Join Testzone, Smartkeeda’s Test Series Platform for:

Eight players P, Q, R, S, T, U, V and W participated in the badminton tournament. In the first round of the tournament these eight players were divided into two groups of four players each. In a group each player had to play twice against each of the other players. Every match had a decisive result, i.e. no match ended in a tie. The player with the highest and second highest number of wins in both the groups reached the semifinal. Q, U, W, V were the four players who qualifed for the semifinal.]
 
It is also known that in first round:
  • Each player of each group had a different number of wins.
  • R lost all of his matches against all the other players except S, who atleast one match against each of the other players except one.
  • V won both the matches against U.
  • P and W won the same number of matches.
1
Four of the following five are alike in the certain way and so form a group. Which is the one that does not belong to the group?
» Explain it
E
Following the final solution to the puzzle set we can say that W is the one that does not belong to the group.

Hence the correct answer is option (E.)

Rank 1st 2nd 3rd 4th
Group A V U P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1

Common Explanation:

References:

V won both the matches against U.

Inference:

Studying the information carefully we can say that V and U were in same group let’s says that Group A. And we also know that Q, U, W, V were the four players who qualifed for the semifinal so we can also say that Q and W were in second group let’s say that Group B.

Rank 1st 2nd 3rd 4th
Group A V/U U/V    
Number of matches won        
Group B Q/W  W/Q    
Number of matches won        
 
References:

Each player of each group had a different number of wins.
P and W won the same number of matches.
R lost all of his matches against all the other players except S, who atleast one match against each of the other players except one.


Inference:

Using the given information we can say that  R and S belongs to Group B and P and T belongs to Group A its because P and w can’t be in the same group and R and S must go together. As it is given that R won only against S so he has only one point.

Rank 1st 2nd 3rd 4th
Group A V/U U/V P/T T/P
Number of matches won        
Group B Q/W  W/Q S R
Number of matches won       1
 
Now, In a group each player had to play twice against each of the other players. So the total number of matches that can be played in each group are equal to 12. And the winning combinations given that Each player of group had a different number of wins can only be

A -  ( 6 4 2 0 )
B-  ( 6 3 2 1 )
C-  ( 5 4 2 1 )
D-  ( 5 4 3 0 )

In all of the combinations only B and C can fit in Group B. But we know that W and P have same number of wins so only combination B and D fits into our requirements.

Rank 1st 2nd 3rd 4th
Group A V/U U/V P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1
 
But U cannot have 5 wins in Group A because he lost both of his matches to V.
Therefore the final scorecard is as follows

Rank 1st 2nd 3rd 4th
Group A V U P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1

2
Who won the least number of matches after the first round?
» Explain it
D
Following the final solution to the puzzle set we can say that T won the least number of matches after the first round.

Hence the correct answer is option (D.)

Rank 1st 2nd 3rd 4th
Group A V U P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1

Common Explanation:

References:

V won both the matches against U.

Inference:

Studying the information carefully we can say that V and U were in same group let’s says that Group A. And we also know that Q, U, W, V were the four players who qualifed for the semifinal so we can also say that Q and W were in second group let’s say that Group B.
 
Rank 1st 2nd 3rd 4th
Group A V/U U/V    
Number of matches won        
Group B Q/W  W/Q    
Number of matches won        
 
References:

Each player of each group had a different number of wins.
P and W won the same number of matches.
R lost all of his matches against all the other players except S, who atleast one match against each of the other players except one.

Inference:

Using the given information we can say that  R and S belongs to Group B and P and T belongs to Group A its because P and w can’t be in the same group and R and S must go together. As it is given that R won only against S so he has only one point.

Rank 1st 2nd 3rd 4th
Group A V/U U/V P/T T/P
Number of matches won        
Group B Q/W  W/Q S R
Number of matches won       1
 
Now, In a group each player had to play twice against each of the other players. So the total number of matches that can be played in each group are equal to 12. And the winning combinations given that Each player of group had a different number of wins can only be
 
A -  ( 6 4 2 0 )
B-  ( 6 3 2 1 )
C-  ( 5 4 2 1 )
D-  ( 5 4 3 0 )

In all of the combinations only B and C can fit in Group B. But we know that W and P have same number of wins so only combination B and D fits into our requirements.

Rank 1st 2nd 3rd 4th
Group A V/U U/V P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1
 
But U cannot have 5 wins in Group A because he lost both of his matches to V.
Therefore the final scorecard is as follows

Rank 1st 2nd 3rd 4th
Group A V U P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1

3
What was the total number of wins of P after the first round?
» Explain it
C
Following the final solution to the puzzle set we can say that P has 3 wins after the first round.

Hence the correct answer is option (C.)

Rank 1st 2nd 3rd 4th
Group A V U P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1

Common Explanation:

References:

V won both the matches against U.

Inference:

Studying the information carefully we can say that V and U were in same group let’s says that Group A. And we also know that Q, U, W, V were the four players who qualifed for the semifinal so we can also say that Q and W were in second group let’s say that Group B.

