Comprehension
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.
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.
The following information is also known.
1. 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.
2. The total score on Day 3 is the same as the total score on Day 4.
3. Bimal’s scores are the same on Day 1 and Day 3.
| Table 1: 2-day averages for Days through 5 | |||
|---|---|---|---|
| Day 2 | Day 3 | Day 4 | Day 5 |
| 15 | 15.5 | 16 | 17 |
| 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 |
1. 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.
2. The total score on Day 3 is the same as the total score on Day 4.
3. Bimal’s scores are the same on Day 1 and Day 3.
Question: 1
What is Akhil's score on Day 1?
What is Akhil's score on Day 1?
Updated On: Nov 7, 2024
- 6
- 7
- 5
- 8
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The Correct Option is B
Solution and Explanation
Let's consider this following table for Akhil's final score
| Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | |
| Akhil | 7 | \(\frac{4}{5}\) | 5 | 3 | \(\frac{5}{4}\) |
| Bimal | 5 | \(\frac{2}{1}\) | 3 | 7 | \(\frac{7}{8}\) |
| Chatur | 3 | 9 | 6 | 6 | 6 |
| Total Score | 15 | 15 | 16 | 16 | 18 |
From the table, we can see that the score of Akhil is 7 on day 1.
So, the correct option is (B): 7
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1
Question: 2
Who attains the maximum total score?
Who attains the maximum total score?
Updated On: Nov 7, 2024
- Cannot be determined
- Akhil
- Bimal
- Chatur
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The Correct Option is D
Solution and Explanation
Lets consider Chatur's scores from the following table.
Therefore we can see that the maximum score is obtained by Chatur.
So, The correct option is (D): Chatur.
| Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 | |
| Akhil | 7 | \(\frac{4}{5}\) | 5 | 3 | \(\frac{5}{4}\) | 23/24/25 |
| Bimal | 5 | \(\frac{2}{1}\) | 5 | 7 | \(\frac{7}{8}\) | 27/26/25 |
| Chatur | 3 | 9 | 6 | 6 | 6 | 30 |
| Total Score | 15 | 15 | 16 | 16 | 18 | 80 |
Therefore we can see that the maximum score is obtained by Chatur.
So, The correct option is (D): Chatur.
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Question: 3
What is the minimum possible total score of Bimal?
What is the minimum possible total score of Bimal?
Updated On: Nov 7, 2024
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Solution and Explanation
Let's consider the following table for minimum possible total score of Bimal
From the table, we can see that the minimum score obtained by Bimal is 25
So, the correct answer is: 25.
| Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Total Score | |
| Akhil | 7 | \(\frac{4}{5}\) | 5 | 3 | \(\frac{5}{4}\) | 23/24/25 |
| Bimal | 5 | \(\frac{2}{1}\) | 5 | 7 | \(\frac{7}{8}\) | 27/26/25 |
| Chatur | 3 | 9 | 6 | 6 | 6 | 30 |
| Total score | 15 | 15 | 16 | 16 | 18 | 80 |
From the table, we can see that the minimum score obtained by Bimal is 25
So, the correct answer is: 25.
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Question: 4
If the total score of Bimal is a multiple of 3, what is the score of Akhil on Day 2?
If the total score of Bimal is a multiple of 3, what is the score of Akhil on Day 2?
Updated On: Nov 7, 2024
- 4
- 5
- 6
- Cannot be determined
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The Correct Option is A
Solution and Explanation
Lets see the final table of total score of Bimal
The question says that Bimal's total score is a multiple of 3,
which means his total score is 27.
This means Akhil's total score is 23.
Akhil scores 23 when his scores on Days 1, 2, 3, 4, and 5 are 7, 4, 5, 3, and 4.
So, Akhil's score on Day 2 is 4.
| Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Total Score | |
| Akhil | 7 | \(\frac{4}{5}\) | 5 | 3 | \(\frac{5}{4}\) | 23/24/25 |
| Bimal | 5 | \(\frac{2}{1}\) | 5 | 7 | \(\frac{7}{8}\) | 27/26/25 |
| Chatur | 3 | 9 | 6 | 6 | 6 | 30 |
| Total Score | 15 | 15 | 16 | 16 | 18 | 80 |
The question says that Bimal's total score is a multiple of 3,
which means his total score is 27.
This means Akhil's total score is 23.
Akhil scores 23 when his scores on Days 1, 2, 3, 4, and 5 are 7, 4, 5, 3, and 4.
So, Akhil's score on Day 2 is 4.
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Question: 5
If Akhil attains a total score of 24, then what is the total score of Bimal?
If Akhil attains a total score of 24, then what is the total score of Bimal?
Updated On: Nov 7, 2024
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Solution and Explanation
To determine Bimal's total score given Akhil's total score of 24, let's analyze the information step-by-step:
2-Day Averages:
Participants' Ranks and Scores:
Therefore, Bimal's total score is 26.
2-Day Averages:
- Day 2: 15
- Day 3: 15.5
- Day 4: 16
- Day 5: 17
- Total score of Day 1 = 𝑥x
- Total score of Day 2 = 𝑦y
- Total score of Day 3 = 𝑧z
- Total score of Day 4 = 𝑧z (same as Day 3)
- Total score of Day 5 = 𝑤w
- (x + y) / 2 = 15 ⟹ x + y = 30
- (y + z) / 2 = 15.5 ⟹ y + z = 31
- (z + z) / 2 = 16 ⟹ 2z = 32 ⟹ z = 16
- (z + w) / 2 = 17 ⟹ 16 + w = 34 ⟹ w = 18
- z = 16
- x + y = 30
- y + 16 = 31 ⟹ y = 15
- x + 15 = 30 ⟹ x = 15
- w = 18
- Day 1: 15
- Day 2: 15
- Day 3: 16
- Day 4: 16
- Day 5: 18
Participants' Ranks and Scores:
- Chatur's score pattern:
- Always multiples of 3.
- Highest unique score on Day 2.
- Lowest score on Day 1, equal to Akhil's score on Day 4.
- Day 2: Chatur's score must be 9 (as it's the unique highest score).
- Day 1: Chatur's score must be 3 (as it's the lowest and matches Akhil's score on Day 4).
- Day 1: Chatur = 3, Bimal and Akhil share the remaining 12 (15 - 3) such that Akhil gets 7 (since Akhil ranks 1 on Day 1).
- Day 2: Chatur = 9, the remaining 6 is shared by Bimal and Akhil. Bimal and Akhil could score 2 and 4 respectively (since Bimal ranks 3 and Akhil ranks 2).
- Day 3: Chatur scores 6 (a multiple of 3 and consistent with the total 16). Akhil and Bimal must share the remaining 10.
- Day 4: Chatur again scores 6 (multiples of 3). Akhil scores 3 (same as Chatur’s score on Day 1), and Bimal takes the remaining 7.
- Day 5: Chatur scores 9 (highest), leaving Akhil and Bimal to share 9. Akhil and Bimal could score 4 and 5 respectively.
- Akhil: 7 (Day 1) + 4 (Day 2) + 5 (Day 3) + 3 (Day 4) + 5 (Day 5) = 24
- Bimal: 5 (Day 1) + 2 (Day 2) + 5 (Day 3) + 7 (Day 4) + 7 (Day 5) = 26
- Chatur: 3 (Day 1) + 9 (Day 2) + 6 (Day 3) + 6 (Day 4) + 9 (Day 5) = 33
Therefore, Bimal's total score is 26.
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