[2018] TIME AIMCAT 1905 (20th October to 22nd October)

Hi guys, this is a Q from TIME LRDI Sectional test. Can someone please help and explain the method (4k+x, 8k+x or 16k+x form) used in the solution for determining general form of opponent's seeding if winner is mentioned?

Q. 128 players participated in a knock out tournament with different rounds. Players are seeded from Seed 1 to Seed 128 such that Seed 1 is the top seed while Seed 128 is the last seeded player. Matches are held in such a manner such that in the first round the 1st seeded player plays the last seeded player and so on. If at any point of time, a lower seeded player beats a higher seeded player, that match is defined as an upset. In case of an upset, the player who caused the upset (the lowest seeded player) would take the designated place of the player he upset (the highest seeded player) in the next round.

1. Player ranked 45 won the tournament. With which of the following seeded players, he must have not played in the Semi Finals?

a) Seed 96 b) Seed 97 c) Seed 57 d) Seed 95

Solution: Seed 45 is of the form 8K+5. He would have played with any person whose seeding is of the form 8K or 8K+1. Seed 95 cannot represent any of these 2 forms, hence answer is (D).

2. Player ranked 3 won the tournament. With which of the following seeded players, he must have not played in the Quarter Finals?

a) Seed 102 b) Seed 103 c) Seed 107 d) Seed 91

Solution: Seed 3 is of the form 16K+3. He would have played with any person whose seeding is of the form 16K+6 or 16K+11. Seed 103 cannot represent any of these 2 forms, hence answer is (B). 

(What is the method is determining the general form of opponent's seeding , ie. how has "16k+6" or "16k +11" for Quarter Finals and "8k" and "8k+1" for Semi Finals been arrived at in above question?) 

Thanks in advance!!