Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A…
Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point. Which of the following statements is/are correct?
I. The result of the match between P and Q is a draw with the score 0 - 0.
II. The number of goals scored by R against Q is 1.
Which of the statements given above is/are correct?
I only
II only
Both I and II
Neither I nor II
Solution
Three teams play 3 matches; total points distributed = 3+2+1 = 6, consistent with each match giving 2 points. P has 3 points (one win + one draw), Q has 2 (one win), R has 1 (one draw). Each team scored exactly one goal. Working out the results, the P-Q match must be a 0-0 draw and R's single goal was scored in its match against Q. Both statements are correct.