Question: Which one of the following statements is true about matches played in the first two rounds?
Explanation:
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:
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:
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:
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,
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,
Compiling the above information, we have the following:
Argentina beat Pakistan by 1 goal to 0.
Hence, option (b).