Comprehension
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. 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 and no match was a draw.
| Team | Games Played | Won | Goals For | Goals Against | Points |
|---|---|---|---|---|---|
| Germany | 2 | 2 | 3 | 1 | 6 |
| Argentina | 2 | 2 | 2 | 0 | 6 |
| Spain | 2 | 1 | 5 | 2 | 3 |
| Pakistan | 2 | 1 | 2 | 1 | 3 |
| New Zealand | 2 | 0 | 1 | 6 | 0 |
| South Africa | 2 | 0 | 1 | 4 | 0 |
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.
Question: 1
Which one of the following statements is true about matches played in the first two rounds?
Which one of the following statements is true about matches played in the first two rounds?
Show Hint
Use goals for and against to deduce match outcomes when points are given.
Updated On: Jul 24, 2025
- Germany beat Pakistan by 2 goals to 1
- Argentina beat Pakistan by 2 goals to 0
- Germany beat Pakistan by 2 goals to 1
- Argentina beat Pakistan by 2 goals to 1
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The Correct Option is D
Solution and Explanation
Step 1: Analyze the table after two rounds:
- Germany: 2 wins, 4 GF, 1 GA, 6 points
- Argentina: 1 win, 2 GF, 2 GA, 3 points
- Spain: 1 win, 5 GF, 2 GA, 3 points
- Pakistan: 1 win, 1 GF, 3 GA, 3 points
- France, Zealand, South Africa: 0 points
Step 2: Known: Spain lost to Germany, Spain vs. Argentina (Spain leading). No draws.
Step 3: Deduce matches:
- Germany’s 2 wins: Beat Spain (say 2-1, as Spain has 5 GF, 2 GA). Other win likely vs. Pakistan (2-1 fits: Pakistan 1 GF, 3 GA).
- Argentina’s 1 win: Likely vs. Pakistan (2-1, as Pakistan’s 1 GF suggests a loss).
- Spain’s 1 win: Likely vs. Zealand or South Africa (say 4-1).
Step 4: Check options:
- (A) Germany 2-1 Pakistan: Possible, as above.
- (B) Argentina 2-0 Pakistan: Pakistan has 1 GF, so false.
- (C) Same as (A), redundant.
- (D) Argentina 2-1 Pakistan: Fits (Pakistan 1 GF, 3 GA includes 2 from Argentina).
Step 5: Option (D) is true based on goal differences.
- Germany: 2 wins, 4 GF, 1 GA, 6 points
- Argentina: 1 win, 2 GF, 2 GA, 3 points
- Spain: 1 win, 5 GF, 2 GA, 3 points
- Pakistan: 1 win, 1 GF, 3 GA, 3 points
- France, Zealand, South Africa: 0 points
Step 2: Known: Spain lost to Germany, Spain vs. Argentina (Spain leading). No draws.
Step 3: Deduce matches:
- Germany’s 2 wins: Beat Spain (say 2-1, as Spain has 5 GF, 2 GA). Other win likely vs. Pakistan (2-1 fits: Pakistan 1 GF, 3 GA).
- Argentina’s 1 win: Likely vs. Pakistan (2-1, as Pakistan’s 1 GF suggests a loss).
- Spain’s 1 win: Likely vs. Zealand or South Africa (say 4-1).
Step 4: Check options:
- (A) Germany 2-1 Pakistan: Possible, as above.
- (B) Argentina 2-0 Pakistan: Pakistan has 1 GF, so false.
- (C) Same as (A), redundant.
- (D) Argentina 2-1 Pakistan: Fits (Pakistan 1 GF, 3 GA includes 2 from Argentina).
Step 5: Option (D) is true based on goal differences.
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Question: 2
Which one of the following statements is true about matches played in the first two rounds?
Which one of the following statements is true about matches played in the first two rounds?
Show Hint
Eliminate impossible options using goals scored and conceded.
Updated On: Jul 24, 2025
- Spain beat Germany by 2 goals to 0
- Spain beat New Zealand by 2 goals to 0
- Spain beat South Africa by 2 goals to 0
- Spain beat New Zealand by 2 goals to 1
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The Correct Option is D
Solution and Explanation
Step 1: From the table: Spain (1 win, 5 GF, 2 GA). Spain lost to Germany, so the win is against another team.
Step 2: Check options:
- (A) Spain beat Germany: False, as Spain lost to Germany.
- (B) Spain 2-0 New Zealand: New Zealand has 1 GF, so false.
- (C) Spain 2-0 South Africa: South Africa has 1 GF, so false.
- (D) Spain 2-1 New Zealand: Possible, as New Zealand’s 1 GF and 4 GA align (Spain’s 5 GF could include 2 here).
Step 3: Spain’s 5 GF, 2 GA suggest a high-scoring win (e.g., 4-1 or 2-1). Option (D) fits with New Zealand’s data.
Step 2: Check options:
- (A) Spain beat Germany: False, as Spain lost to Germany.
- (B) Spain 2-0 New Zealand: New Zealand has 1 GF, so false.
- (C) Spain 2-0 South Africa: South Africa has 1 GF, so false.
- (D) Spain 2-1 New Zealand: Possible, as New Zealand’s 1 GF and 4 GA align (Spain’s 5 GF could include 2 here).
Step 3: Spain’s 5 GF, 2 GA suggest a high-scoring win (e.g., 4-1 or 2-1). Option (D) fits with New Zealand’s data.
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Question: 3
If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?
If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?
Show Hint
Track points across rounds to identify top qualifiers.
Updated On: Jul 24, 2025
- Argentina
- Germany
- Spain
- Cannot be determined
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The Correct Option is B
Solution and Explanation
Step 1: After two rounds: Germany (6 points), Argentina, Spain, Pakistan (3 points each). Third round: All matches drawn (1 point each).
Step 2: After third round: Germany (7 points), Argentina, Spain, Pakistan (4 points each).
Step 3: Fourth and fifth rounds: Spain and Germany win both matches (1-0). Points after five rounds:
- Germany: 7 + 3 + 3 = 13
- Spain: 4 + 3 + 3 = 10
- Argentina, Pakistan: 4 + 0 + 0 = 4 (assuming losses).
Step 4: Top two qualify: Germany (13), Spain (10). If Pakistan qualifies, it must overtake Spain, but points suggest Germany is certain.
Step 5: Thus, the other team is Germany.
Step 2: After third round: Germany (7 points), Argentina, Spain, Pakistan (4 points each).
Step 3: Fourth and fifth rounds: Spain and Germany win both matches (1-0). Points after five rounds:
- Germany: 7 + 3 + 3 = 13
- Spain: 4 + 3 + 3 = 10
- Argentina, Pakistan: 4 + 0 + 0 = 4 (assuming losses).
Step 4: Top two qualify: Germany (13), Spain (10). If Pakistan qualifies, it must overtake Spain, but points suggest Germany is certain.
Step 5: Thus, the other team is Germany.
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Question: 4
Which team finished at the top of the pool after five rounds of matches?
Which team finished at the top of the pool after five rounds of matches?
Show Hint
The team with the most points after all rounds tops the pool.
Updated On: Jul 24, 2025
- Argentina
- Germany
- Spain
- Cannot be determined
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The Correct Option is B
Solution and Explanation
Step 1: From Question 19: After five rounds, Germany has 13 points, Spain 10, others 4.
Step 2: Germany has the highest points, so they top the pool.
Step 3: Verify: No scenario allows Argentina or Spain to surpass 13 points.
Step 2: Germany has the highest points, so they top the pool.
Step 3: Verify: No scenario allows Argentina or Spain to surpass 13 points.
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