Games and Tournament - Logical Reasoning (MCQ) Questions

1)   Read the following information carefully and answer the questions below.
  • In a tournament, Pool A and Pool B have seven teams each.
  • In each pool, every team plays one match with every other team.
  • Two points are awarded for a win, one point for a tie and zero for a loss. At the end of the pool stage, the top three teams in terms of the points scored, advance to the next round called the super stage.
  • In the super stage, all the teams start at zero points and the three teams that advance from Pool A play one match each against the three teams that advanced from Pool B.
  • Points are awarded as in the pool stage.
  • At the end of the matches, the top four teams in terms of the points scored advance to the semi-finals and the winners of the semi-finals play the finals.
  • If two or more teams end up with the same number of points at the end of the pool stage or the super stage, the team with better net run rate is placed higher.
What is the minimum no. of matches won by a team that reaches the finals?

- Published on 08 May 17

a. 1
b. 2
c. 3
d. 4
Answer  Explanation 

ANSWER: 1

Explanation:
To find minimum no. of matches won, consider the case where all matches in first two stages are drawn and teams advance through net run rate.

Pool matches - all matches drawn. Teams advances because of the net run rate. No team won any match yet advanced legally.

Super stage - ALL matches DRAWN. Teams advance because of net run rate.

Pool & Super stage is over without a single win.

Now for any team to reach the finals, it must win the semi-final.

So, a team can reach finals with just that one win in Semi-finals.


2)   Read the following information to answer the given question
  • In a tournament, Pool A and Pool B have seven teams each.
  • In each pool, every team plays one match with every other team.
  • Two points are awarded for a win, one point for a tie and zero for a loss. At the end of the pool stage, the top three teams in terms of the points scored, advance to the next round called the super stage.
  • In the super stage, all the teams start at zero points and the three teams that advance from Pool A play one match each against the three teams that advanced from Pool B.
  • Points are awarded as in the pool stage.
  • At the end of the matches, the top four teams in terms of the points scored advance to the semi-finals and the winners of the semi-finals play the finals.
  • If two or more teams end up with the same number of points at the end of the pool stage or the super stage, the team with better net run rate is placed higher.
What is the total no. of matches played in the tournament?

- Published on 08 May 17

a. 47
b. 51
c. 54
d. 56
Answer  Explanation 

ANSWER: 54

Explanation:
Step 1: Understand the story
Two pools A & B with 7 teams each

Pool Stage: Each play against other teams in the pool
Points - 2 for a win, 1 for a tie, 0 for a loss
3 teams each go to next stage

Super stage: Each team of Pool A teams plays against Pool B teams. (3 in each)

Top 4 teams go to next stage -
A semi-final (2 matches) + 1 final

Total matches = No. of Pool A matches + No. of Pool B matches + Super Stage + Semis + Final
= 7C2 + 7C2 + 3C1 x 3C1 + 2 + 1

= 21 + 21 + 9 + 2 + 1 = 54 matches


3)   Read the following information carefully and answer the question below.
  • From a group of N contenders, a party has to select a leader.
  • Even after holding a series of meetings, the politicians and the general body failed to reach a consensus.
  • It was then proposed that all N contenders be given a number from 1 to N. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1.
  • The counting would be done in a clockwise fashion.
  • The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore, the first person to be eliminated would be the contender number 2.
If N is 18, which position should a contender choose if he has to be the leader?

- Published on 03 May 17

a. 3
b. 5
c. 11
d. 17
Answer  Explanation 

ANSWER: 5

Explanation:
In this question, it would be about identifying a pattern. If you start small, you will find this pattern:

When N is a power of 2, the number of the leader that gets selected is 1 and after that it moves in a sequence of odd numbers till the next power hits.

Once you get the sequence, you would be able to solve the question.

We need to find for N = 18.

Nearest power of 2 is 16, for which the number of leader would be 1.

Every subsequent jump of 1 in N will result in a jump of 2 in number of leader.

Jumps in N = 18 - 16 = 2
Jump in number of Leader = 2 x 2 = 4

So, the number of leader who will get selected is 1 + 4 = 5.

games round 1.jpg
games round 2.jpg
games round 3.jpg

After 3 rounds 5 and 13 will remain, beginning with 5, 13 will have to step down.

Thus, 5 will be the leader.


4)   There are 64 players in a knock out tournament and every player is ranked (seeded) from 1 - 64.

The matches are played in such a manner that in round one the 1st seeded player plays with the 64th, 2nd with the 63rd and so on.
The players who win move on to the next round whereas others are out of the competition.

In second round, the winner of match 1 will play winner of the last match (which was between seed 32 and seed 33), and winner of match 2 will meet the winner of second last match in round 1 and so forth.

Thus, after all rounds winner is declared.

In a tournament of 128 players, who will play 40 in round 2 if there are no upsets?

- Published on 25 Apr 17

a. 25
b. 26
c. 27
d. 28
Answer  Explanation 

ANSWER: 25

Explanation:
In round 2 there will be 64 players. So, the sum of seeding will be 65.
The opponent of 40 will be, 65 - 40 = 25


5)   There are 64 players in a knock out tournament and every player is ranked (seeded) from 1 - 64.

The matches are played in such a manner that in round one the 1st seeded player plays with the 64th, 2nd with the 63rd and so on.
The players who win move on to the next round whereas others are out of the competition.

In second round, the winner of match 1 will play winner of the last match (which was between seed 32 and seed 33), and winner of match 2 will meet the winner of second last match in round 1 and so forth.

Thus, after all rounds winner is declared.

Which seeds will play Match no 7 and Match no 10 in Round 1 of a 32-player tournament?

