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ITMC 2018 Grade 11 National Preliminary set01 Question 24

ITMC · ITMC 2018 Grade 11 National Preliminary set01

Question 24

At the 2018 FIFA World Cup, 32 teams were divided into eight groups A, B, C, D, E, F, G and H of four teams each. In the first round each pair of teams in a group played one match. A winner received 3 points and a loser 0; in a draw each team received 1 point. After the first round, the two highest-scoring teams in each group advanced to the second round.

In group C the first-ranked team earns 7 points and the second-ranked team 5. Consider: (1) Their mutual match is a draw. (2) If the second- and third-ranked teams draw, the group total is 15. (3) If the second- and fourth-ranked teams draw, the group total is 16. Which statements are always true?
  1. Only (1) and (2)
  2. Only (1) and (3)
  3. Only (2) and (3)
  4. All three
  5. Fewer than two