CAT 2025Slot 1DILRQuestion & SolutionQues & Sol
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
1. Setup
At the beginning of Quarter 1:
| Group | Employees |
|---|---|
| Elite | Asha, Bunty, Chintu |
| Novice | Dolly, Eklavya, Falguni |
Since Asha, Bunty, and Chintu are all in Novice at the beginning of Quarter 4, each must have been demoted from Elite at some point.
Bunty receives a rating of 1 from Lalu in Quarter 2, so Bunty must be in Novice in Q2. Therefore, Bunty was demoted after Q1 and must have received the lowest rating in Elite in Q1:
$$ \text{Bunty's Q1 rating}=1 $$
Dolly and Falguni are the only employees whose ratings remain the same across all quarters. Since Dolly receives a rating of 2 in Q3:
$$ \text{Dolly's rating}=2 $$
Thus, in Q1, the Novice ratings are:
| Employee | Q1 Rating |
|---|---|
| Dolly | 2 |
| Eklavya | 1 |
| Falguni | 3 |
Hence, Falguni is promoted to Elite and Bunty is demoted to Novice after Q1.
2. Solution
The groups at the beginning of Q2 are:
| Group | Employees |
|---|---|
| Elite | Asha, Chintu, Falguni |
| Novice | Bunty, Dolly, Eklavya |
In Q2, Lalu gives distinct ratings of 1, 2, and 3 to the three Novice employees.
Given:
- Bunty's Q2 rating = 1
- Dolly's Q2 rating = 2
Therefore, Eklavya must receive the remaining rating:
$$ \text{Eklavya's Q2 rating}=3 $$
Eklavya's cumulative score after Q2 is:
$$ 1+3=4 $$
3. Final Answer
Answer = 4 ✅
Eklavya's score at the end of Quarter 2 is 4.
Question 2
How many employees changed groups more than once up to the beginning of Quarter 4?
Solution
1. Setup
We trace the group membership of each employee after every quarter.
| Quarter | Elite | Novice |
|---|---|---|
| Q1 | Asha, Bunty, Chintu | Dolly, Eklavya, Falguni |
| Q2 | Asha, Chintu, Falguni | Bunty, Dolly, Eklavya |
| Q3 | Chintu, Eklavya, Falguni | Asha, Bunty, Dolly |
| Q4 | Dolly, Eklavya, Falguni | Asha, Bunty, Chintu |
2. Solution
The group changes for each employee are:
| Employee | Group Movement | Number of Changes |
|---|---|---|
| Asha | Elite → Novice | 1 |
| Bunty | Elite → Novice | 1 |
| Chintu | Elite → Novice | 1 |
| Dolly | Novice → Elite | 1 |
| Eklavya | Novice → Elite | 1 |
| Falguni | Novice → Elite | 1 |
Thus, every employee changed groups exactly once.
Therefore, no employee changed groups more than once.
3. Final Answer
Answer = 0 ✅
0 employees changed groups more than once up to the beginning of Quarter 4.
Question 3
What was Bunty's score at the end of Quarter 3?
Solution
1. Setup
Bunty starts in Elite in Q1 and is demoted to Novice after Q1. He remains in Novice through Q3.
Since Bunty is demoted after Q1, his Q1 rating must be the lowest rating in Elite:
$$ \text{Bunty's Q1 rating}=1 $$
His Q2 rating is directly given as 1.
Therefore, his cumulative score after Q2 is:
$$ 1+1=2 $$
2. Solution
In Q3, the Novice group consists of Asha, Bunty, and Dolly.
Lalu assigns distinct ratings of 1, 2, and 3. We know:
- Asha's Q3 rating = 1
- Dolly's Q3 rating = 2
Therefore, Bunty must receive the remaining rating of 3.
| Quarter | Bunty's Rating | Cumulative Score |
|---|---|---|
| Q1 | 1 | 1 |
| Q2 | 1 | 2 |
| Q3 | 3 | 5 |
Hence, Bunty's score at the end of Q3 is:
$$ 1+1+3=5 $$
3. Final Answer
Answer = 5 ✅
Bunty's score at the end of Quarter 3 is 5.
Question 4
For how many employees can the scores at the end of Quarter 3 be determined with certainty?
Solution
1. Setup
We determine whether the complete rating sequence of each employee through Q3 can be uniquely established from the given conditions.
The key ambiguity is between Asha and Chintu's Q1 ratings.
2. Solution
| Employee | Q1 | Q2 | Q3 | Score after Q3 | Certain? |
|---|---|---|---|---|---|
| Bunty | 1 | 1 | 3 | 5 | ✓ |
| Dolly | 2 | 2 | 2 | 6 | ✓ |
| Falguni | 3 | 3 | 3 | 9 | ✓ |
| Eklavya | 1 | 3 | 2 | 6 | ✓ |
| Asha | 2 or 3 | 1 | 1 | 4 or 5 | ✗ |
| Chintu | 3 or 2 | Depends | 1 | Not unique | ✗ |
Bunty
Bunty is demoted after Q1, so his Q1 rating is 1. His Q2 rating is given as 1, and his Q3 rating is 3 by elimination.
$$ 1+1+3=5 $$
Thus, Bunty's score is certain.
Dolly
Dolly receives the same rating in every quarter and gets 2 in Q3.
$$ 2+2+2=6 $$
Thus, Dolly's score is certain.
Falguni
Falguni also receives the same rating in every quarter. Her rating is 3 in each quarter.
$$ 3+3+3=9 $$
Thus, Falguni's score is certain.
Eklavya
Eklavya's Q1 and Q2 ratings are 1 and 3 respectively. The Q3 group is Elite = {Chintu, Eklavya, Falguni}. Since Chintu must be the employee demoted after Q3 and Falguni has a fixed rating of 3, Eklavya must receive 2 in Q3.
$$ 1+3+2=6 $$
Thus, Eklavya's score is certain.
Asha and Chintu
In Q1, Bunty receives 1, while Asha and Chintu receive 2 and 3 in some order.
Therefore, Asha's Q1 rating could be 2 or 3, giving different cumulative scores. Chintu's score is likewise not uniquely determined.
Hence, only Bunty, Dolly, Falguni, and Eklavya have scores that can be determined with certainty.
3. Final Answer
Answer = 4 ✅
The scores at the end of Quarter 3 can be determined with certainty for 4 employees.
Question 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.
Solution
1. Setup
We evaluate each statement using the deductions established from the previous questions.
2. Solution
Statement I
Asha received a rating of 2 in Quarter 1.
This is not necessarily true. Asha's Q1 rating can be either 2 or 3, depending on the rating received by Chintu.
Therefore, Statement I is not necessarily true.
Statement II
Asha received a rating of 1 in Quarter 2.
This is definitely true from the group composition and rating constraints in Quarter 2.
Therefore, Statement II is necessarily true.
Hence, only Statement II is necessarily true.
3. Final Answer
Answer = Option D ✅
Only II is necessarily true.