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. Most 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.

GATE 2023 · General Aptitude · Logical Reasoning · medium

Answer: X — Question excluded in official GATE IN 2023 answer key. No option can be inferred with absolute certainty given ambiguity in the passage.

1. Formalise the premises: P1: forall x (WE(x) -> A(x)). P2: Most x in A satisfy Author(x), i.e., |A intersect Au| > |A|/2.
2. Evaluate option D (Some A are WE): D: exists x (A(x) and WE(x)). From P1, WE subset A, so all WE are in A. If WE is non-empty, there is some x with WE(x) and A(x), making D true. The passage says 'many well-established individuals' implying WE non-empty, so D holds.
3. Evaluate option A (Some WE are Authors): From P1, WE subset A. From P2, more than half of A are Authors. Depending on how large WE is relative to A, some WE members may or may not be Authors. This is not certain without knowing the ratio |WE|/|A|.
4. Official exclusion note: The official GATE IN 2023 answer key marks this question as excluded/bonus (answer code X). Multiple options are arguable depending on interpretation of 'most' and whether the WE set is explicitly non-empty. No option is unambiguously certain.