CAT 2004 — DILR Question 31
Answer the following question based on the information given below.
The year was 2006. All six teams in Pool A of World Cup hockey, play each other exactly once. Each win earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the highest points qualify for the semi-finals. In case of a tie, the team with the highest goal difference (Goal For – Goals Against) qualifies.
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In the opening match, Spain lost to Germany. After the second round (after each team played two matches), the pool table looked as shown below.
In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches.
a. Spain won both the fourth and fifth round matches.
b. Both Argentina and Germany won their fifth round matches by 3 goals to 0.
c. Pakistan won both the fourth and fifth round matches by 1 goal to 0.
If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?
Answer & solution
- A
Argentina
- B
Germany
- C
Spain
Cannot be determined
The following table gives the distribution of games within each round:
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(Note: There is an inconsistency in the question. In Round 4, only 4 teams have played while in Round 5, two teams (NZ and SA) have played 2 matches. This, as we will see later, causes an inconsistency in the question as well.)
The points table will be as follows:
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Since, 4 teams are tied with the same number of points, the qualifying teams will be chosen based on their Goal Difference (GD).
The GFs and GAs for the first two rounds is already given. In the third round, the match of Germany versus Argentina was drawn. Hence, both their GFs and GAs will be equal (say, X). In the fourth round, Spain won the match against Argentina. Hence, if Spain’s score is (say) A:B, where A > B, then Argentina’s will be B:A.
Following along similar lines, we have the following table:
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Hence,
GD for Pakistan = (2 + Y + 1 + 1) – (1 + Y + 0 + 0) = 3
GD for Germany = (3 + X + 0 + 3) – (1 + X + 1 + 0) = 4
GD for Argentina = (2 + X + B + 3) – (0 + X + A + 0) = 5 + (B – A)
Since B < A, hence (B – A) < 0
∴ GD for Argentina < 5
GD for Spain = (5 + Y + A + C) – (2 + Y + B + D) = 3 + (A – B) + (C – D)
Since A > B and C > D, hence (A − B) ≥ 1 and (C – D) ≥ 1
∴ GD for Spain ≥ 5
Hence, Pakistan cannot qualify for the finals! The closest option that can be marked is 'Cannot be determined'.
Hence, option (d).