GATE EC 2026 Set 1 — Question 7

Let the parents be $X$ and $Y$. They are parents to two distinct children from the set $\{P, Q, R\}$. One child has no parent playing.Rule (i): Parent and child cannot be on the same team.
Rule (ii): At most one parent-child pair per match.From MATCH 1: $\{P, X\}$ vs $\{Q, R\}$. Since $P$ and $X$ are on the same team, $X$ cannot be the parent of $P$ (Rule i).
From MATCH 3: $\{R, X\}$ vs $\{Q, Y\}$. Since $R$ and $X$ are on the same team, $X$ cannot be the parent of $R$ (Rule i). Also, since $Q$ and $Y$ are on the same team, $Y$ cannot be the parent of $Q$ (Rule i).Since $X$ is a parent of one of the children and it's not $P$ or $R$, $X$ must be the parent of $Q$.Now, $Y$ must be the parent of either $P$ or $R$.
In MATCH 3: $\{R, X\}$ vs $\{Q, Y\}$. We know $X$ is the parent of $Q$. This forms one parent-child pair $(X, Q)$ in the match. Rule (ii) states there can be at most one such pair. If $Y$ were the parent of $R$, then $(Y, R)$ would be a second parent-child pair in this match. Thus, $Y$ cannot be the parent of $R$.Therefore, $Y$ must be the parent of $P$.Conclusion:

• $X$ is the parent of $Q$.
• $Y$ is the parent of $P$.
• $R$ has no parent playing in the tournament.

Thus, option (C) is correct.