Question

The weight of 6 players in a volleyball team are all different and the average weight is 60 kilograms.

i. Prove that the team has at least one player weighing more than 60 kilograms.

ii. Prove that the team has at least one player weighing less than 60 kilograms.

Answer 1

i. Total weight of 6 players = 60 × 6 = 360 kg 

The team contains players having weights 60, less than 60 or greater than 60. If the weights of all the players are less than 60, the average will also be less than 60. This is not possible. Therefore there will be at least one player having weight greater than 60.

ii. If the weight of all the players are greater than 60, the average will also be greater than 60. Therefore there will be at least one player having weight less than 60.