The 9 participants in a race were divided into 3 teams with 3 runners

The possible number of points are 5,4,3,2,1. We need to see if these points can be spilt between just 2 of the teams or not

A) To take out the worst case scenario, only 2 teams hogging up all the points we will try and fit these points into 2 teams only. Team A takes 3,2,1. Team B will have to take one of 4 or 5 as both combined is more than 6. Hence it is not possible to fit these scores in only 2 teams. All 3 teams will be needed. Sufficient.

B) It is possible to fit in 3 teams. A: 5,3 . B: 4,2. C: 1
and it is also possible to fit in just 2 teams. A: 5,3,1 B: 4,2
Insufficient

A

chetan2u,
Hello Sir, please help me to understand what is the meaning of 6 – n points. how do you come up that the total points are 15. f there are 3 teams with 3 runners each, then why wont the total point is 9.

Hi,

There are 5 positions that will give points..
If some one comes 1, that is n=1, points are 6-1=5..
some one comes 2nd, the points are 6-2=4 and so on 3, 2, 1..
total points = 5+4+3+2+1=15

Hope it helps

positions: 1_2_3_4_5_6_7_8_9
points (6-n) : 5_4_3_2_1_0_0_0_0

because 1 ≤ n ≤ 5

Statement 1: no team was awarded more than 6 points.
:. points a team could earn 0 ≤ sum of points ≤ 6

Possible combination of points(column wise)
1+5+0.......5+0+0......2+4+0......1+3+0
2+3+0.......4+1+0......1+5+0......4+2+0
4+0+0.......2+3+0......3+0+0......5+0+0

Combinations that will not work:
0+0+0......1+0+0.......1+2+0
1+0+5......2+3+0.......5+0+0
4+3+2......4+5+0.......3+4+0 (all total more than 6 points)

Pretty sure there are more, but I guess the point is there is no way a team could have got 0+0+0 points and the other teams would have 6 or less points. Hence, minimum points a team must have got is 1, given there were no ties.

The 9 participants in a race were divided into 3 teams with 3 runners on each team. A team was awarded 6 – n 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 1 point?

My approach --

We have 3 teams with 3 participants per team:

Team 1: A, B, C
Team 2: D, E, F
Team 3: G, H, I

Each participant receives 6-n points for achieving nth place. For example: 5 points for achieving 1st place.

Was each team awarded at least one point?

(1) No team was awarded more than a total of 6 points.

The 1st 5 people will receive a certain amount of points. (5+4+3+2+1 = 15 points)
If no team was awarded more than 6 points, we can maximize two teams by awarding them each 6 points. We're then left with 3 points, which must go to the 3rd team. SUFFICIENT.

(2) No pair of teammates finished in consecutive places among the top five places.

1ST: Team 1
2ND: Team 2
3RD: Team 1
4TH: Team 2
5TH: Team 1

In this situation, Team 3 did not receive any points.

1ST: Team 1
2ND: Team 2
3RD: Team 3
4TH: Team 1
5TH: Team 2

In this situation each team received at least one point. INSUFFICIENT.

Answer is A.

possible points include 1,2,3,4,5

1) If none got > 6, but with 5 spots and 3 teams, 2 teams must have got 2 each (since more than 2 spots violates max 6 points condition). So 1-5, 2-4 and 3 is the only combination in which the spots could have been distributed, indicating that all teams got at least 1 spot. SUFF

2) let the team mates be ABC, DEF, GHI
It is entirely possible that A -> D -> B -> E -> C (leaving out the third team completely)
Hence INSUFF

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