题目信息
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?
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.
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正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Arithmetic Operations with integers
Determine whether each team was awarded at least 1 point.
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. 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.
Determine whether each team was awarded at least 1 point.
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. 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.
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