Question

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

• A. Neither I nor II
• B. Both I and II
• C. Only I
• D. Only II

Answer 1

Correct Answer: 4

Approach: Eklavya's Q2 score is just the sum of his Q1 and Q2 ratings, so we only need to nail those two ratings using the Novice line-up each quarter.

Recall the rules: two groups of three, distinct ratings \(\{1,2,3\}\) per group per quarter, score is the running rating total, and each quarter the top Novice is promoted while the bottom Elite is demoted. Asha, Bunty, Chintu start in Elite; Dolly, Eklavya, Falguni start in Novice. Dolly and Falguni keep constant ratings; only they do.

Step 1 — Eklavya in Q1. In Novice (Q1) with Falguni constant and the highest Q1 Novice rating going to the promoted Falguni, the consistent split is Falguni \(=3\), Dolly \(=2\), so Eklavya \(=1\). Falguni (score \(3\)) is promoted to Elite.

Step 2 — Eklavya in Q2. After Q1, Novice \(=\{\)Bunty, Dolly, Eklavya\(\}\). Given Bunty \(=1\) (Lalu) and Dolly \(=2\) (constant), the remaining rating goes to Eklavya: \(=3\).

Step 3 — add them up.

\[ \text{Eklavya's Q2 score} = 1 + 3 = 4. \]

Final answer: 4.

Answer 2

Build the Quarter 1 picture first. Elite (Kuku) = Asha, Bunty, Chintu; Novice (Lalu) = Dolly, Eklavya, Falguni. Since Bunty is demoted after Quarter 1 (Lalu rates him in Q2, so he must have moved to Novice), Bunty was the lowest-rated Elite member in Q1, so \( \text{Bunty's Q1 rating} = 1 \).
Dolly and Falguni keep the same rating every quarter (given), so their Quarter 1 ratings are two of \( \{1,2,3\} \), leaving Eklavya the third value. Dolly's constant rating turns out to be 2 (confirmed later from her Quarter 3 rating), so Falguni and Eklavya split \( \{1,3\} \).
The Quarter-1-end promotion takes the top scorer of Novice into Elite. Since Falguni is the one who ends up in Elite from Quarter 2 onward, her constant rating must be the group maximum, 3 — so \( \text{Falguni}=3,\ \text{Eklavya}=1 \) in Q1.
Eklavya therefore stays in Novice for Quarter 2, alongside Bunty and Dolly. Lalu's Q2 ratings for this trio must again be \( \{1,2,3\} \): Bunty is given as 1, Dolly stays at her constant value 2, so Eklavya gets the remaining rating, 3.
Eklavya's score at the end of Quarter 2 = Q1 rating + Q2 rating = \( 1 + 3 = 4 \).

Answer 3

To determine how many employees changed groups more than once up to the beginning of Quarter 4, we need to analyze the movements across the three quarters given the rules and initial conditions. 

We start with Asha, Bunty, and Chintu in the Elite group in Q1, implying Dolly, Eklavya, and Falguni are in the Novice group. We know the employee with the highest score in Novice moves to Elite, and the one with the lowest score in Elite moves to Novice at the end of each quarter. Let’s track the movements:

1. Quarter 1 to Quarter 2:
   • Novice members with their ratings in Q1: Assume Dolly (Rating 2), Eklavya, Falguni. Bunty receives a rating of 1 in Q2.
   • Asha receives a rating of 1, ensuring she moves from Elite to Novice after adding their scores and tie-breaking by latest ratings.
   • Chintu moves to Novice after summing the scores and considering tie-breaks.
2. Quarter 2 to Quarter 3:
   • Novice group now includes: Asha, Bunty, Chintu (since Dolly and Falguni have fixed ratings series and wouldn’t tie or have the highest score). Their scores competed with their ratings only per rule explanation.
   • Asha's cumulative higher score keeps her ranking above others & subsequently Alter Chintu lowers for highest.
   • Eklavya arrives in Elite due to errors primarily by tracking the scores & movements.
3. Quarter 3 to Quarter 4:
   • Recorded initial movements show Bunty constantly moves each quarter from Elite to Novice.
   • Asha has returned back to Novice before start of Q4 with scored references challenging all novices.
   • Final notes conclude Dolly & Falguni constant in Novice with ratings.

Now, evaluate the groups:

• Asha: Elite (Q1), Novice (Q2), Elite (Q3). Moves=2.
• Bunty: Elite (Q1), Novice (Q2, moved back to Elite in Q3). Moves=2.
• Chintu: Elite (Q1), changed camps due Novice Q2, less likely to Elite Q3. Total Moves=1.

Conclusively, both Asha and Bunty moved more than once across the quarters, whereas others remained consistent or followed single protocol switches. Verify their exact number within comprehensive & calculated evaluations shows:

Answer: 2 employees changed groups more than once.

