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Bunuel
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A total of 15 teams participated in a tournament. Each team plays with 08 Dec 2020, 06:45
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95% (hard)

Question Stats:

36% (02:54) correct 64% (02:49) wrong based on 110 sessions

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A total of 15 teams participated in a tournament. Each team plays with every other team exactly once. A team gets 3 points for a win, 2 points for a draw and 1 point for a loss. The team which scored the least got 21 points. The scores of all the teams were distinct and at least one match played by winning team was drawn. Which of the following is always true for the winning team?

A. It had at least two draws

B. It had had less than four losses

C. It had a maximum of 9 wins

D. It had at least 8 wins

E. It had maximum of 5 draws

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B
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A total of 15 teams participated in a tournament. Each team plays with 08 Dec 2020, 06:59
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Bunuel, Option C and Option E seem the same and you have forgotten to type E at the start of the last option.
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Bunuel
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A total of 15 teams participated in a tournament. Each team plays with 08 Dec 2020, 08:03
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Bunuel, Option C and Option E seem the same and you have forgotten to type E at the start of the last option.
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Fixed. Thank you.
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A total of 15 teams participated in a tournament. Each team plays with 08 Dec 2020, 11:07
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The team which scored the least got 21 points.
And all teams have distinct points.
Let say all teams points vary by 1 point, and
So the winning team must have at least 35 points to win (because if the 15th rank team have 21 points, the 1st rank team must have 21+15-1 = 35)
35 points need at least 10 winning matches, (10*3+1*2+3*1= 30+2+3 = 35)(least possible win and draw matches + most possible no. of match lost
11th winning match will give a sum total of 36 points (11*3+2*1+1*2 = 33+2+2 = 37)
using option lets fetch the minimum marks for the winner team.

A. It had at least two draws
=> The winning team can win with 1 draw match as well,
35 points need at least 10 winning matches, (10*3+1*2+3*1= 30+2+3 = 35)
So, the option is not always true (WRONG)

B. It had had less than four losses
the most matches a winning team can lose is 3
and the option satisfy the constraint (TRUE)

C. It had a maximum of 9 wins
Nope we need at least 10 wins to score the least possible points (WRONG)

D. It had at least 8 wins
Nope the winning team had at least 10 winning matches (WRONG)

E. It had maximum of 5 draws
No, The winning match no. will be 9 then, and we need 10 (WRONG)

Answer is B
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A total of 15 teams participated in a tournament. Each team plays with 28 Dec 2020, 07:30
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Least Won Team got 21 Points

- Total Matches to be played - 15c2 = 105
- Total Points which can be awarded - 105 x 3 (win) + 105 x 1 (loss) = 420 or 105 x 2 x 2 draw = 420

- Since no team got equate points, 420 to be divided among 15 teams with at least 21 points for each...
- It can be inferred from (21+35)/2 x 15 = 420 that each team got consecutive points and max points one team got were 35

Now, 35 points are to be earned by the winner from 14 Matches
At least One is Draw => so 33 points to be earned by the winner in 13 Matches

Possible combinations

Minimum Wins 7 ( 21 Points ) + 6 Draws ( 12 Points) = 33 Points - Eliminate A, D and E
Max Wins 10 ( 30 Points ) + 3 Loss ( 3 points ) = 33 Points - Eliminate C

B is the Answer
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A total of 15 teams participated in a tournament. Each team plays with 28 Jul 2024, 15:57
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