DI - Games & Tournaments - Previous Year CAT/MBA Questions

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Answer the next 5 questions based on the information given below:

The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals.

The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players.
1. Only one goal was scored in every even numbered match.
2. Harita scored more goals than Bimla.
3. The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
4. Bimla scored a goal in Match 1 and one each in three other consecutive matches.
5. An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.
6. The match in which the highest number of goals was scored was unique and it was not Match 5.

1. CAT 2022 LRDI Slot 1 | DI - Games & Tournaments CAT Question

How many goals were scored in Match 7?

(a)
3
(b)
2
(c)
Cannot be determined
(d)
1

Answer: Option D

Video Explanation

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Text Explanation :

Total 12 goals were scored by 4 players such that each player scored at least one goal and distinct number of total goals.

There are two possibilities for this:
12 = 1 + 2 + 3 + 6
12 = 1 + 2 + 4 + 5

From (1): Only one goal was scored in every even numbered match.

From (5): An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.
Let the number of goals scored in Match 3 and 7 be x each.

From (6): The match in which the highest number of goals was scored was unique and it was not Match 5.
⇒ Highest goals were scored in Match 1.

From (4): Bimla scored a goal in Match 1 and one each in three other consecutive matches.
From (2): Harita scored more goals than Bimla.
⇒ Bimla scored at least 4 goals while Harita scored at least 5 goals.
∴ 12 = 1 + 2 + 4 + 5
⇒ Bimla scored 4 goals while Harita scored at 5 goals.

From (3): The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
∴ Harita can score maximum 1 goal each in Match 4 and 5, hence she scores 3 goals in one more Match.
The only match Harita can score 3 goals is Match 1 since highest numbers of goals are scored in Match 1.

From (4): Bimla scored a goal in Match 1 and one each in three other consecutive matches.
∴ Three consecutive matches Bimla can score in are Match 5, 6 and 7.

Now, a + 1 + x + 1 + b + 1 + x + 1 = 12
⇒ a + b + 2x = 8

[Match 7: x has to be greater than or equal to 1.]

Case 1: x = 1
⇒ a + b = 6
⇒ a = 4 and b = 2 [a has to be uniquely highest and a, b ≠ x]

Case 2: x = 2
⇒ a + b = 4
Rejected as minimum value of a is 4 and that of b is 1.

∴ x = 1, a = 4 and b = 2

Amla or Sarita could have scored 1 or 2 goal in any order.

Number of goals scored in Match 7 = 1.

Hence, option (d).

2. CAT 2022 LRDI Slot 1 | DI - Games & Tournaments CAT Question

Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?

(a)
4, 1, 2, 1
(b)
5, 1, 0, 1
(c)
3, 1, 2, 1
(d)
3, 2, 1, 2

3. CAT 2022 LRDI Slot 1 | DI - Games & Tournaments CAT Question

Which of the following statement(s) is/are false?
Statement-1: In every match at least one player scored a goal.
Statement-2: No two players scored goals in the same number of matches.

(a)
None of the statements
(b)
Both the statements
(c)
Statement-2 only
(d)
Statement-1 only

4. CAT 2022 LRDI Slot 1 | DI - Games & Tournaments CAT Question

If Harita scored goals in one more match as compared to Sarita, which of the following statement(s) is/are necessarily true?
Statement-1: Amla scored goals in consecutive matches.
Statement-2: Sarita scored goals in consecutive matches.

(a)
Statement-1 only
(b)
None of the statements
(c)
Both the statements
(d)
Statement-2 only

Answer the next 4 questions based on the information given

The game of Chango is a game where two people play against each other; one of them wins and the other loses, i.e., there are no drawn Chango games. 12 players participated in a Chango championship. They were divided into four groups: Group A consisted of Aruna, Azul, and Arif; Group B consisted of Brinda, Brij, and Biju; Group C consisted of Chitra, Chetan, and Chhavi; and Group D consisted of Dipen, Donna, and Deb.

Players within each group had a distinct rank going into the championship. The players have NOT been listed necessarily according to their ranks. In the group stage of the game, the second and third ranked players play against each other, and the winner of that game plays against the first ranked player of the group. The winner of this second game is considered as
the winner of the group and enters a semi-final.

