Question Details

Six players – Tanzi, Umeza, Wangdu, Xyla, Yonita and Zeneca competed in an archery tournament. The tournament had three compulsory rounds, Rounds 1 to 3. In each round every player shot an arrow at a target. Hitting the centre of the target (called bull’s eye) fetched the highest score of 5. The only other possible scores that a player could achieve were 4, 3, 2 and 1. Every bull’s eye score in the first three rounds gave a player one additional chance to shoot in the bonus rounds, Rounds 4 to 6. The possible scores in Rounds 4 to 6 were identical to the first three.

A player’s total score in the tournament was the sum of his/her scores in all rounds played by him/her. The table below presents partial information on points scored by the players after completion of the tournament. In the table, NP means that the player did not participate in that round, while a hyphen means that the player participated in that round and the score information is missing.

The following facts are also known.
1. Tanzi, Umeza and Yonita had the same total score.
2. Total scores for all players, except one, were in multiples of three.
3. The highest total score was one more than double of the lowest total score.
4. The number of players hitting bull’s eye in Round 2 was double of that in Round 3.
5. Tanzi and Zeneca had the same score in Round 1 but different scores in Round 3.

What was the highest total score?

Options

A

24

B

21

C

25

D

23

Show Answer

Correct Answer :

Option C

25

Solution :

The correct option is 3 (25).

Let's analyze the rules and the conditions provided:
The bonus rounds (Rounds 4 to 6) are only played if a player gets a bull's eye (score of 5) in the first three rounds. Each bull's eye gives one extra round. Thus, the number of active rounds for a player is 3 + (number of 5s scored in Rounds 1 to 3).

Analyzing the constraints and solving the matrix of scores for CAT 2019 archery puzzle:
The total score of the players must satisfy the given rules:
- Tanzi, Umeza and Yonita have the same total score.
- Five of the six players have total scores that are multiples of 3, and one player has a score that is not.
- By detailed grid analysis of the archery scoring system, the lowest score is 12 and the highest score is 25 (which is indeed one more than double of 12, since 2 × 12 + 1 = 25).

Therefore, the highest total score in the tournament is 25.

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