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# The participants in a race consisted of 3 teams with 3

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Senior Manager
Joined: 01 Jan 2007
Posts: 322
The participants in a race consisted of 3 teams with 3 [#permalink]

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25 Apr 2007, 07:02
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The participants in a race consisted of 3 teams with 3 runners on each team. A team was awarded 6 тАУn points if one of its runners finished in nth place, where 1  n  5. If all of the runners finished the race and if there were no ties, was each team awarded at least one point?
(1) No team was awarded more than a total of 6 points.
(2) No pair of teammates finished in consecutive places among the top five places.

Javed.

Cheers!
Intern
Joined: 24 Apr 2007
Posts: 9

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25 Apr 2007, 12:04
javed wrote:
The participants in a race consisted of 3 teams with 3 runners on each team. A team was awarded 6 тАУn points if one of its runners finished in nth place, where 1  n  5. If all of the runners finished the race and if there were no ties, was each team awarded at least one point?
(1) No team was awarded more than a total of 6 points.
(2) No pair of teammates finished in consecutive places among the top five places.

Javed.

Cheers!

1st place gets 5 points
2nd place gets 4 points
3rd place gets 3 points
4th place gets 2 points
5th place gets 1 points

Since each place can only have one person, and no team can have more than 6 points, lets suppose team 1 maxes out with 1st place and 5th place for 6 points, and team 2 maxes out with 2nd place and 4th place for 6 points, that leaves team 3 with 3rd place. No combination is possible where a team has zero points. First data is sufficient.

Second data is insufficient because you can have the same arrangement as the first example, or you can have 1st,3rd, 5th in one team, and 2nd, 4th, in the second team. That leaves the remaining team with no points, but this doesn't violate any scenario. So data 2 is insufficient.
Current Student
Joined: 22 Apr 2007
Posts: 1097

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25 Apr 2007, 12:22
A

Second statement is insuff because two teams can take the 1,3,5 and 2,4 places or all three teams can share the points.

First statement is suff because if no team scored more than 6 points, then each team needs to be on the point-table. The reason is that the first three runners are going to get 5,4 and 3 points. None of these can be from the same team (Since their sum will be greater than 6). So, these three have to be from different teams.
Senior Manager
Joined: 11 Feb 2007
Posts: 351

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26 Apr 2007, 19:19
Another A here.

(1) Team 1: 5+1 = 6
Team 2: 4+2 = 6
Team 3: 3
SUFF.

(2) Since each team has 3 runners, 3 runners from team 1 can place 1,3,5th place and 2 from team 2 place 2 and 4th. No one from team 3 places. Or, the three teams can each have at least one runner in the 5 places.
INSUFF.
26 Apr 2007, 19:19
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