In a round-robin tournament with 6 teams, each team plays one game aga

Question

In a round-robin tournament with 6 teams, each team plays one game against each other team, and each game results in one team winning and one team losing. At the end of the tournament, the teams are ranked by the number of games won. What is the maximum number of teams that could be tied for the most wins at the end on the tournament?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Archit3110 · Answer

not able to completely solve question 
total games played ; 6c2; 15
let each winning point ; 1 ; so total points if a team wins all games; 15
and out of 6 teams maximum teams which can be tied for most wins can be 5 ; if all wining 3 games at most and 1 team loosing all games.
IMO D

LevanKhukhunashvili · Answer

There will be 15 games. if we assume that the winner gets 1 point, there will be total of 15 points.

15 points can be distributed equally with 5 teams, each earning 3 points (that will be maximum points earned), the sixth team losing every game

I will bet on ans  D

arorni · Answer

Can someone please help with this?

neha283 · Answer

There are 6 teams and each team plays 5 matches, now think like this
Team A - played 5, won 5. 
Team B - played 5, won 4 (lost 1 to A)
Team C - played 5, won 3 (lost 2 to A and B)
Team D - played 5, won 2 (lost 3 to A, B and C)
Team E - played 5, won 1 (lost 4 to A, B, C and D)
Team F - played 5, won 0 (lost 5 to all teams)

Thus, maximum number of teams to win - 5.

Hope it helps.

ScottTargetTestPrep · Answer

Since 6C2 = 15, the 6 teams will play 15 games in total. Since each game results 1 team winning and 1 team team losing, the sum of wins and loses is 15 + 15 = 30. For example, if no teams have the same number of wins and loses, then the 6 teams have W-L records as 5-0, 4-1, 3-2, 2-3, 1-4 and 0-5. As you can see, if you add up all these numbers, the sum is 30.

We see that 30/6 = 5, however, we can’t have all 6 teams to have the same W-L records. That is, they can’t have all have 5-0, 4-1, or 3-2 W-L records. On the other hand, we can let the team with the worst W-L record be 0-5 and for each of the 5 remaining teams to have W-L records as 3-2.

Answer: D

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In a round-robin tournament with 6 teams, each team plays one game aga

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