Problem Solving

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

There are 3*3 = 9 racers.

For least points all racers of one team should come at 7th, 8th and 9th position.

this team will get 6-n points where n is max of 5

so each member got 1 point Total 3 points

great kajcha. thanks!

I do not think that this is the correct solution to the problem because the assumption which you have taken that for least points the team should score 7,8 and 9 position is wrong.
i think you should solve this problem in following way :

Consider three teams to be A, B and C each having three
members...so totally 9 members.

now suppose that 3 persons of Team A come 1st, 2nd and 3rd
then their respective scores will be (6-1)=5, (6-2)=4 and (6-3)=3.

now suppose that Team B has three memebers who came
4th, 5th and 6th...then their respective scores will be
(6-4)=2, (6-5)=1 and 0 (Because n can max be 5).

the team C is supposed to have scored 7th,8th and 9th
positions scoring 0 each.

Adding all the scores together we get:
5+4+3+2+1+0+0+0+0=15

Now the question says no team can score more than 6.
so see if 15 can be divided as 6 6 and some X
X here is the minimum value which we want to determine
yes it is possible

5 and 1
4 and 2
and therefore third team (15-12)=3
so X=3

therefore the answer is 3
!!!