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7 teams compete in a track competition. If there are 20

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7 teams compete in a track competition. If there are 20  [#permalink]

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New post Updated on: 27 Jul 2014, 02:59
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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

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Originally posted by bmwhype2 on 19 Feb 2008, 10:45.
Last edited by Bunuel on 27 Jul 2014, 02:59, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: 7 teams compete in a track competition. If there are 20  [#permalink]

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New post 29 Mar 2015, 19:08
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Hi earnit,

As wordy as this prompt is, it's really just a 'limit' question - you have to think about minimum and maximum possibilities given the restrictions in the question.

We're told a few facts about a track competition:
1) 7 teams compete in the competition.
2) There are 20 events in the competition
3) There are NO ties in the competition.
4) No team wins MORE than 3 events

We're asked for the MINIMUM number of teams that would win at least 1 event at this competition.

It's the last fact that is the most 'limiting' piece of information: NO team won more than 3 events....

Let's start by trying to MAXIMIZE the number of events that each team wins.....
If each of the first 6 teams won the MAXIMUM number of events possible, then that would account for 6(3) = 18 of the events. There are 20 total events though - so who won THOSE last 2 events?

It would have to be the only team that's left: the 7th team.

This means that EVERY team won at least one event (and it really means that every team won at least 2 events).

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Re: 7 teams compete in a track competition. If there are 20  [#permalink]

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New post 19 Feb 2008, 11:11
1
bmwhype2 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?
3
4
5
6
7


7

3(max wins) x 6 =18 (6 teams win three events)

18+2 = 20 (1 team wins 2 events)
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Re: 7 teams compete in a track competition. If there are 20  [#permalink]

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New post 06 Aug 2014, 19:39
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bmwhype2 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


what will happen if one team lost all the events? There will be 6 team left that won at least one event or no more than 3.
Even if each of 6 team won 3 events, there are only 18 events finished ( < 20)--> The possibility of one team lost all the events is 0.
--> there is always at least one team won at least one event
--> E is the answer
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Re: 7 teams compete in a track competition. If there are 20  [#permalink]

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New post 29 Mar 2015, 14:16
bmwhype2 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



Would be great if any expert could guide as to how to go about this question.
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Re: 7 teams compete in a track competition. If there are 20  [#permalink]

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New post 20 Jun 2017, 19:08
bmwhype2 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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Re: 7 teams compete in a track competition. If there are 20  [#permalink]

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New post 13 Jan 2018, 10:22
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bmwhype2 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


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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Re: 7 teams compete in a track competition. If there are 20  [#permalink]

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Re: 7 teams compete in a track competition. If there are 20   [#permalink] 16 Apr 2019, 07:23
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