Question

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.

Hint:

In logical deduction, break down premises using set notation (e.g., All X are Y means X \(\subset\) Y). The word "most" implies "some". Be wary of converse errors (All X are Y does not mean All Y are X). If multiple options seem correct, re-read the question carefully for subtle distinctions.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a logical deduction question based on syllogisms. We need to analyze the given premises and determine which conclusion can be inferred with absolute certainty.
Step 3: Detailed Explanation:
Let's break down the premises:
Let R be the set of residents of the complex.
Let WE be the set of residents who are well-established in their fields.
Let A be the set of residents who are academicians.
Let B be the set of residents who are authors of best-selling books.
Premise 1: All of those residents who are well established in their respective fields happen to be academicians.
This means: All WE are A. (The set WE is a subset of the set A).
Premise 2: Most of these academicians are authors of some best-selling books.
The phrase "these academicians" refers back to the ones who are well-established (from Premise 1).
So, this means: Most (WE who are A) are B. Since all WE are A, this simplifies to: Most WE are B.
The term "most" implies "some" and is stronger than "some". If "most" WE are B, it is certain that at least "some" WE are B.
Now let's evaluate the options:
(A) Some residents of the complex who are well established in their fields are also authors of some best-selling books.
This statement is: Some WE are B. As derived above from Premise 2 ("Most WE are B"), this is a certain inference.
(B) All academicians residing in the complex are well established in their fields.
This statement is: All A are WE. Premise 1 states All WE are A. This is the converse, which is not necessarily true. There could be academicians who are not well-established.
(C) Some authors of best-selling books are residents of the complex who are well established in their fields.
This statement is: Some B are WE. This is equivalent to Some WE are B, which we already established as true from (A). This is also a valid inference.
(D) Some academicians residing in the complex are well established in their fields.
This statement is: Some A are WE. Since we know WE is a non-empty set (the premise talks about them) and all WE are A, it must be true that some A are indeed WE. This is also a valid inference.
Step 4: Final Answer:
Based on strict logical deduction, options (A), (C), and (D) are all correct. This ambiguity is why the official key was likely MTA. If forced to choose the best inference, (A) is the most direct conclusion from the premises.
Step 5: Why This is Correct:
The statement "Most well-established residents are authors" directly and certainly implies that "Some well-established residents are authors". The other options, while also logically derivable, might be considered less direct inferences, but their validity makes the question ambiguous.