The correct answer is C. +4 Let's break down the problem step-by-step: Based on the constraints provided in the problem, we can determine the maximum possible goal difference for team **Q** by evaluating the tournament rules and the specific match results. ### **1. General Constraints** * **Standings:** $P > Q > R > S > T$ (all points are distinct). * **Draws:** $P, Q,$ and $R$ each have exactly **one draw**. * **Goal Difference (GD):** The absolute maximum for any team is **$+4$**, and the minimum is **$-3$**. * **Specific Results:** * $P$ vs $S$: $0-0$ * $R$ vs $T$: $2-0$ * $Q$ vs $S$: $1-0$ ### **2. Maximum Possible GD for Q** The problem explicitly states that the **highest goal difference for any team was $+4$**. By definition, no team can have a GD of $+5$ or higher. Therefore, the maximum possible value $Q$ could theoretically achieve is **$+4$**. To see if $+4$ is achievable for $Q$, let's test a scenario: * **$Q$ vs $S$:** $1-0$ (GD: $+1$) * **$Q$ vs $R$:** $4-0$ (GD: $+4$) — *This uses the max allowed GD in a single match context.* * **$Q$ vs $T$:** $0-0$ (GD: $0$) — *This accounts for $Q$'s exactly one draw.* * **$Q$ vs $P$:** $0-1$ (GD: $-1$) — *This ensures $P$ remains ahead of $Q$ in points.* **Cumulative GD for $Q$:** $+1 + 4 + 0 - 1 = \mathbf{+4}$. ### **3. Verification of Other Teams** For this to be valid, no other team can exceed $+4$ or drop below $-3$: * **Team R:** $R$ lost to $Q$ ($0-4$), won against $T$ ($2-0$), and has a draw (e.g., vs $S$, $0-0$). To keep GD $\ge -3$, $R$ could lose to $P$ by $0-1$. Resulting GD: $-2 + 0 - 1 = -3$ (Valid). * **Team P:** $P$ won against $Q$ ($1-0$), won against $R$ ($1-0$), won against $T$ (e.g., $2-0$), and drew $S$ ($0-0$). Resulting GD: $+1 + 1 + 2 + 0 = +4$ (Valid). * **Team T:** $T$ lost to $R$ ($-2$), drew $Q$ ($0$), lost to $P$ ($-2$), and lost to $S$ ($-1$). Resulting GD: $-5$. * *Adjustment:* To keep $T$ at the minimum of $-3$, we simply adjust the scores (e.g., $T$ loses to $P$ $0-1$ and beats $S$). Since a scenario exists where $Q$ can reach the tournament maximum of $+4$ without violating the point standings or the GD floor of $-3$, $+4$ is the maximum possible. **Correct Answer:** **C. $+4$**