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.
Table 1: 2-day averages for Days through 5
Day 2Day 3Day 4Day 5
1515.51617
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 1Day 2Day 3Day 4Day 5
Akhil12233
Bimal23211
Chatur31122
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.
Question: 1

What is Akhil's score on Day 1?

Updated On: Jan 13, 2026
  • 6
  • 7
  • 5
  • 8
Show Solution

The Correct Option is B

Solution and Explanation

To determine Akhil's Day 1 score, the provided data and conditions are analyzed:
  1. The following equations are derived from the 2-day averages: Day 1 + Day 2 = 2 * 15 = 30 Day 2 + Day 3 = 2 * 15.5 = 31 Day 3 + Day 4 = 2 * 16 = 32 Day 4 + Day 5 = 2 * 17 = 34 It is also stated that Day 3 and Day 4 scores are equal: Day 3 = Day 4 = 16
  2. Using the equality Day 3 = 16: Day 2 + 16 = 31, which implies Day 2 = 15. Substituting Day 2 = 15 into the first equation: Day 1 + 15 = 30, which implies Day 1 = 15. Therefore, the total score for Day 1 is 15.
  3. Day 1 participant ranks are: Akhil: 1 Bimal: 2 Chatur: 3 Chatur's score, being the lowest and a multiple of 3, could be 3, 6, or 9. It is specified that Chatur's minimum score matches Akhil's Day 4 score of 3.
  4. Akhil's rank of 1 on Day 1 signifies the highest score for that day.
  5. Distributing scores based on the conditions leads to the following table:
    ParticipantsScore
    Akhil7
    Bimal5
    Chatur3
    Thus, Akhil's score on Day 1 is 7.
Was this answer helpful?
0
Question: 2

Who attains the maximum total score?

Updated On: Jan 13, 2026
  • Cannot be determined
  • Akhil
  • Bimal
  • Chatur
Show Solution

The Correct Option is D

Solution and Explanation

To determine the participant with the highest total score, an analysis of provided data and logical deduction based on given constraints is required.

Data Provided:
- Two-day average scores from Day 2 to Day 5.
- Daily rankings.
- Specific participant score limitations.

Calculation of Total Scores for Days 1 through 5:

DayTotal Score
Day 1x
Day 2y
Day 3z
Day 4z
Day 5a

Derivations from 2-Day Averages:

  • (x + y) / 2 = 15 ⟹ x + y = 30
  • (y + z) / 2 = 15.5 ⟹ y + z = 31
  • (z + z) / 2 = 16 ⟹ z = 16
  • (z + a) / 2 = 17 ⟹ a = 18

Score Solution:

  • z = 16
  • y + 16 = 31 ⟹ y = 15
  • x + 15 = 30 ⟹ x = 15
  • z + a = 34 ⟹ a = 18

Daily Total Scores:

  • Day 1: 15
  • Day 2: 15
  • Day 3: 16
  • Day 4: 16
  • Day 5: 18

Rank Constraints:

  • Chatur's score is consistently a multiple of 3.
  • The lowest score on Day 1 matches Akhil's score on Day 4.
  • The highest unique score occurred on Day 2.

Chatur's Individual Scores:

  • Day 1: 6 (Equivalent to Akhil's Day 4 score)
  • Day 2: 9 (Unique and highest score)
  • Day 3: 6
  • Day 4: 6
  • Day 5: 12

Bimal's Individual Scores:

  • Day 1: 5
  • Day 2: 4
  • Day 3: 5
  • Day 4: 7
  • Day 5: 7
  • Total: 28

Akhil's Individual Scores:

  • Day 1: 4
  • Day 2: 2
  • Day 3: 5
  • Day 4: 3
  • Day 5: 5
  • Total: 19

Chatur's Cumulative Score: 6 + 9 + 6 + 6 + 12 = 39

Outcome: Chatur achieved the highest total score.

