Aims Grade 8 Mathematics Sample Test And Think-Throughs With Answers Page 30
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36December 2009
The directed graph shows the results of a chess tournament among 4 players. Edgar won
29
his match against Frankie.
Belen
Frankie
Edgar
Ray
Who won the least number of games?
Frankie
A
Belen
B
Ray
C
Edgar
D
This problem is about a tournament. I need to find out who won the least number of games, or in
other words, who won last place.
What do the arrows mean? When I look at the diagram and read the problem again, it says that
Edgar won his match against Frankie.
Frankie
Belen
When I look at only those arrows, if
Edgar won his match against Frankie,
that would mean that the arrow is
pointing to the person who did not win
the match.
Edgar
Ray
So, if I am supposed to figure out who
won the least number of games, that means I should look for the person with the most arrows
pointing toward him.
• Since Edgar has no arrows pointing toward him, he won all three of his games.
• Ray has two arrows pointing toward him, so he lost two games and won one game.
• Belen has one arrow pointing toward her, so she lost one game and won two games.
• Frankie has three arrows pointing toward him, so he lost all three games he played.
In other words, Frankie won last place, or won the least amount of games (none). This makes the
answer choice A.
Arizona Department of Education
30
Grade 8
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