CAT 2023 Slot 2 — DILR Question 12

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.

Who attains the maximum total score?

Answer & solution

A
Bimal
Chatur
C
Cannot be determined
D
Akhil

Solution

Easy

This uses the shared grid built for the set. Compare the three participants' totals — Chatur's is fixed while the other two depend on the free cells.

Set grid (see the first question for the full deduction). Chatur is completely fixed at $3,9,6,6,6$ ; only Akhil's Day-2 and Day-5 scores stay loose, with $A_2,A_5\in\{4,5\}$ .

	D1	D2	D3	D4	D5	Total
Akhil	7	$A_2$	5	3	$A_5$	$15+A_2+A_5$
Bimal	5	$6-A_2$	5	7	$12-A_5$	$35-A_2-A_5$
Chatur	3	9	6	6	6	$30$

Bound the other two totals. Since $A_2,A_5\in\{4,5\}$ , their sum $A_2+A_5\in\{8,9,10\}$ . So

\text{Akhil}=15+(A_2+A_5)\le 25,\qquad \text{Bimal}=35-(A_2+A_5)\le 27.

Compare to Chatur. Akhil $\le25<30$ and Bimal $\le27<30$ , while Chatur is exactly $30$ in every valid case. So Chatur's total is strictly the largest, no matter how the free cells fall.

$\mathbf{Chatur}$ attains the maximum total score ( $30$ ).