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# For a certain race, 3 teams were allowed to enter 3 members

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VP
Joined: 09 Mar 2016
Posts: 1234
For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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25 Sep 2018, 09:34
caiyun wrote:
For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5. There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?

A. 0
B. 1
C. 2
D. 3
E. 4

Here is my approach have no idea if my logic is correct, but i picked D based on the reasoning below

6-2 ---> 4 points but 2nd place

6 -3 ----> 3 points and 3rd place

6-4 ----> 2 points but 4rth place

6-5 ---> 5 points but 1st place

(notice that as the number of points decreases, the team member gets closer to finishline ) though team member finishes the race first, the racer gets 5 points (but question is about the least possible points

since we are asked "what is the least possible score a team could have earned?" It means that one should find a number of points with same the number of same nth place
in other words number of points should be equal to the nth place; THAT implies the racer TRYING TO WIN the race can get what IS LEAST # OF POINTS WITHOUT offsetting his position in the nth place ? did you get me ? YES, YOU!

that's why it is illogical for example to choose 2 points but 4rth place OVER 3 points and 3rd place

Intern
Joined: 20 Aug 2018
Posts: 27
For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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24 Nov 2018, 18:06
A detailed video explanation can be found here:

The person who finishes 1st gets 5 points, the person who finishes 2nd gets 4 points, etc., etc... the 5th place finisher gets 1 point, and no other runner recieves any points.

When you see a math question that asks about minimums, immediately think about maximums, as well (and vice versa).

The total number of poins is 5 + 4 + 3 + 2 + 1 = 15

We're told that the maximum score for one team is 6 points. The minumum score would equal 15 minus the scores of TWO teams that earn a maximum score. The minimum = 15 - 6 - 6 = 3

Its important to check and make sure that two teams can indeed get six points. If you line up 1, 2, 3, 4, 5 you'll see that runners for one team could place 1st and 5th, runners for a second team could place 2nd and 4th, and a third team could get three points by having a runner who places 3rd. Answer D checks out.
_________________
For a certain race, 3 teams were allowed to enter 3 members &nbs [#permalink] 24 Nov 2018, 18:06

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