Data Sufficiency

23. 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.


Hi,

I thought the answer is E) because there are 3*3=9 runnners in total, so even though no team was awarded more than 6 points, there are possibilities that one team did not get any point..... But the answer is A), so I must have misread the text. Can anyone please explain?

We know that the all runners finished the race and the first 5 of them would have obtained the following points (6-n)

5 for position 1
4 for position 2 and so on
3
2
1

(a) tells us that no team was awarded more than a total of 6 points. To fulfill this condition no team could go without points. There are 15 points in total and this cannot be shared by two teams to fulfil this condition.
Hence sufficient.

(b) This does not help us determine whether all team got points.

Hence the answer would be A.

The possible points for a team could be

51
42
12
31
14
23
There can be total of 15 points

Even if 2 teams gets the maximum i.e. 51 and 42 then the total of 2 teams is 12 and it left 15-12 points for the 3rd team