For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n points whenever one of its members

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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


OA D

Source: GMAT Prep

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BTGmoderatorDC wrote:
Thu Nov 11, 2021 2:17 am
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


OA D

Source: GMAT Prep
Let's order the results in a table:

\begin{array}{|c|c|c|c|}
\hline
\text{Team} & \text{Member} & \text{Position} & \text{Score} \\ \hline
& \text{a} & 1 & 5 \\
1 & \text{b} & 5 & 1 \\
& \text{c} & 6 & 0 \\ \hline
& \text{d} & 2 & 4 \\
2 & \text{e} & 4 & 2 \\
& \text{f} & 7 & 0 \\ \hline
& \text{g} & 3 & 3 \\
3 & \text{h} & 8 & 0 \\
& \text{i} & 9 & 0 \\ \hline
\end{array}

So, the least score is \(3\) D