Games And Tournaments Test

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Games And Tournaments Test - 1

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Question 1
3 / -1

Direction: In a knockout tournament 64 players participated. These 64 players are seeded from 1 to 64 with seed 1 being the top seed and seed 64 being the bottom seed. The tournament is conducted in different stages.
In stage 1 seed 1 played with seed 64 and that match is named as match 1 of stage 1, seed 2 played with seed 63 and that match is named as match 2 of stage 1, and so on.
In stage 2, winner of match 1 and match 32 of stage 1 played against each other and that match is named as Match 1 of stage 2, then winner of match 2 and match 31 of stage 1 played against each other and that match is named as Match 2 of stage 2. And so, on
The same procedure is followed in further stages. Now answer the following question.
Q. How many stages are in the tournament?

A
5

B
6

C
7

D
None of these

Solution

Since 64 = 2⁶ hence we will have total 7^th stages in the tournament with last 7th stage is the final match.
Question 2
3 / -1

Direction: In a knockout tournament 64 players participated. These 64 players are seeded from 1 to 64 with seed 1 being the top seed and seed 64 being the bottom seed. The tournament is conducted in different stages.
In stage 1 seed 1 played with seed 64 and that match is named as match 1 of stage 1, seed 2 played with seed 63 and that match is named as match 2 of stage 1, and so on.
In stage 2, winner of match 1 and match 32 of stage 1 played against each other and that match is named as Match 1 of stage 2, then winner of match 2 and match 31 of stage 1 played against each other and that match is named as Match 2 of stage 2. And so, on
The same procedure is followed in further stages. Now answer the following question.
Q. What is the total number of matches in the tournament?

A
63

B
36

C
127

D
None of these

Solution

Total number of matches is 32 + 16 + 8 + 4 +2 + 1 = 63
Or else since total number of players is 64 hence number of matches must be 64 - 1 = 63
Question 3
3 / -1

Direction: In a knockout tournament 64 players participated. These 64 players are seeded from 1 to 64 with seed 1 being the top seed and seed 64 being the bottom seed. The tournament is conducted in different stages.
In stage 1 seed 1 played with seed 64 and that match is named as match 1 of stage 1, seed 2 played with seed 63 and that match is named as match 2 of stage 1, and so on.
In stage 2, winner of match 1 and match 32 of stage 1 played against each other and that match is named as Match 1 of stage 2, then winner of match 2 and match 31 of stage 1 played against each other and that match is named as Match 2 of stage 2. And so, on
The same procedure is followed in further stages. Now answer the following question.
Q. If seed 9 reached final then which one of the following could play with him in final?

A
56

B
24

C
11

D
None of these

Solution

Seed 9 played with seed 56 in stage 1, with seed 24 in stage 2, But seed 11 can reach the final if he beats seeds 6, 3 and 2 in stage 3 4 and 5 respectively.
Question 4
3 / -1

Direction: In a knockout tournament 64 players participated. These 64 players are seeded from 1 to 64 with seed 1 being the top seed and seed 64 being the bottom seed. The tournament is conducted in different stages.
In stage 1 seed 1 played with seed 64 and that match is named as match 1 of stage 1, seed 2 played with seed 63 and that match is named as match 2 of stage 1, and so on.
In stage 2, winner of match 1 and match 32 of stage 1 played against each other and that match is named as Match 1 of stage 2, then winner of match 2 and match 31 of stage 1 played against each other and that match is named as Match 2 of stage 2. And so, on
The same procedure is followed in further stages. Now answer the following question.
Q. Which lowest seeded player can win the tournament without causing an upset by him?

A
32

B
33

C
34

D
None of these

Solution

If all the matches in stage 1 is an upset except the last match where seed 32 won, then in stage 2 seed 32 is the highest seeded player who can win the tournament without causing an upset.
Question 5
3 / -1

Direction: In a knockout tournament 64 players participated. These 64 players are seeded from 1 to 64 with seed 1 being the top seed and seed 64 being the bottom seed. The tournament is conducted in different stages.
In stage 1 seed 1 played with seed 64 and that match is named as match 1 of stage 1, seed 2 played with seed 63 and that match is named as match 2 of stage 1, and so on.
In stage 2, winner of match 1 and match 32 of stage 1 played against each other and that match is named as Match 1 of stage 2, then winner of match 2 and match 31 of stage 1 played against each other and that match is named as Match 2 of stage 2. And so, on
The same procedure is followed in further stages. Now answer the following question.
Q. If seed 15 won the tournament then what is the minimum number of upsets caused by him?

