GATE IN 2023 | GA | Question: 6

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.

Comments

some important points to remember in this type of questions:

1. In everyday language and common reasoning, we often infer "some" from "most." This is usually a safe assumption.

2. However, in formal logic and when we're asked to determine what can be inferred with certainty, we need to be extremely precise and consider all possibilities, no matter how unlikely.

3. The issue arises from the possibility, however improbable, of an empty set. Consider this:

• We know that all well-established residents are academicians.
• We also know that most of these academicians are authors of best-selling books.
• But what if there are no well-established residents in the complex ?

4. If there are no well-established residents, then there are no academicians who fit this description, and consequently, no authors of best-selling books who are well-established residents.

5. The statement "most of these academicians" doesn't guarantee that such academicians exist. It only tells us about the proportion if they do exist.

6. In formal logic, "most" is typically interpreted as "more than half," but this applies only to non-empty sets.

This is why, when asked what can be inferred with absolute certainty, we can't conclude "some" from "most" in this case. It's a matter of logical rigor rather than practical likelihood.

That said, in real-world scenarios, it would be reasonable to assume that there are indeed some well-established residents who are authors. But for the purposes of this logical reasoning question, we must stick to what can be deduced with 100% certainty from the given information alone.

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Ans : option D

Answer 1

Based on the information provided, we can analyze the statements as follows:

We have two key facts:

(1) All residents who are well established in their fields are academicians, and

(2) Most of these well-established academicians (if any exist) are authors of some best-selling books.

We know this complex is a residency (Residency: a famous housing complex with many well-established individuals among its residents.). so, there must exist many well-established individuals among the residents, meaning more than one. so, we can infer some from most with certainty (explained above in my comment).

Now, let's examine each option.

Option 1 is true. Since there are many well-established residents (all of whom are academicians), and most of these are authors of best-selling books, we can conclude with certainty that some well-established residents are authors of best-selling books.

Option 2 is false. While all well-established residents are academicians, we can't conclude that all academicians are well-established.

Option 3 is true. If most of the many well-established academicians are authors of best-selling books, then some authors of best-selling books must be well-established residents of the complex.

Option 4 is true. We know there are many well-established residents, and all of them are academicians, so some academicians residing in the complex are indeed well-established in their fields.

Therefore, based on the given information, we can logically infer with certainty that options 1, 3, and 4 are true, while option 2 is false.

Comments

very concise explanation!

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That a tricky one esp. option (2)

Answer 2

(A) Some residents of the complex who are well established in their fields are also authors of some best-selling books:

This statement is true because the information mentions that most academicians (who are all well-established residents) are authors of best-selling books. While it doesn't guarantee it applies to all well-established residents (as some might be from other professions), it suggests a connection between field success and authorship that applies to at least some residents.

Answer 3

C is the answer.

Comments

Sure?