The members of a city council wanted to assess the opinions of all city residents about converting an open field...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The members of a city council wanted to assess the opinions of all city residents about converting an open field into a dog park. The council surveyed a sample of 500 city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dog park. Which of the following is true about the city council's survey?
It shows that the majority of city residents are in favor of the dog park.
The survey sample should have included more residents who are dog owners.
The survey sample should have consisted entirely of residents who do not own dogs.
The survey sample is biased because it is not representative of all city residents.
1. TRANSLATE the problem information
- Given information:
- Target population: ALL city residents
- Sample: 500 city residents who own dogs
- Result: Majority of sample favored the dog park
- Goal: Assess what the survey tells us
2. INFER the core issue
- The key insight: When you want to understand opinions of ALL city residents, your sample must represent ALL city residents
- Problem: Dog owners likely have different opinions about dog parks than non-dog owners
- This creates sampling bias - the sample isn't representative of the target population
3. APPLY CONSTRAINTS to evaluate each choice
- Choice A: Claims majority of ALL residents favor it
- Constraint: Can only generalize to populations your sample represents
- Violation: Sample only represents dog owners, not all residents
- Choice D: Claims sample is biased and not representative
- This correctly identifies the constraint violation
Answer: D
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students fail to recognize that dog owners are likely to have systematically different opinions than the general population about dog parks.
Without this insight, they may think the survey results can be generalized to all residents simply because "majority rules" or because 500 seems like a large sample size. This may lead them to select Choice A (majority of city residents favor the park).
The Bottom Line:
The key insight is recognizing that WHO you sample matters just as much as HOW MANY you sample. A biased sample cannot produce unbiased results, regardless of size.
It shows that the majority of city residents are in favor of the dog park.
The survey sample should have included more residents who are dog owners.
The survey sample should have consisted entirely of residents who do not own dogs.
The survey sample is biased because it is not representative of all city residents.