DIRECTIONS for questions: Read the information given below and answer the question that follows.

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.

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

The correct answer is 5.

Let us analyze the initial team composition and the quarterly transitions. At the beginning of Q₁, the Elite group consists of Asha, Bunty, and Chintu, while the Novice group consists of Dolly, Eklavya, and Falguni. By the beginning of Q₄, Asha, Bunty, and Chintu are all in Novice. Since one employee is demoted and one is promoted each quarter, Asha, Bunty, and Chintu must have each been demoted exactly once during the first three quarters (Q₁, Q₂, and Q₃) and never promoted. Consequently, Dolly, Eklavya, and Falguni were each promoted exactly once and never demoted.

Next, we determine the exact sequence of demotions and promotions. From the given conditions, Lalu (who leads the Novice group) rated Bunty a 1 in Q₂. This means Bunty was in the Novice group in Q₂, and therefore, must have been the one demoted at the end of Q₁. Lalu also rated Asha a 1 and Dolly a 2 in Q₃. This places Asha in Novice in Q₃, meaning she was demoted at the end of Q₂. By elimination, Chintu was demoted at the end of Q₃. Since Dolly was in Novice in Q₃ (having started there and not yet been promoted), she must be the employee who gets promoted at the end of Q₃.

We know Dolly and Falguni received the same rating across all quarters. In Q₃, Dolly received a rating of 2 in Novice. Therefore, Dolly's rating is 2 in every quarter. In Q₁, the Novice group consists of Dolly, Eklavya, and Falguni. If Falguni's constant rating was 1, then Eklavya would receive a 3 (since ratings 1, 2, and 3 are distinct) and get promoted. In Q₂, the Novice group would then contain Dolly (rating 2), Falguni (rating 1), and Bunty. But we know Bunty received a 1 in Q₂, which would mean two employees got a rating of 1, violating the distinct rating rule. Thus, Falguni's constant rating must be 3.

Let us trace the Novice group's scores quarter by quarter:

In Q₁, the Novice ratings are Falguni (3), Dolly (2), and Eklavya (1). Falguni has the highest score and is promoted.

In Q₂, the Novice members are Dolly (2), Eklavya, and Bunty (1). To have distinct ratings, Eklavya must receive a 3. Dolly's cumulative score becomes:
$2+2=4$
Eklavya's score becomes:
$1+3=4$
They tie, but Eklavya is promoted because his Q₂ rating of 3 is higher than Dolly's 2.

In Q₃, the Novice members are Dolly (2), Bunty, and Asha (1). To maintain distinct ratings, Bunty must receive a 3. Dolly's cumulative score is now:
$2+2+2=6$

For Dolly to be promoted at the end of Q₃ over Bunty, her score must win against Bunty's score. Bunty's cumulative score at the end of Q₃ is his Q₁ rating (while in Elite) plus his Q₂ and Q₃ ratings:
$Q_1+1+3$
If his Q₁ rating had been 2, his total score would be:
$2+1+3=6$
This would result in a tie with Dolly. Bunty would have won this tie because his Q₃ rating of 3 is higher than Dolly's 2. Because Dolly is the one who actually gets promoted, Bunty's score must be strictly less than 6. Thus, Bunty's Q₁ rating must have been 1.

Therefore, Bunty's final score at the end of Q₃ is:
$1+1+3=5$