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MGMAT CAT- non std word problem

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by vkb16 » Wed Oct 14, 2009 11:15 pm
Does someone have a simple method to solve this??

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

OA is 7

thanks
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IMO

by enniguy » Thu Oct 15, 2009 10:43 pm
Yes it is 7. There are 20 events and each team can win a maximum of 3. So, if from start each team start winning 3 events, then we will have 6 team winning 3 events.
7th team will win the rest 2. That makes it 20 events.

Team 1 - upto - Team 6 = Each 3 events = 18 events.
Team 7 = 2 events = 2 events.
Total = 20 events.

Hence, Answer = 7
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by vkb16 » Fri Oct 16, 2009 5:01 am
but the qs says ''what is the minimum possible number of teams that won at least one event?''

can u explain why we are taking the Maximum(7) no. of teams for consideration?? Im not able to understand the logistics behind the qs..

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by enniguy » Fri Oct 16, 2009 5:15 am
vkb16 wrote:but the qs says ''what is the minimum possible number of teams that won at least one event?''

can u explain why we are taking the Maximum(7) no. of teams for consideration?? Im not able to understand the logistics behind the qs..

thanks
We are taking maximum 3 events per team. We are not bothered about 7 teams r 8 teams. We take maximum 3 events because that's the maximum possible, hence it will result in the most teams with 0 event wins. "Team with Atleast 1 event" is nothing but [All Teams ] - [ Teams with 0 wins ].

Now we know [All Teams] number = 20.
Teams with 0 wins can be found by maximizing the wins to other teams.
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by royrijit1 » Sun Apr 26, 2015 6:21 am
Hello all,

In order to properly understand the concepts tested, I need to ask a query I have on this question. Here it is:

What if I modified the question as below:
8 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?

In such scenario, will the minimum number of teams winning at least one event be 8 ?(7th and 8th team won one each)

Also: any thread in this forum that explains the maximizing and minimizing concepts in details.
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by Brent@GMATPrepNow » Sun Apr 26, 2015 8:57 am
royrijit1 wrote:Hello all,

In order to properly understand the concepts tested, I need to ask a query I have on this question. Here it is:

What if I modified the question as below:
8 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?

In such scenario, will the minimum number of teams winning at least one event be 8 ?(7th and 8th team won one each)

Also: any thread in this forum that explains the maximizing and minimizing concepts in details.
What is the minimum possible number of teams that won at least one event?
You might ask, "Is is possible for 1 team to win zero events?" [this would mean that the other 7 teams won at least 1 event]
If 1 team wins zero events, then the 20 wins must be distributed among the remaining 7 teams.
Is this possible?
Sure, 6 teams each win 3 events (for a total of 18 wins), and the 7th team wins 2 events. Perfect.
So, it's possible for 7 teams to win at least 1 event.

Now ask, "Is is possible for 2 teams to win zero events?"
If 2 teams win zero events, then the 20 wins must be distributed among the remaining 6 teams.
Is this possible?
NO.
Even if each of the 6 teams max out and win 3 events (for a total of 18 wins) there are still 2 wins unaccounted for.
So, it's NOT possible for 6 teams to win at least 1 event.

So, 7 is the MINIMUM number of teams that win at least 1 event.

Cheers,
Brent

BTW, my solution to the original question can be found here: https://www.beatthegmat.com/7-teams-t280641.html
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Sun Apr 26, 2015 9:32 am
Hi royrijit1,

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).

Final Answer: [spoiler]7; E[/spoiler]

GMAT assassins aren't born, they're made,
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Contact Rich at [email protected]
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by DavidG@VeritasPrep » Mon Apr 27, 2015 5:54 am
For a good official max/min question, see here https://www.beatthegmat.com/race-problem-t13987.html
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