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# In the diagram above, points A, B, C, D, and E represent the

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In the diagram above, points A, B, C, D, and E represent the [#permalink]  26 Feb 2006, 09:44
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In the diagram above, points A, B, C, D, and E represent the five teams
in a certain league in which each team must play each of the other teams
exactly once. The segments connecting pairs of points indicate that the
two corresponding teams have already played their game. The arrows on the
segments point to the teams that lost; the lack of an arrow on a segment
indicates that the game ended in a tie. After all games have been played,
which of the following could NOT be the percent of games played that ended in a tie?
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
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Re: PS Help [#permalink]  26 Feb 2006, 09:58
Avis wrote:
In the diagram above, points A, B, C, D, and E represent the five teams
in a certain league in which each team must play each of the other teams
exactly once. The segments connecting pairs of points indicate that the
two corresponding teams have already played their game. The arrows on the
segments point to the teams that lost; the lack of an arrow on a segment
indicates that the game ended in a tie. After all games have been played,
which of the following could NOT be the percent of games played that ended in a tie?
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%

A.

Using the games played thus far, there are 2 games that ended in a tie. So far 7 games have been played and the games between between BE, BD and CE have not been played yet.
Total number of games that can be played are 10 (7+3 new games). So far there are 2 ties. Hence, 2/10=20% tie. As each of the new games (BD, BE and CE) are played it could result in a tie. So 3/10=30%, 4/10=40% and 5/10=50%.
Re: PS Help   [#permalink] 26 Feb 2006, 09:58
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