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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?

  1. A
    Both (1) and (2) are true.
  2. B
    Both (1) and (3) are true.
  3. C
    Only (3) is true.
  4. D
    Only (4) is true.

Solution & Step-by-step Explanation

Let's analyze the gender and relationships step-by-step:"P is the brother of Q": P is male. P and Q are siblings."S is the daughter of Q": S is female. Q is a parent of S."T is the sister of S": T is female. Since S and T are siblings, Q is also the parent of T."R is the mother of Q": R is female. R is the parent of Q (and also P).Evaluating the statements:(1) R is the mother of Q, and Q is the parent of S. Therefore, R is the grandmother of S. (True)(2) P is the brother of Q, and Q is the parent of S and T. Therefore, P is the uncle of S and T. (True)(3) R has only one son. We know P is a son, but the gender of Q is unknown (could be a son or a daughter), and R could have other unmentioned children. (Cannot be determined / Not definitively true)(4) Q has only one daughter. We know S and T are sisters, meaning Q has at least two daughters. (False)Therefore, both statements (1) and (2) are definitely true.

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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?
A
Both (1) and (2) are true.
B
Both (1) and (3) are true.
C
Only (3) is true.
D
Only (4) is true.

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