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least possible score a team could have erarned

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by enriqueta26 » Sat Jul 17, 2010 10:17 am
Could someone explain this problem, please?

For a certain race, 03 teams were allowed to enter 03 member each. A team earned 6*n points whenever one of its members finished in n th place. We have: 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?
Source : gmat practice exam

[spoiler]A:31[/spoiler]
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by Patrick_GMATFix » Sat Jul 17, 2010 10:28 am
Hi Enriqueta,

As a general rule, if you are asked to find the 'least' that a value can be, maximize all the other values. Conversely, if you're trying to find the 'most' that a value can be, minimize all the other values.

In this case, to find the least possible score that a team could have earned, maximize the other teams' scores. In this case, we're told that the max for any team is 6 points. So the question can simply be restated as "if team A and team B earn 6 points each, what will be team C's score?"

To represent this clearly, a table would work. Essentially team A can earn 5 (1st place finish) and 1 (5th place). Team B can earn 4 (2nd place finish) and 2 (4th place). Therefore team C will have a member finish 3rd place and earn 3 points. The other team C member will finish last and earn no point.

The least possible score for a team is 3 points. The answer is D.

An illustration (table) and a video solution are available at GMATPrep Question 1580. To practice similar questions, set topic='Functions & Sequences' and difficulty='500-600' in the Drill Engine.

Hope this helps,
-Patrick

This question is also discussed at https://www.beatthegmat.com/for-a-certai ... 59866.html
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