DILR SET | InnovateX 6 Employees Ratings & Scores | Wide Numbers Arrangement | CAT 2025 Slot 1 | Difficult
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.
1. 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.
2. Dolly and Falguni were the only employees who got the same rating across all the quarters.
3. 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.
1. What was Eklavya’s score at the end of Quarter 2? ______
2. How many employees changed groups more than once up to the beginning of Quarter 4? _____
3. What was Bunty’s score at the end of Quarter 3? ______
4. For how many employees can the scores at the end of Quarter 3 be determined with certainty? ____
5. Which of the following statements is/are NECESSARILY true?
I. Asha received a rating of 2 in Quarter 1.
II. Asha received a rating of 1 in Quarter 2.
1. Neither I nor II
2. Both I and II
3. Only I
4. Only II
Solutions to DILR SET | InnovateX 6 Employees Ratings & Scores | Wide Numbers Arrangement | CAT 2025 Slot 1 | Difficult
Quick Answers
What was Eklavya’s score at the end of Quarter 2? — 4
Eklavya started Q1 in Novice and, because Dolly = 2 and Falguni = 3 are constant, the remaining Q1 Novice rating 1 goes to Eklavya. After end-Q1 swaps Eklavya remains Novice and in Q2 the Novice ratings become {1,2,3} with Bunty = 1 given, so Eklavya must take 3 in Q2. Therefore his cumulative after Q2 = 1 (Q1) + 3 (Q2) = 4.
2. How many employees changed groups more than once up to the beginning of Quarter 4? — 0
Only one swap (one promotion + one demotion) happens at the end of each quarter, and the forced sequence (end-Q1, end-Q2, end-Q3) produces at most one move per person. Tracking each employee shows everyone either stayed or moved exactly once, so no one moved more than once — zero employees.
3. What was Bunty’s score at the end of Quarter 3? — 5
Bunty was lowest in Elite in Q1 and thus had Q1 = 1; Q2 = 1 is given; in Q3 Novice (A, B, D) Dolly = 2 and Asha = 1 are fixed, so Bunty must be 3 in Q3. Summing gives 1 + 1 + 3 = 5.
4. For how many employees can the scores at the end of Quarter 3 be determined with certainty? — 4
Dolly and Falguni are constant raters so their Q3 totals are fixed (6 and 9). Bunty and Eklavya’s quarter-by-quarter ratings are uniquely forced, so their end-Q3 totals are fixed (Bunty 5, Eklavya 6). Asha and Chintu’s Q1 ratings can be swapped (2↔3) without violating clues, making their end-Q3 totals ambiguous; hence exactly 4 employees have determinable totals.
5. Which statement(s) is/are NECESSARILY true? — Only II (Asha got 1 in Q2)
To ensure Asha is demoted by end-Q2 (so A, B, C are all Novice by start-Q4), Asha must be the lowest cumulative after Q2; given Falguni’s constant 3 and distinct ratings rule, the only assignment that enforces Asha’s demotion across all valid scenarios is Asha = 1 in Q2. Her Q1 rating, however, can be either 2 or 3, so statement I is not necessary. Therefore Only II is necessarily true.
TableSteps — InnovateX Puzzle
Step 1: Initial groups given → Elite = A, B, C and Novice = D, E, F at start of Q1. (Clue 1)
Step 2: Dolly and Falguni constant ratings → D = 2 always, F = 3 always. (Clue 2)
Step 3: Bunty gets 1 in Q2 → Bunty must be in Novice in Q2 → Bunty was demoted at end Q1. (Clue 3)
Step 4: In Q1 Elite, the lowest rating is 1 → assign Bunty = 1 in Q1 Elite. (Uses promotion rule)
Step 5: Dolly is 2 and Falguni is 3 in Q1 Novice → remaining Novice rating 1 goes to Eklavya. (Clue 2 + Q1 Novice set)
Step 6: At end of Q1, highest in Novice is Falguni (3) → promoted; lowest in Elite is Bunty (1) → demoted. (Rule)
Step 7: Start Q2 Elite becomes A, C, F and Novice becomes B, D, E. (From Step 6)
Step 8: Asha receives 1 in Q3 and Dolly 2 in Q3 → Q3 Novice must contain both Asha and Dolly. (Clue 3)
Step 9: All of A, B, C must be in Novice at start of Q4 → Asha must be demoted by end Q2. (Clue 1 + swap constraints)
Step 10: To demote Asha at end Q2, Asha must have the lowest cumulative score in Q2 → Asha must receive rating 1 in Q2. (Rule + necessity)
Step 11: In Q2 Elite, ratings are {1,2,3} with F = 3 constant → remaining {1,2} assigned as Asha = 1, Chintu = 2. (Step 10 + distinct ratings)
Step 12: After scoring Q1 + Q2, Asha is uniquely the lowest → Asha demoted; Eklavya highest in Novice → promoted. (Rule)
Step 13: Start Q3 Elite becomes C, F, E and Novice becomes A, B, D. (From Step 12)
Step 14: Q3 Novice ratings forced: Asha = 1, Dolly = 2 → Bunty must take 3. (Clue + distinct ratings)
Step 15: Q3 Elite ratings forced: F = 3, Eklavya = 2, Chintu = 1. (Constants + distinct ratings)
Step 16: End Q3 swap: highest in Novice = Bunty (3) but cannot be promoted (final Elite must be D,E,F per Clue 1) → Dolly (2) is promoted instead; lowest in Elite = Chintu (1) → demoted. (Constraint + rule)
Step 17: Start Q4 Elite becomes D, E, F as required; Novice becomes A, B, C. (Matches Clue 1)
Working Table:
Legend:
- Groups: Elite (E), Novice (N) — shown as starting group each quarter.
- Ratings in each quarter are integers 1 (lowest), 2, 3 (highest) within each group.
- “(amb)” marks cells that have two possible values (ambiguous between two scenarios).
| Employee | Asha (A) | Bunty (B) | Chintu (C) | Dolly (D) | Eklavya (E) | Falguni (F) |
| Start Q1 Group | Elite | Elite | Elite | Novice | Novice | Novice |
| Q1 rating | 2 or 3 (amb) | 1 | 3 or 2 (amb) | 2 (constant) | 1 | 3 (constant) |
| Score end Q1 | 2 or 3 | 1 | 3 or 2 | 2 | 1 | 3 |
| Start Q2 Group | Elite | Novice | Elite | Novice | Novice | Elite |
| Q2 rating | 1 | 1 (given) | 2 | 2 | 3 | 3 |
| Score end Q2 | 3 or 4 | 2 | 5 or 4 | 4 | 4 | 6 |
| Start Q3 Group | Novice | Novice | Elite | Novice | Elite | Elite |
| Q3 rating | 1 | 3 | 1 | 2 | 2 | 3 |
| Score end Q3 | 4 or 5 (amb) | 5 | 6 or 5 (amb) | 6 | 6 | 9 |
| Moves (count) | 1 | 1 | 1 | 1 | 1 | 1 |
