83 The participants in a race consisted of 3 teams with 3 : DS Archive
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# 83 The participants in a race consisted of 3 teams with 3

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83 The participants in a race consisted of 3 teams with 3 [#permalink]

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24 Jan 2004, 05:48
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83

The participants in a race consisted of 3 teams with 3 runners on each team. A team was awarded 6 тАУ n points if one of its runners finished in nth place, where 1 ≤ n ≤ 5. If all 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.

Could anyone try to solve the above DS problem?
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24 Jan 2004, 06:52
A is sufficient.
Since there are more than 2*6=12 points to be distributed (there are actually 5+4+3+2+1=15 points to be distributed), then each team got at least 1 point

In B, points could be:
team 1: 5+3+1=9
team 2: 4+2+0=6
team 3: 0+0+0=0
Therefore, not all team got at least 1 point
or it could also be:
team 1: 5+1+0=6
team 2: 4+2+0=6
team 3: 3+0+0=3
Therefore, at least 1 team got 1 point
B is inconclusive
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Paul

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24 Jan 2004, 15:51
Absolutely A. as there are 9 participants and only 5 places from (1) we can say but from (2) we cant say. Paul good explanation.
24 Jan 2004, 15:51
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# 83 The participants in a race consisted of 3 teams with 3

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