Comprehension:

Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches- Xena, Yuki, and Zara. Each coach trained at least two players.Yuki trained only even-numbered players, while Zara trained only odd-numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest. The following additional information is known:

1. Xena trained more players than Yuki.

2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3, and Player-5 were all different.

3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.

4. The average of the ratings of all the players was 4.

5. Player-2 got the highest rating.

6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.

7. Player-4’s rating was double of Player-8’s and less than Player-5’s.

What was the rating of Player-7?

The correct answer is 4.

To find the rating of Player-7, we can analyze the given information step-by-step using the rules of ratings and averages:

1. Understanding the Ratings and Uniqueness
According to the problem description, after the training camp, the coaches gave integer ratings to the players on a scale of 1 to 7.
Condition 3 states: "Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating."
This means:
- Player-5 and Player-7 share the same rating. Let this rating be $r$.
- The remaining 6 players all received unique ratings that are different from each other and different from $r$.
- Therefore, there are exactly 7 distinct rating values distributed among the 8 players. Since the ratings must be integers from the scale of 1 to 7, these 7 distinct ratings must be exactly the integers 1, 2, 3, 4, 5, 6, and 7.

2. Finding the Sum of All Ratings
Since the 8 players' ratings consist of the 7 distinct integers from 1 to 7 plus one repeated rating $r$ (which is the rating of Player-5 and Player-7), we can express the sum of the ratings of all 8 players as:

$\text{Total Sum}=(1+2+3+4+5+6+7)+r$

Simplifying the sum of the integers from 1 to 7:

$1+2+3+4+5+6+7=28$

Thus, the sum of all ratings is:

$\text{Total Sum}=28+r$

3. Using the Average to Solve for the Rating
Condition 4 states: "The average of the ratings of all the players was 4."
Since there are 8 players in total, we can calculate the total sum using the average formula:

$\text{Total Sum}=\text{Average}\×\text{Number of Players}$

$\text{Total Sum}=4\×8=32$

Now, we equate the two expressions for the total sum and solve for $r$:

$28+r=32$

$r=32\−28$

$r=4$

Since $r$ represents the rating of both Player-5 and Player-7, the rating of Player-7 is 4.