| Round-1 | Round-2 | Round-3 | Round-4 | Round-5 | Round-6 | |
| Tanzi | - | 4 | - | 5 | NP | NP |
| Umeza | - | - | - | 1 | 2 | NP |
| Wangdu | - | 4 | - | NP | NP | NP |
| Xyla | - | - | - | 1 | 5 | - |
| Yonita | - | - | 3 | 5 | NP | NP |
| Zeneca | - | - | - | 5 | 5 | NP |
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?
- 24
- 21
- 25
- 23
The Correct Option is C
Solution and Explanation
Tanzi participated in another round, implying a score of 5 in either Round 1 or Round 3. If Tanzi scored x in the other round, the total score for Tanzi would be 14 + x. Umeza played Round 4 and Round 5, indicating a score of 5 in two of the first three rounds. In the remaining round, let Umeza's score be y, making Umeza's total score 13 + y. Since only one person had a total score not divisible by 3, and Tanzi, Umeza, and Yonita had identical total scores, both 14 + x and 13 + y must be multiples of 3. For 14 + x to be a multiple of 3, x must equal 1 or 4, resulting in a total score of 15 or 18. For 13 + y to be a multiple of 3, y must equal 2 or 5. However, if y equals 5, Umeza would have played Round 6, which did not occur. Therefore, y equals 2, and x equals 1. The total score for Umeza, Tanzi, and Yonita is 15.
Wangdu's maximum score, without playing any rounds after Round 3, is 12 when scoring 4 in both Round 1 and Round 3. Since Xyla played all rounds, her minimum total score is 22, considering a score of 1 in Round 6.
Zeneca played Round 4 and Round 5, scoring 5 in two of the first three rounds. Zeneca's minimum and maximum total scores are 21 and 24, respectively. Consequently, Wangdu had the lowest score.
If Wangdu scored 12, the highest score would be 25, achievable only by Xyla (5 in the first three rounds and 4 in Round 6). If Wangdu scored 11, the highest score would be 23, but this is not possible because two total scores would not be multiples of 3. If Wangdu scored 10, the highest score would be 21, contradicting Xyla's minimum score of 22. Any score for Wangdu less than 10 would result in the highest score being less than 20, which conflicts with Xyla's minimum score of 22. Therefore, Wangdu scored 12, and Xyla scored 25, implying Wangdu scored 4 in both Round 1 and Round 3, and Xyla scored 4 in Round 6. Xyla's total score is not a multiple of 3; hence, Zeneca's total score must be a multiple of 3, specifically 21 or 24.
Tanzi and Zeneca scored the same in Round 1. If Tanzi's score in Round 1 is 1, then Zeneca's score in Round 1 would also be 1. However, in this case, both Zeneca and Tanzi would have scored 5 in Round 3, contradicting the information that their scores in Round 3 are different. Therefore, Tanzi scored 5 in Round 1 and 1 in Round 3. The number of players hitting bullseye in Round 2 is either 2 or 4. If it is 2, the total number of 5s in Round 2 and Round 3 combined should be 3. Two of those 5s were scored by Xyla. Umeza and Zeneca would each have scored at least one 5 in Rounds 2 and 3 combined, but this would result in at least 4 total 5s, which is not possible. Therefore, the number of players hitting bullseye in Round 2 is 4. Since Tanzi and Wangdu scored 4 in Round 2, all other players hit bullseye in Round 2. This implies that the number of players hitting bullseye in Round 3 is 2, with Xyla being one of them and the other being either Umeza or Zeneca. However, if Zeneca had scored 5 in Round 3, Zeneca would have played Round 6, which did not happen. Therefore, Umeza is the other person who scored 5 in Round 3. Since Umeza's total score is 15, Umeza scored 2 in Round 1. Yonita's total score is also 15, indicating Yonita scored 2 in Round 1. Zeneca's total score cannot be 21 because, in that case, both Zeneca and Tanzi would have scored the same in Round 3, but they had different scores. Therefore, Zeneca scored 4 in Round 3.
| Round 1 | Round 2 | Round 3 | Round 4 | Round 5 | Round 6 | Total | |
| Tanzi | 5 | 4 | 1 | 5 | NP | NP | 15 |
| Umeza | 2 | 5 | 5 | 1 | 2 | NP | 15 |
| Wangdu | 4 | 4 | 4 | NP | NP | NP | 12 |
| Xyla | 5 | 5 | 5 | 1 | 5 | 4 | 25 |
| Yonita | 2 | 5 | 3 | 5 | NP | NP | 15 |
| Zeneca | 5 | 5 | 4 | 5 | 5 | NP | 24 |
The highest total score was 25.
