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race with 3 teams

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race with 3 teams

by sairamGmat » Tue Jul 27, 2010 5:12 am
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


OA is A. Can any one say how it is OA?
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by nicolezl » Tue Jul 27, 2010 5:43 am
Let's see if I can explain this....

OK, let's call the teams A, B, and C.

(1) If one of the members of team A comes in first place, they get (6-1), or 5, points. The only other top 5 place they could come in is 5th, since no team can have more than 6 points.

Then if B comes in second, they get 4 points, so they can only come in 4th as well to get a total of 6 points.

A member of a team C must therefore come in 3rd, and each team gets at least one point.

Or another way to think about it: The most top 5 places a team can get is 3 (3rd, 4th, and 5th), which gives them 6 points. And since one of the other teams can't get first and second, they each get one of the top 2 places.

Suff.

(2) The top 5 in order could be, for example:

A, B, A, B, A (they don't each get at least one point, since C didn't make the top 5)
A, B, C, A, B (they each get at least one point)

Insuff.

So the answer is A
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by firatb » Wed Jul 28, 2010 11:52 am
sairamGmat wrote: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


OA is A. Can any one say how it is OA?
Statement 1: Total number of points to be delivered is 5*(5+1)/2=15
Since no team gets more than 6 points, Even the most unsuccessful team gets at least 3 points.

Sufficent

Statement 2: This is pretty obvious. There might be many different orders in which a particular team might or might not be in the top 5.
ex: A-B-A-B-A
B-A-B-A-B
A-B-A-C-B

Insufficient
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by GMATGuruNY » Wed Jul 28, 2010 1:01 pm
sairamGmat wrote: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


OA is A. Can any one say how it is OA?
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
Total = 5+4+3+2+1 = 15 points.

Statement 1:
Max for 2 teams = 2*6=12.
So 3rd team must get 15 - 12= 3 points.
So every team gets at least 1 point. Sufficient.

Statement 2:
Team A could be 1st, 3rd, 5th
Team B could be 2nd, 4th.
Only 2 teams get at least one point.

Team A could be 1st, 3rd, 5th.
Team B could be 2nd.
Team C could be 4th.
All 3 teams get at least 1 point.

Insufficient.

The correct answer is A.
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