IPMAT Indore 2021 (MCQ) - Team E was defeated by | PYQs + Solutions

IPMAT Indore 2021

DILR

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	Losses	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

Team E was defeated by

Teams A and B only

Only Team A

Only Team B

Teams A, B and D only

Correct Option: 3

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

, since there will be a total of

15

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=6

points

\newline

F=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 suffered one loss only, i.e. defeated only by one team. Hence, Options 1 and 4 are eliminated. We can also see that E has had 4 matches ending in draws. B has suffered 0 draws, hence it's the only one that has defeated E.

IPMAT Indore 2021 (MCQ) PYQs

Team E was defeated by

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