Q.6 Residency is a famous housing complex with many well–established individuals
among its residents. A recent survey conducted among the residents of the complex
revealed that all of those residents who are well established in their respective fields
happen to be academicians. The survey also revealed that most of these
academicians are authors of some best–selling books.
Based only on the information provided above, which one of the following
statements can be logically inferred with certainty?
(A) Some residents of the complex who are well established in their fields are also
authors of some best–selling books.
(B) All academicians residing in the complex are well established in their fields.
(C) Some authors of best–selling books are residents of the complex who are well
established in their fields.
(D) Some academicians residing in the complex are well established in their fields.
The correct answer is option (D).
The passage states that Residency housing complex has many well-established residents, all of whom are academicians, and most of these academicians are authors of best-selling books. This guarantees that some academicians in the complex are well-established, as “all well-established residents are academicians” logically implies the reverse for the existing well-established group.
Passage Breakdown
The key facts are:
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“Many well-established individuals” exist among residents, confirming a non-empty set of well-established residents.
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All such well-established residents are academicians.
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“Most of these academicians” (referring to the well-established ones) are authors of best-selling books.
This setup allows certain inferences but rejects others due to logical precision in exams like GATE or CSIR NET.
Option Analysis
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(A) Some residents… well established… are also authors…: Uncertain. “Most” does not guarantee “some” if the set were hypothetically empty (though “many” makes it unlikely). Formal logic prioritizes certainty over probability.
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(B) All academicians… are well established: False. The passage does not claim all academicians (possibly including non-established ones) are well-established.
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(C) Some authors… are residents… well established: Uncertain. Similar to (A); authors link only to “most” academicians, not guaranteeing any well-established overlap with certainty.
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(D) Some academicians… are well established: Certain. Since many well-established residents exist and all are academicians, some academicians must be well-established.
The Residency housing complex logical inference question tests precise deduction skills vital for GATE 2023 and CSIR NET exams. This GATE IN GA Question 6 asks what can be inferred with certainty from a survey: all well-established residents are academicians, and most of these academicians author best-selling books.
Why Logical Inference Matters in Competitive Exams
In logical reasoning for CSIR NET or GATE, distinguish “all” (biconditional for non-empty sets) from “most” (probabilistic). The phrase “many well-established individuals” ensures the set exists, enabling reversal: some academicians are well-established.
Detailed Option Breakdown for Residency Question
| Option | Statement | Valid? | Reason |
|---|---|---|---|
| (A) | Some well-established residents are authors | No | “Most” ≠ “some” with certainty |
| (B) | All academicians are well-established | No | Ignores possible non-established academicians |
| (C) | Some authors are well-established residents | No | Reverse of (A); uncertain |
| (D) | Some academicians are well-established | Yes | Follows from “all well-established are academicians” + “many exist” |
CSIR NET Preparation Tips
Practice similar inference questions daily. Focus on empty set traps and quantifier reversal. Resources like GATE official papers confirm (D) as correct across streams.