A
1

B
2

C
3

D
4

Solution

From the solution of previous question we have seen that seed 32 can win the tournament without causing an upset by him. So seed 15 can also win the tournament without causing an upset by him.
Question 6
3 / -1

Direction: 8 terms namely A, B, C, D, E, F, G and H participated in a tournament whose 1^st stage is a round robin stage where each team play with other team exactly once. Following further information is known to us:
(i) A won against B, C and E.
(ii). Number of matches won by A, B and D is 3 each no other team won 3 matches.
(iii) C won against B and D but lost to E.
(iv) H won all the matches.
(v) G won against B but lost to E.
(vi) D lost to F and C won only 2 matches.
Now answer the following question:
Q. How many matches F won

A
2

B
3

C
4

D
None of these

Solution

From the table F won 4 matches.
Question 7
3 / -1

Direction: 8 terms namely A, B, C, D, E, F, G and H participated in a tournament whose 1^st stage is a round robin stage where each team play with other team exactly once. Following further information is known to us:
(i) A won against B, C and E.
(ii). Number of matches won by A, B and D is 3 each no other team won 3 matches.
(iii) C won against B and D but lost to E.
(iv) H won all the matches.
(v) G won against B but lost to E.
(vi) D lost to F and C won only 2 matches.
Now answer the following question:
Q. How many matches G lost?

A
2

B
3

C
4

D
None of these

Solution

From the table G lost 4 matches.
Question 8
3 / -1

Direction: 8 terms namely A, B, C, D, E, F, G and H participated in a tournament whose 1^st stage is a round robin stage where each team play with other team exactly once. Following further information is known to us:
(i) A won against B, C and E.
(ii). Number of matches won by A, B and D is 3 each no other team won 3 matches.
(iii) C won against B and D but lost to E.
(iv) H won all the matches.
(v) G won against B but lost to E.
(vi) D lost to F and C won only 2 matches.
Now answer the following question:
Q. E won against which all teams?

A
C and B

B
C and G

C
C and F

D
None of these

Solution

From the table E won against C and G
Question 9
3 / -1

Direction: 8 terms namely A, B, C, D, E, F, G and H participated in a tournament whose 1^st stage is a round robin stage where each team play with other team exactly once. Following further information is known to us:
(i) A won against B, C and E.
(ii). Number of matches won by A, B and D is 3 each no other team won 3 matches.
(iii) C won against B and D but lost to E.
(iv) H won all the matches.
(v) G won against B but lost to E.
(vi) D lost to F and C won only 2 matches.
Now answer the following question:
Q. Which team won minimum number of matches?

A
C and B

B
C and G

C
C and F

D
None of these

Solution

C and E won 2 matches.
Question 10
3 / -1

Direction: 16 teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in 2 stages. In the first stage, the teams are divided into two groups. Each group consists of 8 teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top 4 teams from each group advance to the 2nd stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup. The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage a team earns 1 point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly 4 teams from each group advance to the next stage.
Q. What is the total number of matches played in the tournament?

A
28

B
55

C
63

D
35

Solution

First Stage: There is two groups of 8 teams each. In each group, each team plays with every other team and hence total number of matches are ⁸c₂ = 8 × ( 7/2 ) = 28 matches So, in both the groups the total number of matches played at the first stage are 28. And hence 56 matches are played in 1^st stage
Second Stage: In this stage there are 8 teams playing in such a way that in one round 4 teams play with 4 other teams. 4 teams win and go to the next round. That is called knock out tournament.
In the 1^stround no of matches ( 8/2 ) = 4,
In the 2^nd round no of matches = ( 4/2 ) = 2,
In the third or the last round number of match = ( 2/2 ) = 1,
So , total no. of matches in 2^nd stage is 4 + 2 + 1 = 7
Hence total match in the tournament = 56 + 7 = 63

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Games And Tournaments Test - 1

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Games And Tournaments Test - 1

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Question 1

5

6

7

None of these

Solution

Question 2

63

36

127

None of these

Solution

Question 3

56

24

11

None of these

Solution

Question 4

32

33

34

None of these

Solution

Question 5

1

2

3

4

Solution

Question 6

2

3

4

None of these

Solution

Question 7

2

3

4

None of these

Solution

Question 8

C and B

C and G

C and F

None of these

Solution

Question 9

C and B

C and G

C and F

None of these

Solution

Question 10

28

55

63

35

Solution

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Score

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