Rank 1st 2nd 3rd 4th
Group A V/U U/V    
Number of matches won        
Group B Q/W  W/Q    
Number of matches won        
 
References:

Each player of each group had a different number of wins.
P and W won the same number of matches.
R lost all of his matches against all the other players except S, who atleast one match against each of the other players except one.


Inference:

Using the given information we can say that  R and S belongs to Group B and P and T belongs to Group A its because P and w can’t be in the same group and R and S must go together. As it is given that R won only against S so he has only one point.

Rank 1st 2nd 3rd 4th
Group A V/U U/V P/T T/P
Number of matches won        
Group B Q/W  W/Q S R
Number of matches won       1
 
Now, In a group each player had to play twice against each of the other players. So the total number of matches that can be played in each group are equal to 12. And the winning combinations given that Each player of group had a different number of wins can only be

A -  ( 6 4 2 0 )
B-  ( 6 3 2 1 )
C-  ( 5 4 2 1 )
D-  ( 5 4 3 0 )

In all of the combinations only B and C can fit in Group B. But we know that W and P have same number of wins so only combination B and D fits into our requirements.

Rank 1st 2nd 3rd 4th
Group A V/U U/V P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1
 
But U cannot have 5 wins in Group A because he lost both of his matches to V.
Therefore the final scorecard is as follows

Rank 1st 2nd 3rd 4th
Group A V U P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1

4
Who won the most number of matches after the first round?
» Explain it
A
Following the final solution to the puzzle set we can say that Q won the most number of matches after the first round.

Hence the correct answer is option (C.)

Rank 1st 2nd 3rd 4th
Group A V U P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1

Common Explanation:

References:

V won both the matches against U.

Inference:

Studying the information carefully we can say that V and U were in same group let’s says that Group A. And we also know that Q, U, W, V were the four players who qualifed for the semifinal so we can also say that Q and W were in second group let’s say that Group B.

Rank 1st 2nd 3rd 4th
Group A V/U U/V    
Number of matches won        
Group B Q/W  W/Q    
Number of matches won        
 
References:

Each player of each group had a different number of wins.
P and W won the same number of matches.
R lost all of his matches against all the other players except S, who atleast one match against each of the other players except one.

Inference:

Using the given information we can say that  R and S belongs to Group B and P and T belongs to Group A its because P and w can’t be in the same group and R and S must go together. As it is given that R won only against S so he has only one point.

Rank 1st 2nd 3rd 4th
Group A V/U U/V P/T T/P
Number of matches won        
Group B Q/W  W/Q S R
Number of matches won       1
 
Now, In a group each player had to play twice against each of the other players. So the total number of matches that can be played in each group are equal to 12. And the winning combinations given that Each player of group had a different number of wins can only be

A -  ( 6 4 2 0 )
B-  ( 6 3 2 1 )
C-  ( 5 4 2 1 )
D-  ( 5 4 3 0 )

In all of the combinations only B and C can fit in Group B. But we know that W and P have same number of wins so only combination B and D fits into our requirements.

Rank 1st 2nd 3rd 4th
Group A V/U U/V P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1
 
But U cannot have 5 wins in Group A because he lost both of his matches to V.
Therefore the final scorecard is as follows

Rank 1st 2nd 3rd 4th
Group A V U P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1

5
Which of the following player lost atleast one match against P in the 1st round?
» Explain it
D
Following the final solution to the puzzle set we can say that V lost atleast one match against P in the 1st round.

Hence the correct answer is option (D.)

Rank 1st 2nd 3rd 4th
Group A V U P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1

Common Explanation:

References:

V won both the matches against U.

Inference:

Studying the information carefully we can say that V and U were in same group let’s says that Group A. And we also know that Q, U, W, V were the four players who qualifed for the semifinal so we can also say that Q and W were in second group let’s say that Group B.

Rank 1st 2nd 3rd 4th
Group A V/U U/V    
Number of matches won        
Group B Q/W  W/Q    
Number of matches won        
 
References:

Each player of each group had a different number of wins.
P and W won the same number of matches.
R lost all of his matches against all the other players except S, who atleast one match against each of the other players except one.


Inference:

Using the given information we can say that  R and S belongs to Group B and P and T belongs to Group A its because P and w can’t be in the same group and R and S must go together. As it is given that R won only against S so he has only one point.

Rank 1st 2nd 3rd 4th
Group A V/U U/V P/T T/P
Number of matches won        
Group B Q/W  W/Q S R
Number of matches won       1
 
Now, In a group each player had to play twice against each of the other players. So the total number of matches that can be played in each group are equal to 12. And the winning combinations given that Each player of group had a different number of wins can only be

A -  ( 6 4 2 0 )
B-  ( 6 3 2 1 )
C-  ( 5 4 2 1 )
D-  ( 5 4 3 0 )

In all of the combinations only B and C can fit in Group B. But we know that W and P have same number of wins so only combination B and D fits into our requirements.

Rank 1st 2nd 3rd 4th
Group A V/U U/V P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1
 
But U cannot have 5 wins in Group A because he lost both of his matches to V.
Therefore the final scorecard is as follows

Rank 1st 2nd 3rd 4th
Group A V U P T
Number of matches won 5 4 3 0
Group B Q  W S R
Number of matches won 6 3 2 1