What was Zeneca's total score?
- 22
- 23
- 21
- 24
The Correct Option is D
Solution and Explanation
Tanzi participated in another round, implying a score of 5 in either Round 1 or Round 3. If Tanzi scored x in the other round, the total score for Tanzi would be 14 + x. Umeza played Round 4 and Round 5, indicating a score of 5 in two of the first three rounds. In the remaining round, let Umeza's score be y, making Umeza's total score 13 + y. Since only one person had a total score not divisible by 3, and Tanzi, Umeza, and Yonita had identical total scores, both 14 + x and 13 + y must be multiples of 3. For 14 + x to be a multiple of 3, x must equal 1 or 4, resulting in a total score of 15 or 18. For 13 + y to be a multiple of 3, y must equal 2 or 5. However, if y equals 5, Umeza would have played Round 6, which did not occur. Therefore, y equals 2, and x equals 1. The total score for Umeza, Tanzi, and Yonita is 15.
Wangdu's maximum score, without playing any rounds after Round 3, is 12 when scoring 4 in both Round 1 and Round 3. Since Xyla played all rounds, her minimum total score is 22, considering a score of 1 in Round 6.
Zeneca played Round 4 and Round 5, scoring 5 in two of the first three rounds. Zeneca's minimum and maximum total scores are 21 and 24, respectively. Consequently, Wangdu had the lowest score.
If Wangdu scored 12, the highest score would be 25, achievable only by Xyla (5 in the first three rounds and 4 in Round 6). If Wangdu scored 11, the highest score would be 23, but this is not possible because two total scores would not be multiples of 3. If Wangdu scored 10, the highest score would be 21, contradicting Xyla's minimum score of 22. Any score for Wangdu less than 10 would result in the highest score being less than 20, which conflicts with Xyla's minimum score of 22. Therefore, Wangdu scored 12, and Xyla scored 25, implying Wangdu scored 4 in both Round 1 and Round 3, and Xyla scored 4 in Round 6. Xyla's total score is not a multiple of 3; hence, Zeneca's total score must be a multiple of 3, specifically 21 or 24.
Tanzi and Zeneca scored the same in Round 1. If Tanzi's score in Round 1 is 1, then Zeneca's score in Round 1 would also be 1. However, in this case, both Zeneca and Tanzi would have scored 5 in Round 3, contradicting the information that their scores in Round 3 are different. Therefore, Tanzi scored 5 in Round 1 and 1 in Round 3. The number of players hitting bullseye in Round 2 is either 2 or 4. If it is 2, the total number of 5s in Round 2 and Round 3 combined should be 3. Two of those 5s were scored by Xyla. Umeza and Zeneca would each have scored at least one 5 in Rounds 2 and 3 combined, but this would result in at least 4 total 5s, which is not possible. Therefore, the number of players hitting bullseye in Round 2 is 4. Since Tanzi and Wangdu scored 4 in Round 2, all other players hit bullseye in Round 2. This implies that the number of players hitting bullseye in Round 3 is 2, with Xyla being one of them and the other being either Umeza or Zeneca. However, if Zeneca had scored 5 in Round 3, Zeneca would have played Round 6, which did not happen. Therefore, Umeza is the other person who scored 5 in Round 3. Since Umeza's total score is 15, Umeza scored 2 in Round 1. Yonita's total score is also 15, indicating Yonita scored 2 in Round 1. Zeneca's total score cannot be 21 because, in that case, both Zeneca and Tanzi would have scored the same in Round 3, but they had different scores. Therefore, Zeneca scored 4 in Round 3.
| Round 1 | Round 2 | Round 3 | Round 4 | Round 5 | Round 6 | Total | |
| Tanzi | 5 | 4 | 1 | 5 | NP | NP | 15 |
| Umeza | 2 | 5 | 5 | 1 | 2 | NP | 15 |
| Wangdu | 4 | 4 | 4 | NP | NP | NP | 12 |
| Xyla | 5 | 5 | 5 | 1 | 5 | 4 | 25 |
| Yonita | 2 | 5 | 3 | 5 | NP | NP | 15 |
| Zeneca | 5 | 5 | 4 | 5 | 5 | NP | 24 |
Zeneca's total score was 24.
