In the Houston Math Olympics, there are six competitors and eight events. The top three competitors in each event receive gold, silver and bronze medals respectively. (There are no ties at the Houston Math Olympics, and no competitor can win more than one medal on the same event.) Each competitor scores 5 points for each gold medal, 3 points for each silver medal, and 1 point for each bronze medal. In 2008, if one of the competitors had a total of 27 points, what is the maximum number of silver medals she could have won?

A. 4 B. 3 C. 2 D. 6

Based on the number of points that the competitor had in total and the number of games available as well as the points per game, the maximum number of silver medals she could have won is A. 4.

How many silver medals could the competitor have won?

The number of silver medals that the competitor could have won should be such that when the points from those silver medals are added up to the points from any other medals, the points can add up to 27 points exactly.

Assuming the competitor won 4 silver medals then the total points for silver are:

= 3 x 4

= 12 points

The number of points left are:

= 27 - 12

= 15 points

Are there 4 other medals (4 games left) where she could have won a total of 15 points?

Yes there are.

She could have won 3 gold medals, and no medal on one event. This would give a total point tally of:
= (5 x 3 golds) + (4 x 3 silvers) + (0 x 1 event)

= 27 points

The maximum the competitor could have gotten is therefore 4 silver medals.

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