Race

[gmat740]

For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5. There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?

A. 0
B. 1
C. 2
D. 3
E. 4


IMO=> minimum points will be when n=Max = 5
so minimum point each earn = 6-n = 6-5 = 1
all three members earn 1+1+1 =3

OA is also 3.

What I think is the Question really that simple or there is something which I am missing out here.

Any opinion will be appreciated.

[ASS1991]

Hey,

if all three team earn 3 points, who got first in the race? Even if each team sends only one participant, there must be a winner, second and third placed. Therefore we have to allocate the points 1 to 5 on three accounts such that the minimum is as high as possible while the maximum stays 6.

Team 1: 5+1=6
Team 2: 4+2=6
Team 3: 3

The least possible score a team can earn is 3.

One other thing to consider, the case that less than 5 players participate is not optimal because in this case, there are not enough small numbers (2 and 1) <- bad explanation, sry about that.

Antoni

[kaulnikhil]

there is only one way u can achieve the condition mentioned in the question ..
let us consider
A1 , A2 ,A3
B1 , B2 , B3
C1, C2 ,C3
are the members ... Remember points of should be less than 6
1st position --- A 1 ---- 5 points as sum of points can only b 6 so A2 can occur at last position
2position -------B1 --- (6-2 = 4 points) since sum is 6 so B2 can occur at last second position
3 position ----- C1 has to occupy therefore points 3
hope u got it

[scoobydooby]

3 members of a team cannot obtain 1 point each (5th position), as there are to be no ties.


to find the minimum possible score of a team, we have to maximize the scores of the two other teams.

max possible score: 6. 9 positions to be taken. positions 6th, 7th, 8th, 9th dont yield points.

let team A get 6 points,
possible with 1st position (6-1= 5points); 5th position (6-5=1point) and another position from 6th to 9th

let team B also get 6 points,
possible with 2nd position (6-2= 4points); 4th position (6-4=2points) and another position from 6th to 9th

at this point, 1st, 2nd, 4th, 5th and 2 positions in 6th-9th have been taken
so team C has to take 3rd position (6-3=3 points) and 2 other remaining positions in 6th-9th yielding no points.

so the least score for any team is 3 points, hence C.