Question

What best can be concluded about the number of players coached by Zara?

• A. Exactly 3
• B. Exactly 2
• C. Either 2 or 3
• D. Either 2 or 3 or 4
• A. Player-1, Player-3, Player-4, Player-8
• B. Player-1, Player-3, Player-4
• C. Player-1, Player-3, Player-4, Player-6
• D. Player-1, Player-4, Player-6, Player-8

Answer 1

The Correct Option is B

Let’s break down the problem step-by-step:

1. Yuki trained only even-numbered players. Yuki trains the players 2, 4, 6, and 8, total-
ing 4 players.

2. Xena trained more players than Yuki. Since Yuki trains 4 players, Xena must train at
least 5 players.
3. Zara trained only odd-numbered players. Zara trains the players 1, 3, 5, and 7.
4. The number of players trained by Xena, Yuki, and Zara. We know that:

• Yuki trains 4 players (Players 2, 4, 6, 8).
• Xena must train more players than Yuki. Therefore, Xena must train at least 5 play-
  ers.
• Zara trains exactly 2 players, Players 1 and 4, as Player-1 and Player-4 were trained
  by the same coach.

5. Conclusion: Zara trains exactly 2 players. Hence, the correct answer is:
Answer: Option 1: Exactly 2

Answer 2

We are given several conditions about the ratings and coaching distribution:
• Yuki trains Players 2, 4, 6, 8.
• Zara trains Players 1, 3, 5, 7.
• Xena trains the remaining players.
By applying the conditions step by step, and using the fact that Player-5 and Player-7 have
the same rating, we assign the following ratings:
• Player-2: 7
• Player-4: 6
• Player-6: 4
• Player-8: 3
• Player-1: 2
• Player-3: 5
• Player-5: 7
• Player-7: 4
Thus, the rating of Player-7 is 4 .

Answer 3

Coaches and Players:

• Yuki: Players 2, 6, 8.
• Zara: Players 3, 5, 7.
• Xena: Players 1, 4.

Key Constraints:

• Total rating sum = 32.
• Player 2 = 7 (highest rating).
• Player 5 = Player 7 = z.
• Player 4 = 2x (double Player 8’s rating x).
• Ratings are unique, except Players 5 and 7.
• Yuki’s average = 2 × Xena’s average = Zara’s average + 2.

Assign Ratings:

• x = 2 (Player 8), so Player 4 = 2x=4.
• z = 6 (Players 5 and 7).
• Player 3 = 3, Player 1 = 5.
• Player 6 = 5.

Hence, player 6’s rating = 5.

Answer 4

We are given several constraints regarding the coaching distribution and the ratings of the
players. Let’s break this down step-by-step:
1. Coaching Distribution:
Yuki trains Players 2, 4, 6, and 8 (even-numbered players).
Zara trains Players 1, 3, 5, and 7 (odd-numbered players).
Xena trains the remaining players.
2. Rating Distribution:
The total sum of all the ratings is 8 × 4 = 32 since the average rating is 4.
Player-2 has the highest rating of 7, so Player-2’s rating is 7.
Player-5 and Player-7 have the same rating.
Player 4’s rating is double that of Player-8’s.
The ratings of Players 5, 3, and 1 are distinct and follow from the constraints.
3. Determining the Ratings: We can deduce the ratings based on the available information:
• Player-2 = 7
• Player-4 = 6
• Player-6 = 5
• Player-8 = 3
• Player-1 = 2
• Player-3 = 4
• Player-5 = 7
• Player-7 = 4

From the above, we have the following ratings assigned with certainty:
Players 2, 4, 6, 8, 1, and 3 have their ratings fully determined.
Therefore, the number of players whose ratings can be determined with certainty is 6.

Thus, the correct answer is: 6 .

Answer 5

Let’s break down the problem step-by-step using the given constraints:

1. Yuki’s Players: Yuki trains Players 2, 4, 6, and 8.
2. Zara’s Players: Zara trains Players 1, 3, 5, and 7.
3. Xena’s Players: Xena trains the remaining players, and based on the conditions: - Xena

must train at least 5 players. - Since Player-1 and Player-4 are trained by the same coach,
Xena must train Player-1 and Player-4. - Xena cannot train Player-2, Player-4, Player-6, or
Player-8 because they are trained by Yuki. - Therefore, Xena must train Player-1, Player-3,
Player-4, Player-6, and Player-8.

Thus, the players trained by Xena are Player-1, Player-3, Player-4, Player-8.