CAT 2024 Slot 2 — DILR Question 21
Answer the following questions based on the information given below.
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.
For how many players the ratings can be determined with certainty?
Answer & solution
Answer: 6
Hard
Tally the ratings now fixed. Six are forced; only P1 and P3 (Xena's remaining two) can swap between the leftover values 3 and 6.
Ratings so far: P2 = 7, P4 = 2, P5 = 4, P6 = 5, P7 = 4, P8 = 1. Remaining for Xena's P1, P3: must sum to and be distinct unused values.
| Player | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Rating | 3 or 6 | 7 | 6 or 3 | 2 | 4 | 5 | 4 | 1 |
P1 and P3 stay ambiguous. The only unused ratings are 3 and 6, and , but no clue orders P1 vs P3.
Count the certain ones. P2, P4, P5, P6, P7, P8 are fixed.