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in a track competition

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by sanju09 » Fri Mar 04, 2011 1:31 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 Anurag@Gurome » Fri Mar 04, 2011 2:51 am
sanju09 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
To minimize the number of teams that won at least one event, we have to maximize the number of teams that lost all the events. This is possible when a single team wins as much as it possible for it to win, i.e. 3 events.

Hence the number of teams that won at least one event will be minimum when all of them won as much as they can, i.e. at max 3 events. Now we have 20 events. So the minimum possible number of teams that won at least one event is 7.

The correct answer is E.
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