DI - Games & Tournaments - Previous Year CAT/MBA Questions
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Answer the next 3 questions based on the information given below.
Six teams are playing in a hockey tournament where each team is playing against every other team exactly once. At an intermediate stage, the status is as follows;
Note:
- The team that scores more goals than it concedes wins the match, while if both the teams score the same no. of goals, the match is declared drawn.
- In a match played between Team X and Team Y, if team X scores 1 and concedes none, then the score line would read. Team X-Team Y (1-0).
Which of the following matches are yet to be played?
- (a)
Team A – Team B and Team C – Team D
- (b)
Team C – Team D and Team E – Team F
- (c)
Team E – Team F and Team B – Team D
- (d)
Team C – Team D and Team A – Team E
- (e)
Team A – Team B and Team E – Team F
Answer: Option E
Text Explanation :
Team A wins both its matches and the only teams to lose a match are E and F.
∴ A played and won against E and F.
D drew both its matches. D would draw its matches against B (1 - 1) and C (0 - 0).
Since team B drew 1-1 with team D, team B must have won the other game 4-0.
If B won (4 - 0) against E, then E would’ve won its other match (1 – 0). But E has to lose both its matches.
∴ B won (4 - 0) against F and F lost its match against A (0 - 3).
Now, since A won against F (3 - 0) hence it won its match against E by (2 - 1)
Now since E lost its match against A by (1 - 2), E would’ve lost its other match by (0 - 2) against C.
[TBP = To be played]
Hence, option (e).
Workspace:
Which of the following score line is a possible outcome in the tournament?
- (a)
Team A – Team D (1-0)
- (b)
Team A – Team E (2-1)
- (c)
Team B – Team D (1-0)
- (d)
Team C – Team F (2-0)
- (e)
None of the above
Answer: Option B
Text Explanation :
Consider the solution to first question of this set.
Team A won against E by (2 - 1).
Hence, option (b).
Workspace:
Which of the following score line is not a possible outcome in the tournament?
- (a)
Team A – Team F (4-0)
- (b)
Team B – Team F (4-0)
- (c)
Team C – Team D (0-0)
- (d)
Team C – Team E (2-0)
- (e)
All of the above options are possible
Answer: Option A
Text Explanation :
Consider the solution to first question of this set.
Team A won against F by (3 - 0).
Hence, option (a).
Workspace:
Answer the following question based on the information given below.
In ISL football competition, eight football teams – Atletico De Kolkata, Chennaiyan FC, Delhi Dynamos, FC Goa, FC Pune City, Kerala Blasters, Mumbai City FC and North-East United FC – participated where each team played against every other team exactly once. Every win earned three points for the teams and a loss earned 0. If there was a draw, each team was rewarded one point. Now as per the fixtures, following are some of the observations:
- Out of the seven matches played by Chennaiyan FC, it won five and the other two matches were drawn.
- FC Pune City won the match against FC Goa and Kerala Blasters but lost the match against Delhi Dynamos and Chennaiyan FC.
- Atletico De Kolkata drew a match against FC Goa, Chennaiyan FC and FC Pune City.
- None of the teams lost all the matches.
If Chennaiyan FC won the match against FC Goa, what could have been the maximum score of FC Goa?
- (a)
11
- (b)
12
- (c)
13
- (d)
14
Answer: Option C
Text Explanation :
FC Goa has lost to FC Pune City and drawn by Atletico de Kolkata. Also, as per the question, FC Goa has lost to Chennaiyan FC.
Hence, FC Goa has 2 losses and 1 draw.
To maximise its score, it should win the remaining four matches.
∴ Maximum score = (4 × 3) + (2 × 0) + (1 × 1) = 13
Hence, option (c).
Workspace:
What could be the minimum absolute difference between the scores of FC Pune City and Chennaiyan FC?
- (a)
0
- (b)
1
- (c)
3
- (d)
4
Answer: Option D
Text Explanation :
Chennaiyan FC have won 5 matches and drawn 2 matches.
∴ Their score = (5 × 3) + (2 × 1) = 17
To minimize the difference of scores between the two team, maximize FC Pune City’s score.
FC City have won 2 matches, lost 2 matches and drawn 1 match. Hence, to maxmiize their score, they should win the reminaing 2 matches. Hence, they should have 4 wins, 2 losses and 1 draw.
∴ Their score = (4 × 3) + (1 × 1) = 13
∴ Minimum absolute difference = 17 – 13 = 4
Hence, option (d).
Workspace:
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