The winners from Groups A and B play against each other in one semi-final, while the winners from Groups C and D play against each other in the other semi-final. The winners of the two semi-finals play against each other in the final to decide the winner of the championship.

It is known that:

Chitra did not win the championship.
Aruna did not play against Arif. Brij did not play against Brinda.
Aruna, Biju, Chitra, and Dipen played three games each, Azul and Chetan played two games each, and the remaining players played one game each.

5. CAT 2021 LRDI Slot 2 | DI - Games & Tournaments CAT Question

Who among the following was DEFINITELY NOT ranked first in his/her group?

(a)
Brij
(b)
Chitra
(c)
Dipen
(d)
Aruna

Answer: Option C

Video Explanation

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Text Explanation :

According to the information given we can draw the following table.

The winner of any group will have to play at least 2 games (at least one game in the group stage and 1 semi-final)

Let us first consider group B:
The winner of group B cannot be Brinda or Brij hence it has to be Biju.

Biju must have played one game each with Brinda and Brij in any order. Biju must have won both his group matches and qualified for the semi-finals.

Now, in the semi-final Biju must have played against the winner of group A. Biju would have lost this match since Biju only plays 3 matches.

∴ The winner of semi-final between group A and B is the winner of group B.

Let us now consider group D:
This case is same as that of group B.

Here, Dipen must have played one game each with Donna and Deb in any order. Dipen must have won both his group matches and qualified for the semi-finals.

Now, in the semi-final Dipen must have played against the winner of group C. Dipen would have lost this match since Dipen only plays 3 matches.

∴ The winner of semi-final between group C and D is the winner of group C.

∴ Final will be played between winners of group A and C.

Now winners of group A and group C must have played at least 3 matches (at least one match in group stage, 1 semi-final and 1 final)

∴ Winner of group A can only be Aruna and winner of group C can only be Chitra.

Since Chitra cannot be the champion hence Aruna will win the final and become the Champion.

As per the rules of the game, one of 2nd or 3rd ranked player of any group will play 2 matches in the group stage and the 1st ranked player will play only 1 match in group stage.

In group D, Dipen is definitely playing 2 matches during group stage, hence Dipen is definitely not the 1st ranked player in group D.

Hence, option (c).

6. CAT 2021 LRDI Slot 2 | DI - Games & Tournaments CAT Question

Which of the following pairs must have played against each other in the championship?

(a)
Azul, Brij
(b)
Chitra, Dipen
(c)
Deb, Donna
(d)
Donna, Chetan

7. CAT 2021 LRDI Slot 2 | DI - Games & Tournaments CAT Question

Who won the championship?

(a)
Brij
(b)
Chitra
(c)
Aruna
(d)
Cannot be determined

8. CAT 2021 LRDI Slot 2 | DI - Games & Tournaments CAT Question

Who among the following did NOT play against Chitra in the championship?

(a)
Aruna
(b)
Biju
(c)
Chetan
(d)
Dipen

Answer the following question based on the information given below.

Six players – Tanzi, Umeza, Wangdu, Xyla, Yonita and Zeneca competed in an archery tournament. The tournament had three compulsory rounds, Rounds 1 to 3. In each round every player shot an arrow at a target. Hitting the centre of the target (called bull’s eye) fetched the highest score of 5. The only other possible scores that a player could achieve were 4, 3, 2 and 1. Every bull’s eye score in the first three rounds gave a player one additional chance to shoot in the bonus rounds, Rounds 4 to 6. The possible scores in Rounds 4 to 6 were identical to the first three. A player’s total score in the tournament was the sum of his/her scores in all rounds played by him/her. The table below presents partial information on points scored by the players after completion of the tournament. In the table, NP means that the player did not participate in that round, while a hyphen means that the player participated in that round and the score information is missing.

The following facts are also known.

Tanzi, Umeza and Yonita had the same total score.
Total scores for all players, except one, were in multiples of three.
The highest total score was one more than double of the lowest total score.
The number of players hitting bull’s eye in Round 2 was double of that in Round 3.
Tanzi and Zeneca had the same score in Round 1 but different scores in Round 3.

