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 the 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
d) 4

the correct answer is D.
this is how i got this answer......
since there are 3 teams, each team would come in either first, second or third. the team that comes in third will be the one with the least points.. the points would equal 6 - 3 for this team, which is 3.

is this the correct rationale?

I am not sure I understood what you did. Here is what I did

9 members in race. no points for standing 6th-9th positions in race.

That means 5 points for first place and 1 point for 5th place

5,4,3,2,1 respectively.

To minimize the number of points for one team max others. no team scored more than 6. 5+1 and 4+2 max two teams score. 3 is left out, the min other team could score.

the main takeaway here is the same as the main takeaway from the "voltage readings" problem, also posted by you today:

TAKEAWAY:

when you have numbers with a fixed sum or product:

if you want to MINIMIZE A QUANTITY, then you must MAXIMIZE ALL OTHER QUANTITIES in the sum or product.

if you want to MAXIMIZE A QUANTITY, then you must MINIMIZE ALL OTHER QUANTITIES in the sum or product.

--

in this problem:

as the above poster has mentioned, the given description of the point system is cryptic, but you should decode it:
the numbers of points awarded are 5, 4, 3, 2, and 1.

therefore, there is a TOTAL OF 15 POINTS.

we want to MINIMIZE the number of points awarded to any one team.

according to the above takeaway, this means that we should MAXIMIZE the number of points awarded to the OTHER teams.

per the restrictions given, the other teams can receive a maximum of 6 points apiece, so, 15 - 6 - 6 = 3.

(you should probably verify that this is indeed possible, as the above poster has done.)