7 teams compete in a track competition. If there are 20 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?
A. 3
B. 4
C. 5
D. 6
E. 7
OA E
Source: Manhattan Prep
7 teams compete in a track competition. If there are 20 events in the competition, no event ends in a tie, and no team
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The first thing we should recognize is that, if each of the 7 teams get their maximum of 3 wins each, then the total number of wins is 21.BTGmoderatorDC wrote: ↑Fri Feb 10, 2023 4:56 pm7 teams compete in a track competition. If there are 20 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?
A. 3
B. 4
C. 5
D. 6
E. 7
OA E
Source: Manhattan Prep
So, the ONLY WAY to distribute 20 wins among 7 teams is for six teams to get 3 wins and one team to get 2 wins.
For example:
Team 1: 3 wins
Team 2: 3 wins
Team 3: 3 wins
Team 4: 3 wins
Team 5: 3 wins
Team 6: 3 wins
Team 7: 2 wins.
So, the minimum possible number of teams that won at least one event must equal 7
Answer: E
Cheers,
Brent