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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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

Answer: E

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Vincen wrote:
Tue Sep 15, 2020 2:01 am
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

Answer: E

Source: Manhattan GMAT
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.

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

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Vincen wrote:
Tue Sep 15, 2020 2:01 am
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

Answer: E

Solution:

Let’s say that 6 teams won (the maximum of) 3 events, and 1 team won 2 events. Thus, the minimum possible number of teams that won at least 1 event is 7.

Answer: E

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