A quality-control team inspects a batch of 250 smartphones and finds that 20 are defective. What percent of the smartphones...

1. TRANSLATE the problem information

• Given information:
  • Total smartphones: 250
  • Defective smartphones: 20
  • Need to find: Percent that are nondefective

2. INFER the solution approach

• Key insight: We can solve this problem two different ways:
  • Method 1: Find nondefective count, then calculate its percentage
  • Method 2: Find defective percentage first, then use the fact that \(\mathrm{defective\%} + \mathrm{nondefective\%} = 100\%\)
• Let's use Method 1 (more direct):

3. Calculate nondefective count

• Nondefective smartphones = Total - Defective = \(250 - 20 = 230\)

4. SIMPLIFY to find the percentage

• Percent nondefective = \(\frac{230}{250} \times 100\%\)
• = \(\frac{23}{25} \times 100\%\)
• = \(0.92 \times 100\% = 92\%\)

Answer: D (92%)

Why Students Usually Falter on This Problem

Most Common Error Path:

Process Skill Error - Weak TRANSLATE reasoning: Students misread the question and calculate the percent of defective smartphones instead of nondefective smartphones.

They correctly calculate \(\frac{20}{250} \times 100\% = 8\%\), but this answers the wrong question. Since they computed a percentage that appears in the answer choices, they confidently select Choice A (8%) without realizing they found defective percent instead of nondefective percent.

Second Most Common Error:

Process Skill Error - Inadequate SIMPLIFY execution: Students make arithmetic errors when converting the fraction to a percentage.

Common calculation mistakes include:

• Incorrectly computing \(\frac{230}{250}\) (mixing up numerator/denominator)
• Errors in decimal conversion or percentage multiplication
• Forgetting to multiply by 100 to convert to percentage form

This leads to confusion and potentially selecting Choice B (20%) or Choice C (80%) based on their incorrect calculations.

The Bottom Line:

This problem tests whether students can carefully read what's being asked (nondefective vs defective) and execute percentage calculations accurately. The key insight is recognizing that there are two valid approaches, but both require attention to what quantity is actually being requested.