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lavanya.18
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30 Sep 2024, 10:48
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KarishmaB
Wow! What an amazing question. And great way to explain it. I had fun solving this one!
23 Apr 2025, 22:19
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Refutation of the “Must Be True” Assumption in the Set Inclusion Problem
Problem Statement:
A set of numbers has the property that for any number t in the set, t + 2 is also in the set.
If –1 is in the set, which of the following must also be in the set?
Official Answer:
II and III only (i.e., 1 and 5 must be in the set)
Critical Refutation:
The conclusion that 5 must be in the set is logically flawed under strict formal reasoning. Here’s why:
The range of the set is undefined.
The problem does not specify whether the set is finite or infinite.
Therefore, a minimal set such as {–1, 1} satisfies the given property (–1 in the set → 1 in the set) without requiring any further elements such as 3 or 5.
There is no justification for assuming the set contains all numbers generated by repeated additions of 2.
No explicit permission for recursive application.
The property applies to any t in the set and ensures that t + 2 is in the set.
However, the problem never states that this rule can be applied again to the resulting number.
Assuming that t + 2 becomes a new t to repeat the rule requires an implicit assumption that is not supported by the prompt.
“Must be true” requires logical necessity.
According to GMAT standards, an answer must logically follow from the premises without introducing new assumptions.
Since the inclusion of 5 requires interpreting the set as infinite and the rule as recursively applicable, it is not a logically necessary consequence.
Therefore, 5 is not guaranteed to be in the set—it is possible, but not certain.
The prompt gives a condition, not a constructive definition.
The wording describes a property of the set, not a rule for generating its elements from a starting point.
Treating the property as a generator is a logical leap beyond what is explicitly stated.
Conclusion:
Unless we are allowed to assume additional structure (e.g., infinite recursion, constructive rules), none of the answer choices can be said to “must” be in the set based solely on the given information.
Therefore, the correct answer under strict logical interpretation is: cannot be determined.
This exposes a subtle but important conflict between formal logic and the assumed conventions in GMAT-style reasoning.
Problem Statement:
A set of numbers has the property that for any number t in the set, t + 2 is also in the set.
If –1 is in the set, which of the following must also be in the set?
Official Answer:
II and III only (i.e., 1 and 5 must be in the set)
Critical Refutation:
The conclusion that 5 must be in the set is logically flawed under strict formal reasoning. Here’s why:
The range of the set is undefined.
The problem does not specify whether the set is finite or infinite.
Therefore, a minimal set such as {–1, 1} satisfies the given property (–1 in the set → 1 in the set) without requiring any further elements such as 3 or 5.
There is no justification for assuming the set contains all numbers generated by repeated additions of 2.
No explicit permission for recursive application.
The property applies to any t in the set and ensures that t + 2 is in the set.
However, the problem never states that this rule can be applied again to the resulting number.
Assuming that t + 2 becomes a new t to repeat the rule requires an implicit assumption that is not supported by the prompt.
“Must be true” requires logical necessity.
According to GMAT standards, an answer must logically follow from the premises without introducing new assumptions.
Since the inclusion of 5 requires interpreting the set as infinite and the rule as recursively applicable, it is not a logically necessary consequence.
Therefore, 5 is not guaranteed to be in the set—it is possible, but not certain.
The prompt gives a condition, not a constructive definition.
The wording describes a property of the set, not a rule for generating its elements from a starting point.
Treating the property as a generator is a logical leap beyond what is explicitly stated.
Conclusion:
Unless we are allowed to assume additional structure (e.g., infinite recursion, constructive rules), none of the answer choices can be said to “must” be in the set based solely on the given information.
Therefore, the correct answer under strict logical interpretation is: cannot be determined.
This exposes a subtle but important conflict between formal logic and the assumed conventions in GMAT-style reasoning.
23 Apr 2026, 23:02
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