An elementary school class tried feeding apples, broccoli, cucumber, hay, and lettuce to a guinea pig and a rabbit. When...
GMAT Two Part Analysis : (TPA) Questions
An elementary school class tried feeding apples, broccoli, cucumber, hay, and lettuce to a guinea pig and a rabbit. When given any two of these foods, each animal clearly and consistently preferred one over the other:
- The guinea pig preferred apples to broccoli, but the rabbit showed the opposite preference.
- The rabbit preferred cucumbers to hay, but the guinea pig showed the opposite preference.
- The guinea pig preferred cucumbers to the rabbit's favourite of the five foods
- The rabbit preferred lettuce to the guinea pig's favourite of the five foods
Base on the information, select for Guinea pig's favourite a pair of foods such that either might have been the guinea pig's favourite and select Rabbit's favourite a pair of foods such that either might have been the rabbit's favourite. Make once two selections, one in each column.
OWNING THE DATASET
Visual Representation of Preferences
Guinea Pig Preferences:
- Apples > Broccoli
- Hay > Cucumbers
- Cucumbers > Rabbit's favorite
Rabbit Preferences:
- Broccoli > Apples
- Cucumbers > Hay
- Lettuce > Guinea pig's favorite
Immediate Inferences
What CANNOT be favorites:
- Lettuce cannot be guinea pig's favorite (because rabbit prefers lettuce to guinea pig's favorite)
- Cucumbers cannot be rabbit's favorite (because guinea pig prefers cucumbers to rabbit's favorite)
SEEKING THE CRITICAL INSIGHT
The key insight is that the cross-references between favorites create constraints:
- Guinea pig: Cucumbers > Rabbit's favorite → Rabbit's favorite ranks below cucumbers for guinea pig
- Rabbit: Lettuce > Guinea pig's favorite → Guinea pig's favorite ranks below lettuce for rabbit
UNDERSTANDING THE QUESTION
We need to identify pairs where each animal's favorite could be either food in that pair.
Analyzing Answer Choices
- "Apples or hay"
- "Broccoli or lettuce"
- "Cucumbers or broccoli"
- "Hay or cucumbers"
- "Lettuce or apples"
PROCESSING THE SOLUTION
Determining Guinea Pig's Possible Favorites
From guinea pig's preferences:
- Hay > Cucumbers > Rabbit's favorite
- Apples > Broccoli
Could guinea pig's favorite be hay?
- Yes, hay is at the top of one preference chain
Could guinea pig's favorite be apples?
- Need to check if apples could rank above hay
- This depends on rabbit's favorite and how the chains connect
- If rabbit's favorite is apples: Guinea pig has Cucumbers > Apples, contradicting Apples being favorite
- If rabbit's favorite is broccoli or lettuce: Apples could still be guinea pig's favorite
Could guinea pig's favorite be cucumbers?
- No, because Hay > Cucumbers
Could guinea pig's favorite be broccoli?
- No, because Apples > Broccoli
Could guinea pig's favorite be lettuce?
- No, eliminated by constraint
Conclusion: Guinea pig's favorite must be either hay or apples
Determining Rabbit's Possible Favorites
From rabbit's preferences:
- Lettuce > Guinea pig's favorite
- Broccoli > Apples
- Cucumbers > Hay
Could rabbit's favorite be lettuce?
- Yes, lettuce appears at the top of a preference chain
Could rabbit's favorite be broccoli?
- Yes, if guinea pig's favorite is apples, then rabbit has: Broccoli > Apples and Lettuce > Apples
- Broccoli and lettuce could both rank highly
Could rabbit's favorite be cucumbers?
- No, eliminated by constraint
Could rabbit's favorite be apples?
- No, because Broccoli > Apples
Could rabbit's favorite be hay?
- No, because Cucumbers > Hay
Conclusion: Rabbit's favorite must be either lettuce or broccoli
FINAL SOLUTION SYNTHESIS
Step-by-Step Recap
- Identified that lettuce cannot be guinea pig's favorite and cucumbers cannot be rabbit's favorite
- Built preference chains for each animal
- Tested each food as potential favorite
- Found guinea pig's favorite must be hay or apples
- Found rabbit's favorite must be lettuce or broccoli
Final Answer
- Guinea pig's favourite: "Apples or hay"
- Rabbit's favourite: "Broccoli or lettuce"
Configuration Analysis
Multiple valid configurations exist depending on how the preference chains connect. The constraints allow for flexibility in the exact rankings while maintaining the required relationships.
Key Insight
The cross-referential constraints (each animal's preference involving the other's favorite) create a web of dependencies that limit possible favorites while still allowing multiple valid configurations.
Exam Strategy
In TPA questions with preference chains:
- First eliminate impossible options using direct constraints
- Build partial orderings from given information
- Use answer choices to guide testing of possibilities
- Verify consistency rather than building complete rankings