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by sana.noor » Sat Feb 02, 2013 10:04 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

Their is no such team that win at-least ONE event but he answer is 7
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by GMATGuruNY » Sat Feb 02, 2013 10:21 am
sana.noor 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

Their is no such team that win at-least ONE event but he answer is 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 Feb 02, 2013 10:21 am
sana.noor 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
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 sana.noor » Sat Feb 02, 2013 10:39 am
Thankyou to both of you, i thought that i have to find number of teams winning just 1 event. But question actually ask the number of teams winning at least one event.
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