9. CAT 2019 LRDI Slot 1 | DI - Games & Tournaments CAT Question

What was the highest total score?

(a)
23
(b)
21
(c)
24
(d)
25

Answer: Option D

Video Explanation

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Text Explanation :

Tanzi, Umeza, Xyla, Yonita and Zeneca got 1,2,3,1,2 chances to shoot in the bonus rounds respectively. Therefore, in the compulsory round, 9 bull’s eye were hit. From (4), it can be concluded that number of bull’s eye hit in Rounds 1, 2 and 3 were 3, 4 and 2 respectively.

Note that Xyla got three chances in the bonus round. So she must have hit three bull’s eye in the compulsory rounds. Therefore, Xyla’s minimum score is 5 × 4 + 1 + 1 = 22.

Zeneca’s maximum score could be 5 × 4 + 4 = 24. Her minimum score could be 5 × 4 + 1 = 21. If her score was the maximum score, it must be an odd number. So, 23 is the maximum score. Now using (3), the lowest score = 11. But both 11 and 23 are not divisible by 3. Using (2), we can conclude that 23 is not the maximum score. So, Xyla’s must have scored maximum. And Zeneca’s score was either 21(5 × 4 + 1) or 24(5 × 4 + 4).

Thus, Xyla scored 5 in each of the compulsory rounds and 4 in round 6.

Tanzi hit one bull’s eye either in round 1 or in round 3. So her minimum score = 5 + 4 + 1 + 5 = 15 and her maximum score = 5 + 4 + 4 + 5 = 18.

Yonita’s maximum score = 5 + 4 + 3 + 5 = 17.

So from (1) and (2), Tanzi, Umeza and Yonita each had total score 15. And hence, Wangdu scored least points i.e., 12 points. The only possible combination is 4 points in each of the compulsory rounds.

So, Tanzi scored 1 and 5 in rounds 1 and 3 in some order. Assume that she scored 1 in round 1 and 5 in round 3. From (5), Zeneca scored 1 in round 1. But then she must also have scored 5 in round 3 as she hit bull’s eye twice in the compulsory rounds. But this is contradiction to (5). So, Tanzi and Zeneca scored 5 in round 1. Tanzi scored 1 in round 3.

Thus, Tanzi, Zeneca and Xyla hit bull’s eye in round 1. Therefore Yonita (total score =15) must have hit bull’s eye in the second round and scored 2 points in the first round.

Umeza must have hit two bull’s eye in rounds 2 and 3. Also, she must have scored 2 points in the first round.

Thus, Umeza and Xyla hit the bull’s eye in the third round. Therefore, Zeneca hit bull’s eye in the second round and scored 4 points in the third round.

Thus, we have

So, the highest total score was 25.

Hence, option (d).

10. CAT 2019 LRDI Slot 1 | DI - Games & Tournaments CAT Question

What was Zeneca's total score?

(a)
23
(b)
22
(c)
21
(d)
24

11. CAT 2019 LRDI Slot 1 | DI - Games & Tournaments CAT Question

Which of the following statements is true?

(a)
Xyla was the highest scorer.
(b)
Zeneca’s score was 23.
(c)
Zeneca was the highest scorer.
(d)
Xyla’s score was 23.

12. CAT 2019 LRDI Slot 1 | DI - Games & Tournaments CAT Question

What was Tanzi's score in Round 3?

(a)
1
(b)
5
(c)
3
(d)
4

Answer the following questions based on the information given below.

Ten players, as listed in the table below, participated in a rifle shooting competition comprising of 10 rounds. Each round had 6 participants. Players numbered 1 through 6 participated in Round 1, players 2 through 7 in Round 2,..., players 5 through 10 in Round 5, players 6 through 10 and 1 in Round 6, players 7 through 10, 1 and 2 in Round 7 and so on. The top three performances in each round were awarded 7, 3 and 1 points respectively. There were no ties in any of the 10 rounds. The table below gives the total number of points obtained by the 10 players after Round 6 and Round 10.

The following information is known about Rounds 1 through 6:

Gordon did not score consecutively in any two rounds.
Eric and Fatima both scored in a round.

