单选题 The 9 participants in a race were divided into 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 1 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.

A、 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、 Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、 BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、 EACH statement ALONE is sufficient.
E、 Statements (1) and (2) TOGETHER are NOT sufficient.

【正确答案】 A

【答案解析】Determine whether each team was awarded at least 1 point.(1) It is given that no team was awarded more than 6 points. Since there were no ties, one of the nine runners had to have finished in first place. Say this runner was on Team A, and Team A was awarded 5 points. Since Team A was awarded at most 6 points, the best finish for one of the two other runners on Team A could be fifth place, leaving second place to a runner on one of the other teams. Say a runner on Team B finished in second place, and Team B was awarded 4 points. Since Team B was awarded at most 6 points, the best finish for one of the two other runners on Team B could be fourth place, leaving third place to a runner on the only team remaining, which would then be awarded 3 points. Thus, each team was awarded at least 1 point; SUFFICIENT.(2) Given that no pair of teammates finished in consecutive places, it is possible that each team was awarded at least 1 point and it is also possible that at least one team was not awarded at least 1 point. For example, if the three runners on Team A placed first, third, and fifth and two runners on Team B placed second and fourth, then no pair of teammates finished in consecutive places, and Team C was awarded 0 points. On the other hand, if the three runners on Team A placed first, third, and fifth, a runner on Team B placed second, and a runner on Team C placed fourth, then no pair of teammates finished in consecutive places and each team was awarded at least 1 point; NOT sufficient.The correct answer is A; statement 1 alone is sufficient.