CAT 2025 Slot 1 · DILR · Question 6

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 LevelType in the answer (TITA)Hard

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.

What was Eklavya's score at the end of Quarter 2?

Answer & solution

Answer: 4

Each quarter sends exactly one person down from Elite and one up from Novice.

Clue 1 requires all three starters in Elite to end up in Novice by Quarter 4, which takes three demotions in three quarters — so one of Asha, Bunty and Chintu goes down each quarter and nobody returns.

Clue 3 has Lalu rating Bunty in Quarter 2, so Bunty was already in Novice then and was demoted at the end of Quarter 1.

Clue 3 also has Lalu rating Asha in Quarter 3, so Asha was demoted at the end of Quarter 2, leaving Chintu to go at the end of Quarter 3.

Dolly is still with Lalu in Quarter 3, so she is the one promoted at the end of Quarter 3, and her Quarter 3 rating of 2 plus clue 2 makes her rating 2 in every quarter.

In Quarter 1 the Novice trio is Dolly, Eklavya and Falguni with distinct ratings, and Dolly takes the 2, so Eklavya and Falguni hold 1 and 3.

The one rated 3 has the highest score and is promoted at the end of Quarter 1.

Suppose Eklavya took the 3. Then Eklavya moves up and Falguni, rated 1, must keep rating 1 in Quarter 2 by clue 2 — but Bunty is also rated 1 in Quarter 2 and both are in Novice, which breaks the distinct-ratings rule.

So Falguni took the 3 in Quarter 1 and holds 3 throughout, while Eklavya took the 1.

In Quarter 2 the Novice trio is Bunty, Dolly and Eklavya, with Bunty on 1 and Dolly on 2, so Eklavya is rated 3.

Eklavya's score at the end of Quarter 2 is 1+3=4.

Shortcut. Clue 2 is the lever: whoever is promoted first must leave a partner behind whose fixed rating would clash with Bunty's 1 in Quarter 2. That single clash settles Eklavya's Quarter 1 rating without building the full table.

CAT 2025 Slot 1 · DILR · Question 6

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