A survey taken by 1,000 students at a school asked whether they played school sports. The table below summarizes all...

1. TRANSLATE the table information

• Given information:
  • Total students surveyed: 1,000
  • Males who play school sport: 312
  • Females who play school sport: 220
  • Females who don't play school sport: 216
  • Males who don't play school sport: unknown (what we're finding)

• What this tells us: These four categories represent ALL 1,000 students with no overlap

2. INFER the relationship

• Since the table shows ALL responses from ALL 1,000 students, the four cells must add up to exactly 1,000
• We can set up an equation: \(\text{(known values)} + \text{(unknown value)} = 1,000\)

3. SIMPLIFY to find the answer

• Set up the equation: \(312 + 220 + 216 + x = 1,000\)
• Add the known values: \(748 + x = 1,000\)
• Solve for x: \(x = 1,000 - 748 = 252\)

Answer: B. 252

Why Students Usually Falter on This Problem

Most Common Error Path:

Poor SIMPLIFY execution: Making arithmetic errors when adding the three known values

Students might incorrectly calculate 312 + 220 + 216, getting something like 738 or 758 instead of 748. This leads to wrong final answers like 262 or 242, causing confusion when these don't match any answer choice. This leads to guessing among the provided options.

Second Most Common Error:

Weak TRANSLATE reasoning: Misunderstanding what the table represents

Some students might not fully grasp that the four cells represent ALL 1,000 students. They might try more complex approaches, like calculating percentages or looking for other relationships, rather than recognizing the simple total constraint. This leads to confusion and abandoning the systematic solution.

The Bottom Line:

This problem tests whether students can recognize that a frequency table's entries must sum to the total sample size - a fundamental principle that turns a seemingly complex table into a simple arithmetic problem.