Answer 4

Track every employee's group across the quarters using the timeline built from the clues:
Quarter 1: Elite = Asha, Bunty, Chintu; Novice = Dolly, Eklavya, Falguni.
Quarter-1-end: Bunty demoted, Falguni promoted → Quarter 2 Elite = Asha, Chintu, Falguni; Novice = Bunty, Dolly, Eklavya.
Quarter-2-end: Asha demoted (she is rated by Lalu in Q3), Eklavya promoted (her score ties Dolly's but her higher Q2 rating breaks the tie in her favour) → Quarter 3 Elite = Chintu, Falguni, Eklavya; Novice = Asha, Bunty, Dolly.
Quarter-3-end: Chintu demoted (needed so Asha, Bunty and Chintu are all in Novice by Quarter 4), Dolly promoted (she has the highest Novice score that quarter) → Quarter 4 Elite = Falguni, Eklavya, Dolly; Novice = Asha, Bunty, Chintu.
Counting moves: Bunty once, Falguni once, Asha once, Eklavya once, Chintu once, Dolly once. Every employee changes groups exactly once across the three quarter-ends — nobody switches twice.

Answer 5

Approach: Bunty's Q3 score is the sum of his three ratings. We already know two of them and can deduce the third from the Q3 Novice line-up.

Recall: distinct ratings \(\{1,2,3\}\) per group per quarter; Bunty starts in Elite; Bunty got \(1\) from Lalu in Q2; Asha got \(1\) and Dolly got \(2\) from Lalu in Q3.

Step 1 — Bunty in Q1. Bunty is demoted from Elite at the end of Q1 (he is in Novice in Q2), so he was the lowest-scoring Elite that quarter; his Q1 rating is \(1\).

Step 2 — Bunty in Q2. Given directly: Bunty \(=1\).

Step 3 — Bunty in Q3. In Q3 the Novice trio is Asha, Bunty, Dolly with Asha \(=1\) and Dolly \(=2\). The remaining distinct rating is \(3\), so Bunty \(=3\).

Step 4 — total.

\[ \text{Bunty's Q3 score} = 1 + 1 + 3 = 5. \]

Final answer: 5.

Answer 6

From the Quarter-1-end swap, Bunty is the Elite member demoted, meaning he had the lowest of the three distinct Elite ratings \( \{1,2,3\} \) in Quarter 1, so \( \text{Bunty's Q1 rating} = 1 \).
Bunty's Quarter 2 rating is given directly by Lalu: \( 1 \).
In Quarter 3, Bunty is still in Novice, now alongside Asha and Dolly (Asha having been demoted after Quarter 2). Lalu's Quarter 3 ratings are given as Asha = 1 and Dolly = 2; since Novice ratings that quarter must be the distinct set \( \{1,2,3\} \), Bunty is left with the only unused value, 3.
Bunty's score at the end of Quarter 3 is his cumulative rating: \( 1 + 1 + 3 = 5 \).

Answer 7

Approach: 'Determined with certainty' means the score is forced no matter which valid filling we pick. So find every rating that is pinned by the clues, and flag whoever still has a free choice.

What is pinned. Dolly \(=2\) and Falguni \(=3\) every quarter (constant). Bunty \(=1\) in Q1 (demoted), \(=1\) in Q2 (given), \(=3\) in Q3 (only value left in Novice). Eklavya \(=1\) in Q1, \(=3\) in Q2, and \(=2\) in Q3 (forced by his Elite trio).

Step 1 — the four certain scores after Q3:

Bunty: \(1+1+3 = 5\).
Dolly: \(2+2+2 = 6\).
Eklavya: \(1+3+2 = 6\).
Falguni: \(3+3+3 = 9\).

Step 2 — the uncertain ones. Asha's Q1 Elite rating is not forced (she can be \(2\) or \(3\)), so her Q3 score is either \(4\) or \(5\). Chintu's Q1 Elite rating shifts correspondingly, so his Q3 score is either \(5\) or \(6\). Neither is fixed.

Step 3 — count. Exactly four employees — Bunty, Dolly, Eklavya, Falguni — have a Q3 score that is determined with certainty.

Final answer: 4.

Answer 8

Working out every employee's Quarter 3 end score: Bunty = \( 1+1+3 = 5 \); Dolly = \( 2+2+2 = 6 \) (constant rating 2 every quarter); Falguni = \( 3+3+3 = 9 \) (constant rating 3 every quarter); Eklavya = \( 1+3+2 = 6 \). These four are pinned down completely by the direct clues and the distinct-ratings rule, with no leftover choice.
Asha and Chintu are different: the only fact fixing their Quarter 1 Elite ratings is that together with Bunty's rating of 1, the pair \( \{Asha, Chintu\} \) must take \( \{2,3\} \) in Quarter 1 — but nothing in the clues says which of them gets 2 and which gets 3. Both assignments survive every check (the Quarter 2-end tie-break and the Quarter 3-end demotion of Chintu both work out consistently either way), giving Asha a score of either 4 or 5, and Chintu correspondingly either 6 or 5, at the end of Quarter 3.
So only 4 of the 6 employees (Bunty, Dolly, Eklavya, Falguni) have a Quarter 3 score that can be pinned down with certainty.

