GATE2025_CS1_Q4

Consider the relationships among P, Q, R, S, and T:

• P is the brother of Q.
• S is the daughter of Q.
• T is the sister of S.
• R is the mother of Q.

The following statements are made based on the relationships given above.

1. R is the grandmother of S.
2. P is the uncle of S and T.
3. R has only one son.
4. Q has only one daughter.

Which one of the following options is correct?

✅ Final Answer:

The correct option is (A) Both (1) and (2) are true.

🔹 Short Answer:

By mapping the relationships, we can deduce: (1) R is Q's mother, and Q is S's parent, making R the grandmother of S (True). (2) P is Q's brother, and Q is the parent of S and T, making P their uncle (True). (3) P is a son of R, but Q's gender is unknown; if Q is male, R has two sons (Not necessarily true). (4) S and T are sisters and daughters of Q, so Q has two daughters (False). Therefore, only statements (1) and (2) are verifiably true.

🔸 Long Answer:

To solve this logical reasoning problem, the best approach is to construct a family tree based on the given relationships. This helps in visualizing the connections and accurately evaluating the statements.

Step 1: Construct the Family Tree

• R is the mother of Q. We start with this parent-child link. (R is female).
• P is the brother of Q. This means P and Q are siblings, and P is male. They share the same mother, R.
• S is the daughter of Q. Q is the parent of S. (S is female).
• T is the sister of S. T is also a daughter of Q. (T is female).

A crucial point here is that the gender of Q is not specified. Q could be the father or the mother of S and T.

Step 2: Evaluate Each Statement

1. R is the grandmother of S.
   • R is the mother of Q.
   • Q is the parent of S.
   • Therefore, the parent's mother is a grandmother. R is the grandmother of S. This statement is TRUE.
2. P is the uncle of S and T.
   • P is the brother of Q.
   • Q is the parent of S and T.
   • The brother of one's parent is their uncle. So, P is the uncle of S and T. This statement is TRUE.
3. R has only one son.
   • We know P is the brother of Q, which makes P a son of R.
   • However, we don't know Q's gender.
     • If Q is female (mother of S and T), then R has only one son (P).
     • If Q is male (father of S and T), then R has two sons (P and Q).
   • Since we cannot be certain, this statement is NOT NECESSARILY TRUE.
4. Q has only one daughter.
   • The problem states S is the daughter of Q.
   • It also states T is the sister of S. This implies T is also a female child of the same parent(s).
   • Therefore, Q has at least two daughters: S and T. This statement is FALSE.

Step 3: Conclusion

Based on the analysis, only statements (1) and (2) are demonstrably true from the information provided. Therefore, the correct option is (A).

Bibliography:
- Aggarwal, R. S. (2019). A Modern Approach to Verbal & Non-Verbal Reasoning. S. Chand Publishing. (Chapter on Blood Relations).

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