what is the least possible score a team could have earned

[Needgmat]

For a certain race 3 tams, were allowed t enter 3 members each. A team earned 6-n points whenever one of its members finished in nth place, where 1< equal n < equal 5. There were no ties, disqualifications, or withdrawals. If no teams 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

OAD

[MartyMurray]

Teams: 3 (A, B, C)

Members Per Team: 3

Total People Involved: 9 (AAA, BBB, CCC)

Scoring Simplified:

1st Place: 6 - 1 = 5 points
2nd Place: 6 - 2 = 4 points
3rd Place: 6 - 3 = 3 points
4th Place: 6 - 4 = 2 points
5th Place: 6 - 5 = 1 point

Have to fill places 1 to 5 with 5 people.

Restriction: No team more than 6 points.

To create the lowest possible score for one team do the following.

- Choose a team to be lowest scoring, C.

- Fill the highest scoring slots with members of other teams, A and B, and fill the lower scoring slots and 0 scoring slots with members of team C.

1 A - 5 points
2 B - 4 points
3 C - 3 points
4 B - 2 points
5 A - 1 point
6 (The rest are all 0. So the order does not matter after 5th place.)
7
8
9

By putting a C in 3rd place, you give C 3 points. That's lower than what you would get were a C in 1st or 2nd. So definitely don't put a C in 1st or 2nd.

If an A is in 1st, then the highest other slot an A can fill is 5th, for a total of 5 + 1 = 6 points.

If a B is in 2nd, then the highest other slot a B can fill is 4th, for a total of 4 + 2 = 6 points.

So C gets 3 + 0 + 0 = 3 points.

The correct answer is D.

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Hi Needgmat,

There's a full discussion of this question here:

https://www.beatthegmat.com/least-possib ... 90755.html

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

We know that there are 1 + 2 + 3 + 4 + 5 => 15 points for the three teams.

We want to MINIMIZE the score for Team A, so let's MAXIMIZE the scores for Teams B and C. Since nobody got above 6 points, we'll say

Team B = 6 points
Team C = 6 points

We know A + B + C = 15, so A = 3.