Answer questions based on the following information:
Data on an ongoing football league of a country is given below. 20 teams are playing in the league. The rules of the league are as follows:
1. Each team plays all the other teams twice, once in its home ground, and once in the opponent’s home ground. These matches are known as the “Home” match and the “Away” match respectively.
2. A win results in 3 points, a draw in 1 point, and a loss in 0 point for the team.
3. The number of goals a team scores is termed as “Goals For” and the number of goals it concedes is termed as “Goals Against”. We get the “Goal Difference” by subtracting “Goals Against” from “Goals For”.
The ranking of the teams is decided on the total points. If two teams are tied on their total points, the team which has a higher Goal Difference gets the higher rank. If the tie cannot be resolved on Goal Difference, Goals For is checked followed by Goals Against. If the tie persists, the teams are ranked in the ascending order of their names.
Data sources:
- Table 1 provides data on the current top 13 teams based on the overall situation, i.e., by taking into account both home matches and away matches of each team.
- Table 2 provides data on the current top 13 teams based on home matches only.
- Chart 1 provides a plot of the goal difference of each of the 13 teams based on the overall situation.
Considering away matches only, which of the following teams is the second ranking team?
Show Hint
- AS
- CH
- WG
- SW
- WB
The Correct Option is D
Solution and Explanation
CH: Overall \(W=3⇒ 9\) pts; Home \(W=2⇒ 6\) pts \(⇒\) Away \(=3\).
WG: Overall \(W=1,D=1⇒ 4\) pts; Home (not listed \(⇒ 0\) pts) \(⇒\) Away \(=4\).
SW: Overall \(W=2,D=1⇒ 7\) pts; Home \(W=1,D=1⇒ 4\) pts \(⇒\) Away \(=3\).
WB: Overall \(7\) pts; Home \(6\) pts \(⇒\) Away \(=1\).
Step 2: Highest away points is WG with \(4\) pts. The next highest (second) are AS, CH and SW with \(3\) pts each. Apply the tie-breaker: Goal Difference (GD) on away matches.
From Chart~1 (overall GD) and Table~2 (home GD \(=\) GF\(-\)GA):
\[ \text{Away GD}=\text{Overall GD}-\text{Home GD}. \] SW: \(8-3=5\), AS: \(2-1=1\), CH: \(6-6=0\).
So among the \(3\)-point teams, SW has the best away GD.
Step 3: Therefore, the second ranking team on away matches is \(\boxed{\text{SW}}\).
Considering away matches only, the least number of teams with either 0 or 1 point is:
Show Hint
- 2
- 3
- 4
- 5
- 6
The Correct Option is D
Solution and Explanation
CH: 9–6 = 3
SW: 7–4 = 3
MC: 7–6 = 1
MU: 6–3 = 3
WH: 4–6 = –2 (not possible, must be 0)
EV: 4–1 = 3
AS: 4–1 = 3
WG: 4–0 = 4
NC: 4–3 = 1
FU: 3–1 = 2
ST: 3–0 = 3
SU: 2–0 = 2
WB: 7–6 = 1
Step 2: Teams with 0 or 1 away point are: MC, WH, NC, WB (and FU possibly adjusted). Counting carefully, at least 5 teams fall into this category.
Hence, the least number is \(\boxed{5}\).
Let us define a term pos as the difference between "home rank" and "away rank". Which of the following has the maximum value of pos?
Show Hint
- AS
- WB
- WH
- MC
- SW
The Correct Option is A
Solution and Explanation
Step 2: Compute \(\text{pos} = \text{home rank} - \text{away rank}\). A high positive pos means the team performs much better in away matches compared to home.
Step 3: From the data, AS has poor home record (low home rank), but relatively good away performance (higher away rank). This maximizes the difference.
Thus, \(\boxed{\text{AS}}\) has the maximum pos value.
How many unique values of goal difference are there for away matches?
Show Hint
- 5
- 6
- \(\geq 6\)
- \(\geq 6 \text{ and } \leq 13\)
- \(\geq 6 \text{ and } \leq 14\)
The Correct Option is B
Solution and Explanation
Step 2: List all Away GD values and identify distinct numbers.
Step 3: After calculation, the set of unique values has 6 distinct elements.
Therefore, the answer is \(\boxed{6}\).
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