The table shown summarizes the number of employees at each of the 17 restaurants in a town.Number of employeesNumber of...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The table shown summarizes the number of employees at each of the \(\mathrm{17}\) restaurants in a town.
| Number of employees | Number of restaurants |
|---|---|
| \(\mathrm{2\ to\ 7}\) | \(\mathrm{2}\) |
| \(\mathrm{8\ to\ 13}\) | \(\mathrm{4}\) |
| \(\mathrm{14\ to\ 19}\) | \(\mathrm{2}\) |
| \(\mathrm{20\ to\ 25}\) | \(\mathrm{7}\) |
| \(\mathrm{26\ to\ 31}\) | \(\mathrm{2}\) |
Which of the following could be the median number of employees for the restaurants in this town?
2
9
15
21
1. TRANSLATE the problem information
- Given information:
- 17 restaurants total with employee counts in ranges
- Need to find possible median value
- What this tells us: With grouped data, we can only determine the range where the median falls, not the exact value
2. INFER the median position
- With 17 restaurants (odd number), the median is the middle value
- Middle position = 9th restaurant when arranged from lowest to highest
- The median will be whatever number of employees the 9th restaurant has
3. SIMPLIFY by finding cumulative positions
- Count up positions to locate where the 9th restaurant falls:
- Positions 1-2: 2 to 7 employees (2 restaurants)
- Positions 3-6: 8 to 13 employees (4 restaurants)
- Positions 7-8: 14 to 19 employees (2 restaurants)
- Positions 9-15: 20 to 25 employees (7 restaurants)
- Positions 16-17: 26 to 31 employees (2 restaurants)
4. APPLY CONSTRAINTS to select the answer
- The 9th restaurant falls in the "20 to 25 employees" range
- Only choice D (21) falls within this range
Answer: D. 21
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students don't realize they need to find which position represents the median (9th out of 17), instead trying to calculate an average or picking a value from the most frequent range.
Students might think the median should be from the range with the most restaurants (20-25, which has 7 restaurants) but pick this for the wrong reason. This could lead them to select Choice D (21) for incorrect reasoning, or cause confusion about why ranges matter.
Second Most Common Error:
Poor SIMPLIFY execution: Students miscalculate cumulative positions, perhaps thinking the 9th restaurant falls in the 14-19 range instead of the 20-25 range.
This computational error may lead them to select Choice C (15) instead of the correct answer.
The Bottom Line:
This problem tests whether students understand that median position depends on the total number of values, and that with grouped data, you locate which group contains the median position rather than calculating exact values.
2
9
15
21