lheiannie07 wrote:A particular gymnastics tournament awards a gold, a silver, and a bronze medal in each of four events: Floor, Beam, Bars, and Vault. A platinum Best All-Around� medal is awarded to the competitor who gains the most points from winning the other medals: 3 points for gold, 2 points for silver, 1 point for bronze. If McKenzie won the Best All-Around medal, and no one can win more than one medal in any of the four events, did she win at least one gold medal?

(1) All of the gold, silver, and bronze medals were won by fewer than six competitors, including McKenzie
(2) Another competitor in the tournament has 8 points.

Each of the 4 events awards a 3-point medal, a 2-point medal, and 1-point medal, for a total of 6 points per event.
Since there are 4 events, the total number of points awarded = 4*6 = 24.

Question stem, rephrased:
If McKenzie earns the greatest number of points, did she win at least one 3-point medal?

Statement 1:
Case 1: McKenzie wins by earning four 2-point medals -- for a total of 8 points -- with the remaining 16 points divided among 4 other competitors
In this case, McKenzie does NOT earn at least one 3-point medal, so the answer to the question stem is NO.
Case 2: McKenzie wins by earning four 3-point medals -- for a total of 12 points -- with the remaining 12 points divided among 4 other competitors
In this case, McKenzie DOES earn at least one 3-point medal, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statement 2:
Here -- since one of her competitors earns 8 points -- McKenzie must win by earning at least 9 points.
If McKenzie does NOT earn a 3-point medal, then the greatest number of points that she could earn is four 2-point medals, for a total of 8 points.
Implication:
To earn 9 points, must earn at least one 3-point medal.
SUFFICIENT.

The correct answer is B.