CAT 2023 Slot 2 — DILR Question 13

Mixed PracticeEasy

Passage / Data

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.

What is the minimum possible total score of Bimal?

Answer & solution

Answer: 25

Solution

Easy

From the shared grid, Bimal's total is $35-(A_2+A_5)$ . To minimise it, maximise the two free Akhil cells.

From the set deduction: Bimal's total $=35-A_2-A_5$ with $A_2\in\{4,5\}$ and $A_5\in\{4,5\}$ .

Maximise the subtracted sum. Bimal's total shrinks as $A_2+A_5$ grows. The largest allowed values are $A_2=5$ and $A_5=5$ , giving $A_2+A_5=10$ .

Compute.

\text{Bimal}_{\min}=35-10=25.

Check: then Akhil $=15+10=25$ , Chatur $=30$ ; daily totals stay $15,15,16,16,18$ — all consistent.

Minimum possible total score of Bimal $=\mathbf{25}$ .