There are 50 students in the drama club, 20 of whom are sophomores. A sample of the sophomores in the...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
There are \(\mathrm{50}\) students in the drama club, \(\mathrm{20}\) of whom are sophomores. A sample of the sophomores in the drama club was selected at random and asked whether they intend to participate in the upcoming play. Of those surveyed, \(\mathrm{30\%}\) responded that they intend to participate. Based on this survey, which of the following is the best estimate of the number of sophomores in the drama club who intend to participate in the upcoming play?
- \(\mathrm{6}\)
- \(\mathrm{15}\)
- \(\mathrm{20}\)
- \(\mathrm{50}\)
6
15
20
50
1. TRANSLATE the problem information
- Given information:
- Total drama club students: 50
- Sophomores in drama club: 20
- Sample survey of sophomores conducted
- 30% of surveyed sophomores intend to participate
- Need to find: Best estimate of sophomores who intend to participate
2. INFER the estimation approach
- The key insight: When we survey a random sample and find that 30% intend to participate, this percentage likely represents the entire sophomore population
- Strategy: Apply the sample percentage (30%) to the total sophomore population (20)
3. TRANSLATE the calculation
- "30% of the 20 sophomores" becomes: \(0.30 \times 20\)
4. SIMPLIFY to find the answer
- \(0.30 \times 20 = 6\) sophomores
Answer: A (6)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak APPLY CONSTRAINTS skill: Students apply the 30% to the wrong population - the total 50 students instead of just the 20 sophomores.
Their reasoning: "30% of all drama club students intend to participate, so \(30\% \text{ of } 50 = 15\)"
This leads them to select Choice B (15).
Second Most Common Error:
Poor INFER reasoning: Students misunderstand what the survey represents and think the answer is simply the total number of sophomores surveyed or total sophomores in the club.
Their thinking: "The problem is asking about sophomores, so the answer must be 20" or "The answer is the total number of students: 50"
This may lead them to select Choice C (20) or Choice D (50).
The Bottom Line:
This problem tests whether students understand that survey results from a sample can be used to estimate characteristics of the larger population - but only the population that was actually sampled (sophomores, not all students).
6
15
20
50