CAT 2025 Slot 1 · DILR · Question 9

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.

For how many employees can the scores at the end of Quarter 3 be determined with certainty?

Answer & solution

Answer: 4

Four of the six scores are forced outright.

Bunty is rated 1, 1 and 3 across the three quarters, giving 5.

Dolly holds rating 2 in every quarter, giving 6.

Falguni holds rating 3 in every quarter, giving 9.

Eklavya is rated 1 in Quarter 1 and 3 in Quarter 2; in Quarter 3 the Elite trio is Chintu, Eklavya and Falguni, and Falguni's fixed 3 leaves 1 and 2 for the other two.

Chintu must be demoted at the end of Quarter 3, so he needs the lower score, which requires Chintu to take the 1 and Eklavya the 2 — giving Eklavya 1+3+2=6.

Asha and Chintu are the two that stay open.

In Quarter 1 Bunty takes the rating 1, so Asha and Chintu share 2 and 3; in Quarter 2 Falguni takes 3, so Asha and Chintu share 1 and 2.

Asha must be demoted at the end of Quarter 2, and checking the possibilities leaves two consistent arrangements: Asha 2 then 1 with Chintu 3 then 2, or Asha 3 then 1 with Chintu 2 then 2.

Those give Asha a Quarter 3 score of 4 or 5, and Chintu 6 or 5, so neither is certain.

The count of employees with a determinable score is therefore 4.

Shortcut. Everyone whose ratings are fixed by a constant or by a leftover is certain; only the pair who share two unordered pairs of ratings stays open. Spotting that Asha and Chintu are that pair answers the question without evaluating either branch.

CAT 2025 Slot 1 · DILR · Question 9

More Quant Based Puzzles and Optimisation questions