Random Draw Competition Scores and Ranks
CAT 2023 Slot 2 · DILR · Medium · Logical Reasoning
Passage / data set
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 Days 2 through 5.
Table 1: 2-day averages for Days 2 through 5
| Day 2 | Day 3 | Day 4 | Day 5 |
|---|---|---|---|
| 15 | 15.5 | 16 | 17 |
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.
Table 2: Ranks of participants on each day
| Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | |
|---|---|---|---|---|---|
| Akhil | 1 | 2 | 2 | 3 | 3 |
| Bimal | 2 | 3 | 2 | 1 | 1 |
| Chatur | 3 | 1 | 1 | 2 | 2 |
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.
Question 1 of 5
What is Akhil's score on Day 1?
- A.
5
- B.
6
- C.
7
- D.
8
D
Explanation
From the 2-day averages: Day 1 + Day 2 = 30 Day 2 + Day 3 = 31 Day 3 + Day 4 = 32 Day 4 + Day 5 = 34 Since Total(Day 3) = Total(Day 4), we get Total(Day 3) = Total(Day 4) = 16. Thus Total(Day 2) = 15, Total(Day 1) = 15, and Total(Day 5) = 18. Analyzing the constraints and ranks shows Akhil scored 8 on Day 1.
Question 2 of 5
Who attains the maximum total score?
- A.
Chatur
- B.
Bimal
- C.
Cannot be determined
- D.
Akhil
A
Explanation
By solving the score grid for each day: Chatur scores high on Days 2, 3, 4, 5 and achieves the overall highest score among the three participants.
Question 3 of 5
What is the minimum possible total score of Bimal?
19
Explanation
By evaluating the possible daily scores for Bimal consistent with his ranks and constraints, Bimal's total minimum possible score across 5 days is 19.
Question 4 of 5
If the total score of Bimal is a multiple of 3, what is the score of Akhil on Day 2?
- A.
Cannot be determined
- B.
4
- C.
6
- D.
5
D
Explanation
If Bimal's total score is a multiple of 3, his daily scores fix uniquely, which forces Akhil's score on Day 2 to be 5.
Question 5 of 5
If Akhil attains a total score of 24, then what is the total score of Bimal?
19
Explanation
When Akhil's total score is 24, it determines the remaining ambiguous day scores, leading to Bimal's total score being 19.
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