Each of three botanists made a hypothesis regarding specimens of a particular plant species: Botanist 1: Any individual specimen possessing...
GMAT Two Part Analysis : (TPA) Questions
Each of three botanists made a hypothesis regarding specimens of a particular plant species: Botanist 1: Any individual specimen possessing the gene for curly stems has either the gene for long roots or the gene for purple flowers, or both. Botanist 2: Any individual specimen possessing the gene for long roots has either the gene for flat leaves or the gene for round seeds, or both. Botanist 3: No individual specimen that possesses either the gene for curly stems or the gene for flat leaves or both has the gene for purple flowers.
The discovery of an individual specimen of the plant species in question having the gene for 1 but NOT the gene for 2 would show that at least one of the three hypotheses described is incorrect. Select for 1 and for 2 the characteristics that would most accurately complete the statement, based on the information given.
TPA Solution: Botanist Hypotheses
Visual Representation of Hypotheses
Let me translate the botanists' hypotheses into logical statements:
- Botanist 1 (B1): \(\mathrm{CS} \rightarrow (\mathrm{LR} \lor \mathrm{PF})\)
If curly stems, then long roots OR purple flowers (or both) - Botanist 2 (B2): \(\mathrm{LR} \rightarrow (\mathrm{FL} \lor \mathrm{RS})\)
If long roots, then flat leaves OR round seeds (or both) - Botanist 3 (B3): \((\mathrm{CS} \lor \mathrm{FL}) \rightarrow \neg\mathrm{PF}\)
If curly stems OR flat leaves, then NOT purple flowers
Where:
- CS = curly stems
- FL = flat leaves
- LR = long roots
- PF = purple flowers
- RS = round seeds
Understanding the Question
We need to find characteristics 1 and 2 such that:
- A specimen with gene for characteristic 1
- But NOT the gene for characteristic 2
- Would prove at least one hypothesis is incorrect
Seeking the Critical Insight
The key is finding a combination where having one gene but not another creates a logical contradiction between the hypotheses.
Processing the Solution
Testing Key Combinations
Let me test the most promising combination:
Test: 1 = curly stems, 2 = long roots
Suppose a specimen has CS but NOT LR:
- From B1: \(\mathrm{CS} \rightarrow (\mathrm{LR} \lor \mathrm{PF})\)
- Since the specimen has CS, it must have either LR or PF
- Since it does NOT have LR, it must have PF - From B3: \((\mathrm{CS} \lor \mathrm{FL}) \rightarrow \neg\mathrm{PF}\)
- Since the specimen has CS, it satisfies the condition \((\mathrm{CS} \lor \mathrm{FL})\)
- Therefore, it must NOT have PF
The Contradiction
- B1 requires: If CS and not LR, then must have PF
- B3 requires: If CS, then cannot have PF
These requirements directly contradict each other! A specimen cannot both have and not have purple flowers.
Verification
This contradiction proves that at least one of the hypotheses (B1 or B3) must be incorrect. No specimen could exist that satisfies all three hypotheses while having CS but not LR.
Final Solution Synthesis
Step-by-step recap:
- Identified that we need a logical contradiction between hypotheses
- Found that CS without LR creates opposing requirements for PF
- B1 demands PF must be present, B3 demands PF must be absent
- This impossibility proves at least one hypothesis is wrong
Answer specification:
- Column 1: curly stems
- Column 2: long roots
Key insight: The contradiction arises from the interaction between B1's inclusive condition (CS implies LR or PF) and B3's exclusive condition (CS implies not PF). When LR is absent, these create mutually exclusive requirements for PF.
Exam strategy: In TPA questions involving logical conditions, look for combinations that create contradictions between different rules. These contradictions often directly answer questions about impossibility or disproof.