CAT 2004 — DILR Question 29
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.
Which one of the following statements is true about matches played in the first two rounds?
Answer & solution
- A
Pakistan beat South Africa by 2 goals to 1.
Argentina beat Pakistan by 1 goal to 0.
- C
Germany beat Pakistan by 2 goals to 1.
- D
Germany beat Spain by 2 goals to 1.
Since Pakistan’s ‘Goals For’ (GF) and ‘Goals Against’ (GA) is 2 and 1 respectively, and it won 1 game and lost the other, the only possible combination of scores for Pakistan in its two matches will be 2:0 and 0:1.
Similarly, Germany’s scores in its two matches will be 2:1 and 1:0; while Argentina’s scores in its two matches will be 1:0 and 1:0.
Hence, we have the following table:
(G stands for Germany, A for Argentina, S for Spain, P for Pakistan, NZ for New Zealand and SA for South Africa)
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Since Spain lost to Germany in the opening round, one of Spain’s score could be either 0:1 or 1:2. Since Spain’s total GF = 5 and GA = 2 for the first 2 rounds, we have the following possible scores for Spain:
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Since the GF for both South Africa and New Zealand is 1, for each of these teams the GF for one match will be 1 while the GF of the second match will be 0. Hence, the different possibilities are as follows:
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Combining the above possibilities for Spain, SA and NZ with the table showing the scores of Germany, Argentina and Pakistan, we see that the 1st possibility for SA is not possible since no possibility for any other team has the score 3:1. Similarly, the 2nd and 3rd possibility for NZ can also be eliminated. Hence, we have,
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Looking at the GF and GA values, we can guess which teams played against others, for certain cases. (For example, SA has a score of 1:2 and Germany is the only team to have 2:1.) These are filled in the first column of the above table.
Also, since Germany beats SA with a score of 2:1, it beats Spain with a score of 1:0. This eliminates the 2nd possibility for Spain. This implies that Spain beats NZ with 5:1, eliminating NZ’s 1st possibility. Hence, we have,
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Compiling the above information, we have the following:âââââââ
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Argentina beat Pakistan by 1 goal to 0.
Hence, option (b).