Multiple choice

Passage

Directions: Study the following information and answer the question. Players are selected for Judo based on their body weights from the following 10 weight groups: 1. (48 kg – 52 kg) 6. (68 kg – 72 kg) 2. (52 kg – 56 kg) 7. (72 kg – 76 kg) 3. (56 kg – 60 kg) 8. (76 kg – 80 kg) 4. (60 kg – 64 kg) 9. (80 kg – 84 kg) 5. (64 kg – 68 kg) 10. (84 kg – 88 kg) The average weight of the players after selecting one player from each group is 68 kg. If one of the players (named S) leaves the team, their average weight comes down to 66.5 kg.

If S leaves the group and two new players join the group, their average weight increases to 68 kg. These players can NOT be from groups:

  1. 1 and 3

  2. Both from group 7

  3. 4 and 10

  4. 5 and 9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The initial average of 10 players is 68, so the total weight is 680 kg. When S leaves, the average is 66.5 for 9 players, so the new total is 598.5 kg. Thus, S weighs 680 - 598.5 = 81.5 kg, placing S in group 9. When two new players join, the average returns to 68 for 11 players, meaning the new total is 748 kg. The two new players must weigh 748 - 598.5 = 149.5 kg. Option A (groups 1 and 3) ranges from 48-52 and 56-60, max sum 112 kg, which is too low.

AI explanation

When S leaves, the average weight of the remaining 9 players is 66.5 kg, making their total weight 598.5 kg. If two new players join to bring the average of the 11 players back to 68 kg, their combined weight must be 748 kg minus 598.5 kg, which equals 149.5 kg. Option A specifies groups 1 and 3, where the maximum possible combined weight is the upper limit of group 3 plus the upper limit of group 1 (60 kg plus 52 kg), totaling only 112 kg, making it impossible for them to achieve the required weight.

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