The following information is known about Rounds 7 through 10:

Only two players scored in three consecutive rounds. One of them was Chen. No other player scored in any two consecutive rounds.
Joshin scored in Round 7, while Amita scored in Round 10.
No player scored in all the four rounds.

13. CAT 2019 LRDI Slot 2 | DI - Games & Tournaments CAT Question

What were the scores of Chen, David, and Eric respectively after Round 3?

(a)
3, 0, 3
(b)
3, 3, 0
(c)
3, 3, 3
(d)
3, 6, 3

Answer: Option C

Video Explanation

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Text Explanation :

As the top three performances in each round were awarded 7, 3 and 1 respectively, remaining all performances were awarded 0 points.

Amita was participant in round 1 and in rounds 6 through 10.
So, in all she scored 8(= 1 + 7) points in round 1 and round 6. Also she scored 10 points in rounds 7 through 10 together.

Bala was participant in rounds 1 and 2 and also in rounds 7 through 10.
As he scored 2 points in first two rounds, he must have scored 1 point in each of the two rounds. He scored 3(= 3 or 1+1+1) points in rounds 7 through 10.

Chen scored 3 points in first three rounds and as he scored in three consecutive rounds among 7 through 10, he must have scored 1 point each in round 8, 9 and 10.

David scored 6 points in first four rounds together and 0 (i.e., 6 – 6) each in 9th and 10th rounds.

Eric scored 3(= 3 or 1+1+1) points in five rounds together and hence 10 – 3 = 7 points in the 10th round.

Gordon scored 17 points in rounds 2 through 6 together and hence, 17 – 17 = 0 points in the 7th round.

As he did not scored consecutively in any two rounds, he must have scored 0 in 3rd and 5th round and 7, 7, and 3 points in 2nd, 4th and 6th rounds, not necessarily in the given sequence.

Hansa scored 1 point in one of the rounds 3-6. So, she must have scored 4 – 1 = 3 points in either 7th or 8th rounds.

Ikea scored 2 points in 4th, 5th and 6th rounds together. Therefore, remaining 15 points must have been scored in 7th, 8th and 9th round in some order.

As Chen scored 1 point in the 8th and 9th round, Ikea must have scored 1 point in 7th round and 7 points each in the 8th and 9th round.

Joshin scored 14 points in 5th and 6th rounds. So he scored 7 points in each of 5th and 6th rounds.

Now we need to decide about remaining 3 points in the last four rounds.

As Joshin scored in round 7, and Chen has scored 1 point in each of the last three rounds, Joshin must have scored all 3 points in the 7th round and 0 points in the last three rounds.

Therefore, we can tabulate this information as

As Joshin scored 3 points in the 7th round, Hansa must have scored 3 in 8th round and 0 in the 7th round. Now consider 7th round. Only Amita must have scored 7 in the 7th round.

As she has scored in round 10, the remaining 3 points she must have scored in round 10. Thus, we can now conclude that Bala scored 3 points in the 9th round.

As Joshin scored 7 points in the 6th round Amita must have scored 1 point in this round and hence7 points in the first round.

Gordon scored 7, 7 and 3 points in 2nd, 4th and 6th rounds. Joshin scored 7 points in the 6th round so, Gordon scored 7, 7 and 3 points in 2nd, 4th and 6th rounds respectively.

So we can fill remaining values as 0 in the table for the 6th round.

Thus, Ikea scored 1 point each in 4th and 5th rounds. And hence, Hansa scored 1 point in the 3rd round.

So far we have entered values 1 and 7 for all the rounds. Now we have to enter 3 points of each of Bala, Chen, David and Fatima and 7 points for Fatima.

Eric and Fatima both scored in a round. This is possible only when Fatima scored 7 points and Eric scored 3 points. This must be round 3.

No one other than Fatima scored 3 points in round 5. Similarly, David scored 3 points in the 4th round. Chen and David scored 3 points in 1st and 2nd round in some order.

Thus we have

After round 3, the scores of Chen, David and Eric were 3, 3, 3.

Hence, option (c).

14. CAT 2019 LRDI Slot 2 | DI - Games & Tournaments CAT Question

Which three players were in the last three positions after Round 4?

