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7 teams

by j_shreyans » Sat Nov 01, 2014 10:56 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

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by GMATGuruNY » Sat Nov 01, 2014 11:48 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?
3
4
5
6
7
To MINIMIZE the number of teams that win at least one event, we must MAXIMIZE the number of teams that win 3 events.
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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by Brent@GMATPrepNow » Sat Nov 01, 2014 12:15 pm
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
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 [spoiler]7 = E[/spoiler]

Cheers,
Brent
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by Mathsbuddy » Mon Nov 03, 2014 9:33 am
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
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by Scott@TargetTestPrep » Fri Dec 15, 2017 10:29 am
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
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.

Answer: E

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by Brent@GMATPrepNow » Sat Jan 13, 2018 9:21 am
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
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

Cheers,
Brent
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