- Published on 25 Apr 17

a. 26, 23
b. 27, 24
c. 28, 25
d. 29, 26
Answer  Explanation 

ANSWER: 26, 23

Explanation:
For solving these type of problems -

Notice that the sum of the seeding in every match will be equal to total players + 1. i.e. 1 + 32 = 33, 2 + 31 = 33.

In round of 64, sum of seeds will be 65, and in round of 16, sum of seeds will be 17. And so forth.

Thus, for 32 player tournaments, it will be 32 + 1 = 33.

For, match 7, opponent will be 33 -7 = 26
Similarly, for match 10, opponent will be 23.


6)   16 teams participated in a cricket tournament.

The tournament was conducted in two stages.

First stage
  • In the first stage, the teams are divided into two equal groups.
  • Each team plays every other team in its group exactly once.
  • At the end of first stage, the top four teams from each group advance to the second stage.
  • Rest teams are eliminated.
Second stage
  • The second stage comprised 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.
Rules
  • The tournament rules such that each match results in a winner and a loser with no possibility of a tie.
  • In the first stage, a team earns one 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 four teams from each group advanced to the next stage.
What is the minimum number of wins required for a team to guarantee advance (or possible advance) to next stage?

- Published on 12 Apr 17

a. 5
b. 6
c. 7
d. 8
Answer  Explanation 

ANSWER: 6

Explanation:
For a team to advance to the second stage, it should be among the top 4 in its group.

Total points on stake in a group is the same as the total number of matches which is 8C2 = 28.

To guarantee advance, it can have 3 teams with the same or more points. There can be 5 teams with 5 points.

So, 5 wins is not good enough to ensure advancement to round 2. However, 6 wins will guarantee its advance.


7)   16 teams participated in a cricket tournament.

The tournament was conducted in two stages.

First stage
  • In the first stage, the teams are divided into two equal groups.
  • Each team plays every other team in its group exactly once.
  • At the end of first stage, the top four teams from each group advance to the second stage.
  • Rest teams are eliminated.
Second stage
  • The second stage comprised 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.
Rules
  • The tournament rules such that each match results in a winner and a loser with no possibility of a tie.
  • In the first stage, a team earns one 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 four teams from each group advanced to the next stage.
What would be the total number of matches in the tournament?

- Published on 14 Apr 17

a. 55
b. 56
c. 63
d. 66
Answer  Explanation 

ANSWER: 63

Explanation:
In first stage, teams are divided into two groups of 8 teams each.
They play a match against everyone exactly one i.e. 8C2 matches in every group.

So,
2 x 8C2 = 56 matches for the first stage.

8C2 = 8! / (2!)(6!) = 4 x 7 = 28

In second stage, there are 8 teams in a “knockout stage”.
There will be one winner, so 8 – 1 = 7

So, total number of matches is 56 + 7 = 63


8)   1. There are 16 teams divided into 2 pools of 8 each.
2. Each team in a group plays against one another on a round-robin basis.
3. The top four teams from each group will qualify for the next round i.e. round 2.
4. In case of teams having the same number of wins, the team with better run-rate would be ranked ahead.
5. Draws are not allowed.

What is the minimum number of wins required to guarantee qualification in the next round?

- Published on 14 Apr 17

a. 4
b. 5
c. 6
d. 7
Answer  Explanation 

ANSWER: 6

Explanation:
In this case consider the mean of first 5 higher seeded teams (7+6+5+4+3)/5=5 So, it may be the case that 5 teams can end up having 5 wins each.

And hence 1 team will miss the second round.
So, minimum number of wins to guarantee a place would be 6.


9)   Directions :
1. There are 16 teams divided into 2 pools of 8 each.
2. Each team in a group plays against one another on a round-robin basis.
3. The top four teams from each group will qualify for the next round i.e. round 2.
4. In case of teams having the same number of wins, the team with better run-rate would be ranked ahead.
5. Draws are not allowed.

What is the minimum number of wins required to qualify for the next round?

- Published on 14 Apr 17

a. 1
b. 2
c. 3
d. 4
Answer  Explanation 

ANSWER: 2

Explanation:
Each group consists of 8 teams.

So, each team will play 7 matches each.

Suppose each of the 8 teams were seeded and we consider the case where a higher seeded team will always win.

So, the number of wins for the 8 teams would be 7, 6, 5, 4, 3, 2, 1, 0 with highest seeded team winning all and lowest seeded team losing all.

For minimum number of wins we allow 3 teams to win maximum number of matches.

Of the remaining 5 teams just find out the mean of their number of wins.

In this case, it would be - (4+3+2+1+0)/5=2.

So, 5 teams can end up with 2 wins each and a team with better run rate will qualify with 2 wins.

The minimum number of wins required to qualify for next round with better run-rate is 2.


10)   A team of 5 players Ashwin, Rahul, Sachin, Virat and Rohit participated in a tournament and played four matches.

The following table gives partial information about their individual scores and the total runs scored by the team in each match.

Each column has two values missing. These are the runs scored by the two lowest scorers in that match.

None of the two missing values is more than 10% of the total runs scored in that match.

Runs scoredMatch 1Match 2Match 3Match 4
Ashwin10053
Rahul886552
Sachin110
Virat72752056
Rohit6078
Total270300240200

The players are ranked 1 to 5 on the basis of the total runs scored by them in the four matches, with the highest scorer getting Rank 1.

If it is known that no two players scored the same number of total runs, who is placed at rank 4?

- Published on 14 Apr 17

a. Ashwin
b. Rahul
c. Rohit
d. Virat
Answer  Explanation 

ANSWER: Rohit

Explanation:
Range of every player’s minimum and maximum score is:

Ashwin - 189-199
Rahul - 218-224
Sachin - 182-187
Virat - 223
Rohit - 187-188
So, we can conclude that
Ashwin - Rank 3
Rohit - Rank 4
Sachin - Rank 5


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