = 5\% \times 2 = 10\%\), giving \(5,880 \times 1.10 = 6,468\).

This may lead them to select Choice D (6,468)

Second Most Common Error:

Poor INFER reasoning: Confusing percent increase with the actual increase value

Some students correctly find that 2012-2013 had a 280-subscription increase, then think they should add half of 280 (140) directly to the 2013 value: \(5,880 + 140 = 6,020\). They're mixing up the percent increase concept with raw number increases.

This may lead them to select Choice A (6,020)

The Bottom Line:

This problem tests whether students can correctly parse complex verbal relationships about percentages and distinguish between percent increases versus actual value increases. The key insight is recognizing that "double the percent increase" creates an inverse relationship for the unknown percentage.