GATE CS 2025 Set 1 Q4 — General Aptitude

Let us analyze the given family relationships step-by-step:

• $P$ is the brother of $Q$: $P$ is male ($P^+$), and $P$ and $Q$ are siblings. The gender of $Q$ is not yet known.
• $S$ is the daughter of $Q$: $S$ is female ($S^-$), and $Q$ is the parent of $S$.
• $T$ is the sister of $S$: $T$ is female ($T^-$). Since $T$ and $S$ are sisters, both are daughters of $Q$.
• $R$ is the mother of $Q$: $R$ is female ($R^-$). Since $P$ and $Q$ are siblings, $R$ is the mother of both $P$ and $Q$.

Now, let us evaluate the given statements:

1. $R$ is the grandmother of $S$:
   Since $R$ is the mother of $Q$, and $Q$ is the parent of $S$, $R$ is indeed the grandmother of $S$.
   (True)
2. $P$ is the uncle of $S$ and $T$:
   Since $P$ is the brother of $Q$, and $Q$ is the parent of $S$ and $T$, $P$ is the uncle of $S$ and $T$.
   (True)
3. $R$ has only one son:
   We know $P$ is a son of $R$. However, the gender of $Q$ is not specified. If $Q$ is male, $R$ has two sons; if $Q$ is female, $R$ has only one son. Thus, this statement cannot be definitively concluded.
   (Cannot be determined)
4. $Q$ has only one daughter:
   Both $S$ and $T$ are daughters of $Q$. Therefore, $Q$ has at least two daughters.
   (False)

Thus, both statements (1) and (2) are true.