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
OAE
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7 teams
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j_shreyans
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To MINIMIZE the number of teams that win at least one event, we must MAXIMIZE the number of teams that win 3 events.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?
3
4
5
6
7
6*3 = 18.
Thus, the maximum number of teams that could win 3 events = 6.
If 18 of the 20 events are won by these 6 teams, the number of events remaining = 20 -18 = 2.
These 2 events must be won by the 7th team.
Thus, all 7 teams must win at least one event.
The correct answer is E.
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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.j_shreyans wrote: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
OAE
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 [spoiler]7 = E[/spoiler]
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Mathsbuddy
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7 teams
Max no. of wins each = 3
20 events shared between 3 max wins = 6.6666... minimum number of teams to win at least one.
Therefore answer = all 7
Max no. of wins each = 3
20 events shared between 3 max wins = 6.6666... minimum number of teams to win at least one.
Therefore answer = all 7
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Scott@TargetTestPrep
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Let's say 6 teams won 3 events and 1 team won 2 events. Thus, the minimum possible number of teams that won at least 1 event is 7.j_shreyans wrote: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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Brent@GMATPrepNow
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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.j_shreyans wrote: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
OAE
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
Brent Hanneson - Creator of GMATPrepNow.com
