CAT 2025 Slot 1 · DILR · Question 10

CAT 2025 Slot 1 previous year question on Quant Based Puzzles and Optimisation, with the answer and a step-by-step solution.

Quant Based Puzzles and OptimisationLOGICAL REASONING - High LevelMultiple choiceMedium

Set 2: InnovateX — Elite and Novice Ratings — this question belongs to a set. Read the full set with all 5 questions →

At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu.

At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3.

The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher.

Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4.

Dolly and Falguni were the only employees who got the same rating across all the quarters.

The following is known about ratings given by Lalu:

• Bunty received a rating of 1 in Quarter 2.

• Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.

Which of the following statements is/are NECESSARILY true?

I. Asha received a rating of 2 in Quarter 1.

Asha received a rating of 1 in Quarter 2.

  1. A
    Only I
  2. B
    Both I and II
  3. C
    Neither I nor II
  4. D
    Only II
Pick an option, then check.
Answer & solution

Answer: Option D

In Quarter 1 the Elite trio is Asha, Bunty and Chintu, and Bunty's demotion forces his rating to 1.

That leaves ratings 2 and 3 for Asha and Chintu, in either order for now.

In Quarter 2 the Elite trio is Asha, Chintu and Falguni, and Falguni's fixed rating is 3.

So Asha and Chintu share the ratings 1 and 2 in Quarter 2.

Asha must be demoted at the end of Quarter 2, so her two-quarter score must be the lowest in Elite.

Falguni's score is 3+3=6, comfortably above either candidate, so the contest is between Asha and Chintu.

If Asha takes the 2 in Quarter 2 then Chintu takes the 1, and Asha's score beats or ties Chintu's with a higher latest rating — so Chintu would go down instead.

Hence Asha must take the rating 1 in Quarter 2, making statement II necessarily true.

For Quarter 1 both splits survive: Asha 2 with Chintu 3 gives scores 3 and 5, and Asha 3 with Chintu 2 gives 4 and 4 with Asha ranked lower on the latest rating — Asha is demoted either way.

So statement I is not necessarily true, and the answer is "Only II", the fourth option.

Shortcut. The demotion rule bites in Quarter 2 but not in Quarter 1, because the tie-break rescues the second arrangement there. Checking which quarter the rule actually constrains answers the question in one pass.

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