Answer 9

Approach: 'Necessarily true' means true in every valid filling. Test each statement against the one free choice in the grid; if it survives both cases it is necessary, otherwise it is not.

The one free choice. Bunty's Q1 Elite rating is \(1\) (he is demoted). The other two Elite values \(\{2,3\}\) split between Asha and Chintu in either order — that is the only freedom the clues leave.

Statement I: Asha received rating \(2\) in Q1. Asha could take \(2\) or \(3\) in Q1 — both lead to consistent grids. So this is possible but not forced. Not necessarily true.

Statement II: Asha received rating \(1\) in Q2. After Q1, Asha is still in Elite; she is demoted to Novice at the end of Q2. In Q2 the Novice trio (Bunty, Dolly, Eklavya) already uses up the ratings Bunty \(=1\), Dolly \(=2\), Eklavya \(=3\). When Asha lands in Novice for Q3 she is rated \(1\) there... and tracing the Elite side, Asha's Q2 rating in Elite is forced to the value that makes her the demoted member: \(1\). Every valid grid gives Asha \(=1\) in Q2. Necessarily true.

Conclusion. Only Statement II must hold.

Final answer: Only II.

Answer 10

Step 1: Recall the structure of valid scenarios. & nbsp;
From the earlier analysis (Q.5–Q.8), all valid configurations must satisfy:

• Group memberships at the beginning of each quarter are fixed (who is in Elite/Novice each quarter).
• Dolly and Falguni have the same rating in all 4 quarters, and no one else does.
• Bunty gets rating \(1\) in Quarter 2 from Lalu (so he is in Novice in Q2).
• In Quarter 3 Novice, Asha gets rating \(1\) and Dolly gets rating \(2\) from Lalu.

Under these constraints, there are multiple possible assignments of ratings over the 4 quarters. 
Step 2: Exhibit two valid global scenarios.
Below are two complete rating patterns (for Q1--Q3) that both satisfy all the puzzle conditions, including promotions/demotions and tie-breaking rules. Scenario I: \[ \begin{array}{c|ccc} \text{Employee} & amp; \text{Q1} & amp; \text{Q2} & amp; \text{Q3} \\ \hline \text{Asha (A)} & amp; 2 & amp; 1 & amp; 1 \\ \text{Bunty (B)} & amp; 1 & amp; 1 & amp; 3 \\ \text{Chintu (C)} & amp; 3 & amp; 2 & amp; 1 \\ \text{Dolly (D)} & amp; 2 & amp; 2 & amp; 2 \\ \text{Eklavya (E)} & amp; 1 & amp; 3 & amp; 2 \\ \text{Falguni (F)} & amp; 3 & amp; 3 & amp; 3 \\ \end{array} \] Scenario II: \[ \begin{array}{c|ccc} \text{Employee} & amp; \text{Q1} & amp; \text{Q2} & amp; \text{Q3} \\ \hline \text{Asha (A)} & amp; 3 & amp; 1 & amp; 1 \\ \text{Bunty (B)} & amp; 1 & amp; 1 & amp; 3 \\ \text{Chintu (C)} & amp; 2 & amp; 2 & amp; 1 \\ \text{Dolly (D)} & amp; 2 & amp; 2 & amp; 2 \\ \text{Eklavya (E)} & amp; 1 & amp; 3 & amp; 2 \\ \text{Falguni (F)} & amp; 3 & amp; 3 & amp; 3 \\ \end{array} \] In both scenarios:

• Each group in each quarter has ratings \(1,2,3\) exactly once.
• Dolly and Falguni keep constant ratings (2 and 3 respectively) across quarters.
• Bunty is in Novice in Q2 with rating \(1\).
• In Q3 Novice, Asha has rating \(1\), Dolly has rating \(2\).
• Promotions/demotions based on cumulative scores (with latest-quarter rating as tie-breaker) produce the required group memberships, including Asha, Bunty, and Chintu all being in Novice at the beginning of Q4.

Thus both scenarios are fully consistent with all the given information. Step 3: Check statements I and II.
From the two valid scenarios: \[ \begin{array}{c|cc} & amp; \text{Scenario I} & amp; \text{Scenario II} \\ \hline \text{Asha's Q1 rating} & amp; 2 & amp; 3 \\ \text{Asha's Q2 rating} & amp; 1 & amp; 1 \\ \end{array} \]

• Statement I: “Asha received a rating of 2 in Quarter 1.” In Scenario I this is true, but in Scenario II it is false. So it is not necessarily true.
• Statement II: “Asha received a rating of 1 in Quarter 2.” In both scenarios Asha’s Q2 rating is \(1\), and in fact in every valid configuration this is forced (once all constraints and movements are applied). Hence, Statement II is necessarily true.

Therefore, only Statement II is necessarily true. \[ \boxed{\text{Correct option: 4. Only II}} \]