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IPMAT Indore 2021 (MCQ) PYQs

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IPMAT Indore 2021

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Tournaments

Hard

In a football tournament six teams A, B, C, D, E, and F participated. Every pair of teams had exactly one match among them. For any team, a win fetches 2 points, a draw fetches 1 point, and a loss fetches no points. Both teams E and F ended with less than 5 points. At the end of the tournament points table is as follows (some of the entries are not shown):
Teams Played
 Wins
 Losses
 Draws
 Points
A
 5
 0
 8
B
 5
 2
 6
C
 5
 2
 5
D
 5
 1
 5
E
 5
 1
F
 5
It is known that: (1) team B defeated team C, and (2) team C defeated team D

Which team has the highest number of draws

✅ Correct Option: 4
Teams Played
 Wins
 Losses
 Draws
 Points
A
 5
 3 0
 2 8
B
 5
 3 2
 0 6
C
 5
 2 2
 1 5
D
 5
 1 1
 3 5
E
 5
 1
F
 5
From the given points, we can figure out from A to D how their matches went, i.e. how many they won, lost, or ended with a draw. \newline
Teams Played
 Wins
 Losses
 Draws
 Points
A
 5
 3 0
 2 8
B
 5
 3 2
 0 6
C
 5
 2 2
 1 5
D
 5
 1 1
 3 5
E
 5
 0 1
 4 4
F
 5
We know that E and F have less than 5 points each. It's given that E has one loss, so now he has 4 more matches. All 4 of these have to be draws, because that's the only case where E will have less than 5 points. Even a single win would exceed the points and contradict what's given.
Teams Played
 Wins
 Losses
 Draws
 Points
A
 5
 3 0
 2 8
B
 5
 3 2
 0 6
C
 5
 2 2
 1 5
D
 5
 1 1
 3 5
E
 5
 0 1
 4 4
F
 5
 0 3 2 2
Things to note: \newline Total Number of Points =30=30, since there will be a total of 1515 matches and each match results in two points (if a team loses, the winning team gets two points and if a match ends in a draw, both teams get one point each)
Hence, E+F=6E+F=6 points \newline F=2F=2 points
F could have either 1 win, 4 losses, 0 draws or 0 wins, 3 losses, and 2 draws.
The table becomes inconsistent with the former, since no two teams can have 0 draws and B already has 0 draws.
Hence, the table above is our table.
From it, we can see that E has the highest number of draws.

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Which team was not defeated by team A

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Total points Team F scored was

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