Was this answer helpful?
0
Question: 3

What is the minimum possible total score of Bimal?

Updated On: Jan 13, 2026
Show Solution

Solution and Explanation

The following table displays the minimum possible total score for Bimal:

Day 1Day 2Day 3Day 4Day 5Total Score
Akhil7\(\frac{4}{5}\)53\(\frac{5}{4}\)23 / 24 / 25
Bimal5\(\frac{2}{1}\)57\(\frac{7}{8}\)27 / 26 / 25
Chatur3966630
Total score151516161880


According to the table, Bimal's minimum score is 25.

The determined answer is 25.

Was this answer helpful?
0
Question: 4

If the total score of Bimal is a multiple of 3, what is the score of Akhil on Day 2?

Updated On: Jan 13, 2026
  • 4
  • 5
  • 6
  • Cannot be determined
Show Solution

The Correct Option is A

Solution and Explanation

Below is the final table of Bimal's total scores:

Day 1Day 2Day 3Day 4Day 5Total Score
Akhil7\(\frac{4}{5}\)53\(\frac{5}{4}\)23 / 24 / 25
Bimal5\(\frac{2}{1}\)57\(\frac{7}{8}\)27 / 26 / 25
Chatur3966630
Total Score151516161880

Given that Bimal's total score is a multiple of 3, his score is 27.
This implies Akhil's total score is 23.
Akhil achieved a score of 23 with individual scores of 7, 4, 5, 3, and 4 on Days 1 through 5, respectively.
Therefore, Akhil's score on Day 2 is 4.

Was this answer helpful?
0
Question: 5

If Akhil attains a total score of 24, then what is the total score of Bimal?

Updated On: Jan 13, 2026
Show Solution

Solution and Explanation

Bimal's Total Score

To calculate Bimal's total score, given Akhil's total score is 24, we will proceed systematically.

2-Day Averages:

  • Day 2: \(15\)
  • Day 3: \(15.5\)
  • Day 4: \(16\)
  • Day 5: \(17\)

Let the total scores for each day be denoted as follows:

  • Day 1: \(x\)
  • Day 2: \(y\)
  • Day 3 and Day 4: \(z\)
  • Day 5: \(w\)

Applying the average formulas:

  • \(\frac{x + y}{2} = 15 \Rightarrow x + y = 30\)
  • \(\frac{y + z}{2} = 15.5 \Rightarrow y + z = 31\)
  • \(\frac{z + z}{2} = 16 \Rightarrow z = 16\)
  • \(\frac{z + w}{2} = 17 \Rightarrow w = 18\)
  • From these, we derive: \(y = 15\), \(x = 15\)

The daily total scores are thus:

  • Day 1: \(15\)
  • Day 2: \(15\)
  • Day 3: \(16\)
  • Day 4: \(16\)
  • Day 5: \(18\)

Participants’ Scores

  • Chatur: Scores are always multiples of 3.
  • Chatur achieved their highest score on Day 2, which was a unique maximum.
  • The lowest score on Day 1 is equal to Akhil's score on Day 4, which is \(3\).

Score Distribution:

  • Day 1: Chatur = 3, Akhil = 7 (ranked 1st), Bimal = 5
  • Day 2: Chatur = 9, Akhil = 4 (ranked 2nd), Bimal = 2 (ranked 3rd)
  • Day 3: Chatur = 6, Akhil = 5, Bimal = 5
  • Day 4: Chatur = 6, Akhil = 3, Bimal = 7
  • Day 5: Chatur = 9, Akhil = 4, Bimal = 5

Summary of Total Scores:

  • Akhil: \(7 + 4 + 5 + 3 + 5 = 24\)
  • Bimal: \(5 + 2 + 5 + 7 + 7 = 26\)
  • Chatur: \(3 + 9 + 6 + 6 + 9 = 33\)

Consequently, Bimal's total score is: 26

Was this answer helpful?
0

Top Questions on Table

Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
View Solution