What number is 20% greater than 60?

1. TRANSLATE the problem information

• Given information:
  • Starting number: \(60\)
  • Increase: \(20\%\)
  • Need to find: The number that is \(20\%\) greater than \(60\)

• What this tells us: We need to add \(20\%\) of \(60\) to the original \(60\)

2. INFER the most efficient approach

• \(20\%\) greater than \(60\) can be calculated two ways:
  • Method A: Find \(20\%\) of \(60\), then add it to \(60\)
  • Method B: Recognize this as \(120\%\) of \(60\) (since \(100\% + 20\% = 120\%\))

• Both methods work, but Method B is often faster

3. SIMPLIFY using your chosen method

Method A (Step-by-step):

• Calculate \(20\%\) of \(60\): \(0.20 \times 60 = 12\)
• Add to original: \(60 + 12 = 72\)

Method B (Direct):

• Convert to decimal: \(120\% = 1.20\)
• Multiply: \(1.20 \times 60 = 72\)

Answer: B. 72

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misinterpreting \(20\%\) greater than as simply \(20\%\) of

Students calculate \(0.20 \times 60 = 12\) and stop there, thinking this is the final answer. They don't realize they need to add this to the original \(60\). This leads them to select an answer that isn't even among the choices, causing confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Making arithmetic errors in the percentage calculations

Students understand the concept correctly but make calculation mistakes like:

• Confusing \(1.20\) with \(2.20\), leading to \(2.20 \times 60 = 132\)
• Mixing up \(20\%\) and \(25\%\), calculating \(1.25 \times 60 = 75\)

This may lead them to select Choice D (132) or Choice C (75).

The Bottom Line:

This problem tests whether students truly understand what percent greater than means versus just percent of. The key insight is recognizing that an increase requires adding to the original amount, not replacing it.