(a)
Bala, Ikea, Joshin
(b)
Bala, Hansa, Ikea
(c)
Bala, Chen, Gordon
(d)
Hansa, Ikea, Joshin

15. CAT 2019 LRDI Slot 2 | DI - Games & Tournaments CAT Question

Which player scored points in maximum number of rounds?

(a)
Ikea
(b)
Chen
(c)
Amita
(d)
Joshin

16. CAT 2019 LRDI Slot 2 | DI - Games & Tournaments CAT Question

Which players scored points in the last round?

(a)
Amita, Chen, David
(b)
Amita, Bala, Chen
(c)
Amita, Chen, Eric
(d)
Amita, Eric, Joshin

Answer the following questions based on the information given below:

In a sports event, six teams (A, B, C, D, E and F) are competing against each other. Matches are scheduled in two stages. Each team plays three matches in Stage-I and two matches in Stage-II. No team plays against the same team more than once in the event. No ties are permitted in any of the matches. The observations after the completion of Stage-I and Stage-II are as given below.

Stage-I:

One team won all the three matches.
Two teams lost all the matches.
D lost to A but won against C and F.
E lost to B but won against C and F.
B lost at least one match.
F did not play against the top team of Stage-I.

Stage-II:

The leader of Stage-I lost the next two matches.
Of the two teams at the bottom after Stage-I, one team won both matches, while the other lost both matches.
One more team lost both matches in Stage-II.

17. CAT 2008 LRDI | DI - Games & Tournaments CAT Question

The team(s) with the most wins in the event is (are):

(a)
A
(b)
A & C
(c)
F
(d)
E
(e)
B & E

18. CAT 2008 LRDI | DI - Games & Tournaments CAT Question

The two teams that defeated the leader of Stage-I are:

(a)
F & D
(b)
E & F
(c)
B & D
(d)
E & D
(e)
F & D

19. CAT 2008 LRDI | DI - Games & Tournaments CAT Question

The only team(s) that won both the matches in Stage-II is (are):

(a)
B
(b)
E & F
(c)
A, E & F
(d)
B, E & F
(e)
B & F

20. CAT 2008 LRDI | DI - Games & Tournaments CAT Question

The teams that won exactly two matches in the event are:

(a)
A, D & F
(b)
D & E
(c)
E & F
(d)
D, E & F
(e)
D & F

Answer the following question based on the information given below.

In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed # 32) which is designated match No. 1 of first round; the 2nd seeded player plays the 31st seeded player which is designated match No. 2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the 17th seeded player. In the second round, the winner of match No. 1 of first round plays the winner of match No. 16 of first round and is designated match No. 1 of second round. Similarly, the winner of match No. 2 of first round plays the winner of match No. 15 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for later rounds as well.

21. CAT 2005 LRDI | DI - Games & Tournaments CAT Question

If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals?

(a)
Justine Henin
(b)
Nadia Petrova
(c)
Patty Schnyder
(d)
Venus Williams

22. CAT 2005 LRDI | DI - Games & Tournaments CAT Question

If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia Petrova make it to the semifinals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals?

(a)
Dinara Safina
(b)
Justine Henin
(c)
Nadia Petrova
(d)
Patty Schnyder

23. CAT 2005 LRDI | DI - Games & Tournaments CAT Question

If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then who could be the lowest seeded player facing Maria Sharapova in semi-finals?

(a)
Anastasia Myskina
(b)
Flavia Pennetta
(c)
Nadia Petrova
(d)
Svetlana Kuznetsova

24. CAT 2005 LRDI | DI - Games & Tournaments CAT Question

If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?

(a)
Amelie Mauresmo
(b)
Elena Dementieva
(c)
Kim Clijsters
(d)
Lindsay Davenport

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.

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.

25. CAT 2004 LRDI | DI - Games & Tournaments CAT Question

Which one of the following statements is true about matches played in the first two rounds?

(a)
Pakistan beat South Africa by 2 goals to 1.
(b)
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.

Answer: Option B

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Text 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:
(G stands for Germany, A for Argentina, S for Spain, P for Pakistan, NZ for New Zealand and SA for South Africa)

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).

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