A study was done on the weights of different types of fish in a pond. A random sample of fish...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A study was done on the weights of different types of fish in a pond. A random sample of fish were caught and marked in order to ensure that none were weighed more than once. The sample contained \(\mathrm{150}\) largemouth bass, of which \(\mathrm{30\%}\) weighed more than \(\mathrm{2}\) pounds. Which of the following conclusions is best supported by the sample data?
The majority of all fish in the pond weigh less than 2 pounds.
The average weight of all fish in the pond is approximately 2 pounds.
Approximately 30% of all fish in the pond weigh more than 2 pounds.
Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.
1. TRANSLATE the problem information
- Given information:
- Random sample of fish caught and marked (no repeats)
- Sample contained 150 largemouth bass
- 30% of these largemouth bass weighed more than 2 pounds
- What this tells us: We have sample data specifically about largemouth bass only
2. INFER the key limitation
- Critical insight: The sample only included largemouth bass - no other fish types were studied
- This means any conclusions must be limited to largemouth bass, not all fish in the pond
- Random sampling allows us to generalize from our largemouth bass sample to all largemouth bass in the pond
3. INFER which conclusion is supported
- Since 30% of the random sample of largemouth bass weighed more than 2 pounds, we can conclude that approximately 30% of all largemouth bass in the pond weigh more than 2 pounds
- We cannot make any claims about other fish types since they weren't sampled
Answer: D. Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students fail to recognize the sampling limitation and think the sample represents all fish types in the pond.
They see '30% weighed more than 2 pounds' and jump to conclusions about all fish, selecting Choice C (Approximately 30% of all fish in the pond weigh more than 2 pounds) without recognizing that the sample only contained largemouth bass.
Second Most Common Error:
Poor TRANSLATE reasoning: Students misinterpret what '30% weighed more than 2 pounds' means in context.
Some might think this automatically means 70% weigh less than 2 pounds and apply this to all fish, leading them to select Choice A (The majority of all fish in the pond weigh less than 2 pounds) without understanding the sampling limitation.
The Bottom Line:
This problem tests understanding of a fundamental statistical principle: you can only generalize sample results to the population that was actually sampled. The key insight is recognizing what population your sample represents.
The majority of all fish in the pond weigh less than 2 pounds.
The average weight of all fish in the pond is approximately 2 pounds.
Approximately 30% of all fish in the pond weigh more than 2 pounds.
Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.