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CAT 2025Slot 1DILRQues & Sol

Logical ReasoningHard

Data Set

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.

Question 1

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

Solution

Setup: We reconstruct group memberships quarter by quarter using promotion/demotion rules, alongside the fixed-rating constraints for Dolly and Falguni, and the given clue about Bunty's Q2 rating to determine Eklavya's ratings in Q1 and Q2.

Steps:

  1. Initial Setup: Q1 starts with Elite = {A, B, C} and Novice = {D, E, F}. Since A, B, C must all be in Novice by Q4, each must be demoted exactly once.
  2. Bunty's Q1 demotion: Bunty receives rating 1 from Lalu in Q2, meaning Bunty is in Novice during Q2. So Bunty was demoted after Q1. For Bunty to be demoted from Elite after Q1, Bunty must have received the lowest rating in Elite in Q1 → Bunty gets rating 1 in Q1.
  3. Dolly's fixed rating: Dolly is in Novice throughout Q1–Q3 (at minimum). Since Dolly gets rating 2 in Q3 (given by Lalu), and Dolly's rating is the same every quarter → Dolly gets rating 2 in Q1, Q2, and Q3.
  4. Falguni's fixed rating: In Q1 Novice = {D, E, F}. Dolly takes rating 2. Falguni must have the same rating every quarter. If Falguni gets rating 3 in Q1, Falguni's cumulative after Q1 = 3, which is the highest in Novice → Falguni gets promoted to Elite after Q1. This is consistent and Falguni continues to get rating 3 in all subsequent quarters.
  5. Eklavya's Q1 rating: In Q1 Novice = {D=2, E=?, F=3}. The only remaining rating is 1 → Eklavya gets rating 1 in Q1.
  6. Eklavya's Q2 rating: After Q1, Falguni is promoted to Elite, and Bunty is demoted to Novice. Q2 Novice = {B, D, E}. Bunty gets 1 (given), Dolly gets 2 (fixed) → Eklavya gets rating 3 in Q2.
  7. Eklavya's cumulative score after Q2: Q1 + Q2 = 1 + 3 = 4.

Final Answer: 4

Question 2

How many employees changed groups more than once up to the beginning of Quarter 4?

Solution

Setup: We trace each employee's group membership across all four quarters using the promotion/demotion logic, checking if any employee moved between Elite and Novice more than once before the start of Q4.

Steps:

  1. Reconstruct Q1 start: Elite = {A, B, C}, Novice = {D, E, F}.
  2. After Q1 movements: Bunty (lowest in Elite, rating 1) is demoted; Falguni (highest in Novice, rating 3, cumulative 3) is promoted. Q2 start: Elite = {A, C, F}, Novice = {B, D, E}.
  3. After Q2 movements: Asha must be demoted (since Asha must be in Novice by Q4, and Chintu must still be demoted later). Asha gets rating 1 in Q2 (established by demotion logic). Eklavya (cumulative 1+3=4) is the highest scorer in Novice after Q2 → Eklavya promoted. Q3 start: Elite = {C, E, F}, Novice = {A, B, D}.
  4. After Q3 movements: Chintu must be demoted (since Chintu must be in Novice at Q4 start). Chintu gets the lowest score in Elite after Q3. Among Novice {A, B, D}: Asha gets 1 (given), Dolly gets 2 (fixed), Bunty gets 3 (by elimination). Dolly has the highest cumulative and is promoted. Q4 start: Elite = {D, E, F}, Novice = {A, B, C}. ✓
  5. Group change count per employee:
    • Asha: Elite→Elite→Novice→Novice — changed once (after Q2)
    • Bunty: Elite→Novice→Novice→Novice — changed once (after Q1)
    • Chintu: Elite→Elite→Elite→Novice — changed once (after Q3)
    • Dolly: Novice→Novice→Novice→Elite — changed once (after Q3)
    • Eklavya: Novice→Novice→Elite→Elite — changed once (after Q2)
    • Falguni: Novice→Elite→Elite→Elite — changed once (after Q1)
  6. Count: Every employee changed groups exactly once. No employee changed groups more than once.

Final Answer: 0

Question 3

What was Bunty's score at the end of Quarter 3?

Solution

Setup: Bunty is in Elite during Q1 and in Novice from Q2 onward. We use Bunty's known ratings — derived from the demotion rule for Q1 and the given clue for Q2 — and then apply elimination within the Q3 Novice group to find Bunty's Q3 rating.

Steps:

  1. Bunty's Q1 rating: Bunty is in Elite (with Asha and Chintu) in Q1 and gets demoted after Q1. The demotion rule states the employee in Elite with the minimum score is demoted. Since Q1 is the first quarter, cumulative score = Q1 rating. For Bunty to be demoted, Bunty must have received the lowest rating in Elite in Q1 → Bunty gets rating 1 in Q1.
  2. Bunty's Q2 rating: Directly given — Lalu assigns Bunty a rating of 1 in Q2. Bunty's cumulative after Q2 = 1 + 1 = 2.
  3. Bunty's Q3 rating: In Q3, Novice = {A, B, D}. Lalu assigns distinct ratings 1, 2, 3. Given: Asha gets 1, Dolly gets 2 (fixed rating). The only remaining rating is 3 → Bunty gets rating 3 in Q3.
  4. Bunty's score at end of Q3: Cumulative = Q1 + Q2 + Q3 = 1 + 1 + 3 = 5.

Final Answer: 5

Question 4

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

Solution

Setup: We check whether each employee's complete rating sequence through Q1, Q2, and Q3 can be uniquely determined from the given constraints. The key ambiguity lies in the Q1 Elite ratings shared between Asha and Chintu.

Steps:

  1. Bunty (B): Q1=1 (demotion rule), Q2=1 (given), Q3=3 (elimination in Novice). Score = 1+1+3 = 5. ✓ Certain.
  2. Dolly (D): Fixed rating of 2 every quarter. Score = 2+2+2 = 6. ✓ Certain.
  3. Falguni (F): Fixed rating of 3 every quarter. Score = 3+3+3 = 9. ✓ Certain.
  4. Eklavya (E): Q1=1 (elimination in Novice with D=2, F=3), Q2=3 (elimination in Novice with B=1, D=2). Q3 Eklavya is in Elite = {C, E, F}. Falguni gets 3 (fixed). For Chintu to be demoted after Q3, Chintu must have the lowest cumulative. Analysis of possible Q1/Q2 ratings for C and E in Elite shows that Chintu must get rating 1 and Eklavya must get rating 2 in Q3 for the demotion to work correctly. So E's Q3 rating = 2. Score = 1+3+2 = 6. ✓ Certain.
  5. Asha (A): In Q1 Elite, Bunty gets 1 and Asha/Chintu share ratings 2 and 3. Asha could get 2 or 3. Asha's Q2=1 (certain, by elimination), Q3=1 (given). But Q1 rating is either 2 or 3, giving score of 4 or 5. ✗ Not certain.
  6. Chintu (C): Chintu gets the opposite of Asha in Q1 (3 or 2). Q2 rating for Chintu also depends on the scenario. Q3=1 (by elimination in Elite). Score is not uniquely determined. ✗ Not certain.
  7. Count of employees with certain Q3 scores: Bunty, Dolly, Falguni, Eklavya → 4 employees.

Final Answer: 4