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ITMC 2018 Grade 10 National Preliminary set01 Question 24

ITMC · ITMC 2018 Grade 10 National Preliminary set01

Question 24

At the 2018 FIFA World Cup,32 teams were divided into 8 groups A–H of 4 teams. In round 1, each pair in a group plays one match. A winner earns 3 points and a loser 0; each team earns 1 for a draw. The two highest-scoring teams in each group advance to round 2.

After the first round of the 2018 FIFA world cup tournaments ended, the team in first rank of group D got 9 points, the team in second rank got 4 points, and the 4 teams got different points. Consider the following statements.

(1) After the first round of the 2018 FIFA world cup tournaments ended, total points of the 4 teams of group D could be 15, 16, or 17.

(2) If the game of the teams in second and third rank of group D ended a tie, the total points of 4 teams after the first round of the 2018 FIFA world cup tournaments ended is equal to 15.

(3) If the game of the teams in second and forth rank of group D ended a tie, the total points of 4 teams after the first round of the 2018 FIFA world cup tournaments ended is equal to 17.

Which one of the following statements is always true?
  1. Only (1),(2) are true.
  2. Only (1),(3) are true.
  3. Only (2),(3) are true.
  4. All three are true.
  5. Fewer than two statements are true.