Which of the following statements is true?
- Zeneca’s score was 23.
- Xyla was the highest scorer.
- Zeneca was the highest scorer.
- Xyla’s score was 23.
The Correct Option is B
Solution and Explanation
Tanzi participated in another round, implying a score of 5 in either Round 1 or Round 3. If Tanzi scored x in the other round, the total score for Tanzi would be 14 + x. Umeza played Round 4 and Round 5, indicating a score of 5 in two of the first three rounds. In the remaining round, let Umeza's score be y, making Umeza's total score 13 + y. Since only one person had a total score not divisible by 3, and Tanzi, Umeza, and Yonita had identical total scores, both 14 + x and 13 + y must be multiples of 3. For 14 + x to be a multiple of 3, x must equal 1 or 4, resulting in a total score of 15 or 18. For 13 + y to be a multiple of 3, y must equal 2 or 5. However, if y equals 5, Umeza would have played Round 6, which did not occur. Therefore, y equals 2, and x equals 1. The total score for Umeza, Tanzi, and Yonita is 15.
Wangdu's maximum score, without playing any rounds after Round 3, is 12 when scoring 4 in both Round 1 and Round 3. Since Xyla played all rounds, her minimum total score is 22, considering a score of 1 in Round 6.
Zeneca played Round 4 and Round 5, scoring 5 in two of the first three rounds. Zeneca's minimum and maximum total scores are 21 and 24, respectively. Consequently, Wangdu had the lowest score.
If Wangdu scored 12, the highest score would be 25, achievable only by Xyla (5 in the first three rounds and 4 in Round 6). If Wangdu scored 11, the highest score would be 23, but this is not possible because two total scores would not be multiples of 3. If Wangdu scored 10, the highest score would be 21, contradicting Xyla's minimum score of 22. Any score for Wangdu less than 10 would result in the highest score being less than 20, which conflicts with Xyla's minimum score of 22. Therefore, Wangdu scored 12, and Xyla scored 25, implying Wangdu scored 4 in both Round 1 and Round 3, and Xyla scored 4 in Round 6. Xyla's total score is not a multiple of 3; hence, Zeneca's total score must be a multiple of 3, specifically 21 or 24.
Tanzi and Zeneca scored the same in Round 1. If Tanzi's score in Round 1 is 1, then Zeneca's score in Round 1 would also be 1. However, in this case, both Zeneca and Tanzi would have scored 5 in Round 3, contradicting the information that their scores in Round 3 are different. Therefore, Tanzi scored 5 in Round 1 and 1 in Round 3. The number of players hitting bullseye in Round 2 is either 2 or 4. If it is 2, the total number of 5s in Round 2 and Round 3 combined should be 3. Two of those 5s were scored by Xyla. Umeza and Zeneca would each have scored at least one 5 in Rounds 2 and 3 combined, but this would result in at least 4 total 5s, which is not possible. Therefore, the number of players hitting bullseye in Round 2 is 4. Since Tanzi and Wangdu scored 4 in Round 2, all other players hit bullseye in Round 2. This implies that the number of players hitting bullseye in Round 3 is 2, with Xyla being one of them and the other being either Umeza or Zeneca. However, if Zeneca had scored 5 in Round 3, Zeneca would have played Round 6, which did not happen. Therefore, Umeza is the other person who scored 5 in Round 3. Since Umeza's total score is 15, Umeza scored 2 in Round 1. Yonita's total score is also 15, indicating Yonita scored 2 in Round 1. Zeneca's total score cannot be 21 because, in that case, both Zeneca and Tanzi would have scored the same in Round 3, but they had different scores. Therefore, Zeneca scored 4 in Round 3.
| Round 1 | Round 2 | Round 3 | Round 4 | Round 5 | Round 6 | Total | |
| Tanzi | 5 | 4 | 1 | 5 | NP | NP | 15 |
| Umeza | 2 | 5 | 5 | 1 | 2 | NP | 15 |
| Wangdu | 4 | 4 | 4 | NP | NP | NP | 12 |
| Xyla | 5 | 5 | 5 | 1 | 5 | 4 | 25 |
| Yonita | 2 | 5 | 3 | 5 | NP | NP | 15 |
| Zeneca | 5 | 5 | 4 | 5 | 5 | NP | 24 |
The statement, “Xyla was the highest scorer”, is true.
