Data Sufficiency

The participants in a race consisted of 3 teams with 3 runners on each team. A team was awarded 6 - n points if one of its runners finished in nth place, where 1 ≤ n ≤ 5. If all of the runners finished the race and if there were no ties, was each team awarded at least one point?

(1) No team was awarded more than a total of 6 points.

(2) No pair of teammates finished in consecutive places among the top five places.

We know that whoever comes in first place (n=1) will earn 6-1 = 5 points for her team. Whoever comes in second will earn 6-2 = 4 points. And so on, until we get the to fifth place finisher who will earn just 6-5 = 1 point. So there will be 5+4+3+2+1 = 15 points up for grabs.

S1: If there are three teams, and no team earns more than 6 points, then the worst case scenario for one team would be if the other two teams each earned 6 points, leaving 3 points left for the stragglers. If the worst a team can do in this scenario is earn 3 points, clearly each team must be awarded at least one point. Sufficient.

S2: Scenario 1: One team has the first, third and fifth place finishers. And one team has the second and fourth place finishers. The remaining team will not have anyone who finishes in the top five, and therefore will not earn any points, so the answer to the question would be NO.

Scenario 2: One team has the first and third place finishers. And one team has the second and fourth place finishers. The remaining team will have the fifth place finisher, and earn exactly one point. In this case, every team wins at least one point, and the answer to the question is YES. Because we can get a NO or a YES, this statement alone is not sufficient.

Answer is A

Incidentally, a very similar problem has appeared as a problem solving question: https://www.beatthegmat.com/race-problem-t8444.html