Problem Solving

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%

The no of games that can be played where each team actually plays the other once= 5c2=10

now the figure shows 7 such games with their results.

now 2 of the 7 matches have ended in a draw

there are 3 other remaining matches
E vs B
D vs B
E vs C

if all of these end in a tie=> total no of tied matches=5
% of tied matches=50%(possible)
if only 2 end in a tie=> 40%
if only 1 ends in a tie= 30%
if none ends in a tie than tie %= 2/10*100=20%

thus clearly 10% cannot be a answer in any case