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Games and Tournament                                                                                281
            Lets sum up the information,                         32.  (b)
            The teams who played semifinal round is B, F, G and H  33.  (b) Number of matches in stage 1 is 2(7 × 8/2) = 56,
            Given that F lost both the matches to G i.e F and G is in   at semifinal stage we have 3 matches (2 semifinal
                                                                                      rd
            the same group, then B and H is in the same group.        and 1 match for 3  place) and 1 final match, hence
            Since number of matches won by A and G is same hence      total number of matches is 56 + 3 + 1 = 60
            they must belong to two different groups, and C won only   34.  (a) Seed 9 will play with seed, 1, 3, 5, 7, 11, 13, and
            I match against D hence they must be in the same group.   15 without an upset seed 9 can win with seed 11,
            So we can divide the group now-                           13, and 15, for minimum number of upset let seed 1
            Group 1: F, G, C, D                                       won all the matches and seed 9 won against seed 3
                                                                      and 5, in that case number of wins of seed 3 and 9 is
            Group 2: B, H, A, E                                       5 but with tie breaker rule seed 9 will advance to the
            In one group number of matches is 2(3 × 4/2) = 12 since   next stage.
            each team won a different number of matches and total   35.  (d) Total number of matches is 60 and out of those
            number of matches is 12 so we have following possibilities   more than 45 matches are upset. But seed 1 need
            for number of matches won by 4 teams-                     only 9 matches to win the tournament hence seed 1
            Case (i) 6, 4, 2, 0                                       may win the tournament.
            Case (ii) 6, 3, 2, 1                                 36.  (b) Total number of matches in the 1st stage is 4 × 7

            Case (iii) 5, 4, 2, 1                                     = 28, lets consider group 1 here if seed 1 won all the
            Case (iv) 5, 4, 3, 0                                      matches then remaining 21 matches or points can be
            Since number of matches won by A and G is the same but    equally distributed to 7 player (3 points each) and
            then also A eliminated so only possibility is case (ii) and   the lowest possible player  would  advance  to next
            (iv) and they won 3 matches.                              stage with tie breaker rule. In this stage seed 13 can
                                                                      get 3 points after 2 upsets caused by him. So from
            Lets sum up the conclusion till now                       this group seed 1 and 13 would advance to the next
            Group 1: F, G, C, D and their points F = 6, G = 3, C =    stage. Similarly from 2  group seed 2 and 14 would
                                                                                          nd
            1 and D = 2                                               advance to the next stage.
            Group 2:  B, H, A, E and their points B and H 5 and 4 in      Now as per the rule seed 1 will play with seed 14 and
            any order and A = 3, E = 0                                seed 2 will play with seed 13,
            Now lets draw the table for Group 1                       If seed 13 and 4 meet in the tournament then seed
                         F      G       C      D                      13 will win with 3 upset.
                  F     X      W W    W W     W W      6         37.  (a) Here only problem is stage 1, so a player has to
                 G      LL      X      WW      WL      3              qualify for semifinal without any upset. In previous
                                                                      question we have seen that with 3 points/win a team
                  C     LL      LL      X      WL      1              can advanced to next stage.
                 D      LL     LW      LW      X       2
                                                                      Consider group 1: Here players are seeded 1, 3,
            Now lets draw the table for Group 2                       5, 15. The player who can win 3 matches without an

                       B/H     H/B      A      E                      upset is seed 9.
                B/H     X      WW      LW     WW       5              Consider  group  2:  same as previous case  seed
                H/B     LL      X      WW     WW       4              10 can advanced to next stage without causing an
                  A     WL      LL      X     WW       3              upset.
                  E     LL      LL     LL      X       0              So seed 10 is the answer.
                                                                      Consider 1 such case semifinal round Group 1: seed
            28.  (a) option (a) is correct                            13 and 15
                     nd
            29.  (d) 2  Highest is either B or H so cant determine.
                                                                      Group 2: seed 2 and 10
            30.  (c) E lost the maximum number of matches.            Final match: seed 10 and 15
            31.  (d) A lost both the matches to B or H not B and H
            hence option C is incorrect.
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