What was Tanzi's score in Round 3?
- 4
- 3
- 1
- 5
The Correct Option is C
Solution and Explanation
Tanzi participated in another round, implying a score of 5 in either Round 1 or Round 3. If Tanzi scored x in the other round, the total score for Tanzi would be 14 + x. Umeza played Round 4 and Round 5, indicating a score of 5 in two of the first three rounds. In the remaining round, let Umeza's score be y, making Umeza's total score 13 + y. Since only one person had a total score not divisible by 3, and Tanzi, Umeza, and Yonita had identical total scores, both 14 + x and 13 + y must be multiples of 3. For 14 + x to be a multiple of 3, x must equal 1 or 4, resulting in a total score of 15 or 18. For 13 + y to be a multiple of 3, y must equal 2 or 5. However, if y equals 5, Umeza would have played Round 6, which did not occur. Therefore, y equals 2, and x equals 1. The total score for Umeza, Tanzi, and Yonita is 15.
Wangdu's maximum score, without playing any rounds after Round 3, is 12 when scoring 4 in both Round 1 and Round 3. Since Xyla played all rounds, her minimum total score is 22, considering a score of 1 in Round 6.
Zeneca played Round 4 and Round 5, scoring 5 in two of the first three rounds. Zeneca's minimum and maximum total scores are 21 and 24, respectively. Consequently, Wangdu had the lowest score.
If Wangdu scored 12, the highest score would be 25, achievable only by Xyla (5 in the first three rounds and 4 in Round 6). If Wangdu scored 11, the highest score would be 23, but this is not possible because two total scores would not be multiples of 3. If Wangdu scored 10, the highest score would be 21, contradicting Xyla's minimum score of 22. Any score for Wangdu less than 10 would result in the highest score being less than 20, which conflicts with Xyla's minimum score of 22. Therefore, Wangdu scored 12, and Xyla scored 25, implying Wangdu scored 4 in both Round 1 and Round 3, and Xyla scored 4 in Round 6. Xyla's total score is not a multiple of 3; hence, Zeneca's total score must be a multiple of 3, specifically 21 or 24.
Tanzi and Zeneca scored the same in Round 1. If Tanzi's score in Round 1 is 1, then Zeneca's score in Round 1 would also be 1. However, in this case, both Zeneca and Tanzi would have scored 5 in Round 3, contradicting the information that their scores in Round 3 are different. Therefore, Tanzi scored 5 in Round 1 and 1 in Round 3. The number of players hitting bullseye in Round 2 is either 2 or 4. If it is 2, the total number of 5s in Round 2 and Round 3 combined should be 3. Two of those 5s were scored by Xyla. Umeza and Zeneca would each have scored at least one 5 in Rounds 2 and 3 combined, but this would result in at least 4 total 5s, which is not possible. Therefore, the number of players hitting bullseye in Round 2 is 4. Since Tanzi and Wangdu scored 4 in Round 2, all other players hit bullseye in Round 2. This implies that the number of players hitting bullseye in Round 3 is 2, with Xyla being one of them and the other being either Umeza or Zeneca. However, if Zeneca had scored 5 in Round 3, Zeneca would have played Round 6, which did not happen. Therefore, Umeza is the other person who scored 5 in Round 3. Since Umeza's total score is 15, Umeza scored 2 in Round 1. Yonita's total score is also 15, indicating Yonita scored 2 in Round 1. Zeneca's total score cannot be 21 because, in that case, both Zeneca and Tanzi would have scored the same in Round 3, but they had different scores. Therefore, Zeneca scored 4 in Round 3.
| Round 1 | Round 2 | Round 3 | Round 4 | Round 5 | Round 6 | Total | |
| Tanzi | 5 | 4 | 1 | 5 | NP | NP | 15 |
| Umeza | 2 | 5 | 5 | 1 | 2 | NP | 15 |
| Wangdu | 4 | 4 | 4 | NP | NP | NP | 12 |
| Xyla | 5 | 5 | 5 | 1 | 5 | 4 | 25 |
| Yonita | 2 | 5 | 3 | 5 | NP | NP | 15 |
| Zeneca | 5 | 5 | 4 | 5 | 5 | NP | 24 |
Tanzi’s score in Round 3 was 1
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