In the Gauss 2004 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 Gauss 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. If one of the competitors had a total of 27 points, what is the maximum number of silver medals she could have won?
(A) 6
(B) 2
(C) 3
(D) 4
(E) 5
We consider each possible number of silver medals starting with 8 .

Could she have won 8 silver medals? This would account for 24 points in 8 events, but since she won 27 points in 8 events, this is not possible.

Could she have won 7 silver medals? This would account for 21 points in 7 events, and so in the remaining 1 event, she would have won 6 points, which is impossible, since she could not score more than 5 points (a gold medal) on this event.

Could she have won 6 silver medals? This would account for 18 points in 6 events, and so in the remaining 2 events, she would have won 9 points, which is impossible, since we cannot combine either two 5 s, two 1 s or a 1 and a 5 to get 9 .

Could she have won 5 silver medals? This would account for 15 points in 5 events, and so in the remaining 3 events, she would have won 12 points, which is impossible. (Try combining up to three $5 \mathrm{~s}$ and $1 \mathrm{~s}$ to get 12 . We need at least two $5 \mathrm{~s}$ and two $1 \mathrm{~s}$ to make 12.)

Could she have won 4 silver medals? This would account for 12 points in 4 events, and so in the remaining 4 events, she would have won 15 points. This is possible - she could win gold on 3 of the 4 remaining events (for 15 points in total) and no medal on the last event (there are 6 competitors and only 3 medals for each event, so there are competitors who do not win medals).

Thus, the maximum number of silver medals she could have won is 4 .

Answer: (D)