CAT 2023 Slot 2 — DILR Question 15
Answer the following questions based on the information given below:
Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants’ scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for
Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2.
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The following information is also known.
- Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil’s score on Day 4.
- The total score on Day 3 is the same as the total score on Day 4.
- Bimal’s scores are the same on Day 1 and Day 3.
If Akhil attains a total score of 24, then what is the total score of Bimal?
Answer & solution
Answer: 26
Easy
Akhil and Bimal split a fixed pool. Once Akhil's total is given, Bimal's follows immediately.
From the set deduction: the grand total is and Chatur is fixed at , so Akhil Bimal always.
Use the fixed pool. Since Akhil Bimal :
Consistency check. Akhil means (e.g. ), which is allowed since both lie in . Then Bimal — matching the pool computation.
Bimal's total score .