Comprehension

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. & nbsp;
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 (Novice manager):
– Bunty received a rating of 1 in Quarter 2. & nbsp;
– 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?

Show Hint

For multi-step promotion puzzles:

First fix the group memberships quarter by quarter using “must be in this group” clues.
Then use special constraints (like “same rating every quarter”) to pin down exact values.
Often, even if many full tables are possible, the quantity asked (like one person’s score) is uniquely determined.
Updated On: Jul 4, 2026
Show Solution

Correct Answer: 4

Solution and Explanation

Step 1: Falguni and Dolly keep one fixed rating every quarter. Since the Quarter-1-end promotion goes to the top Novice scorer, and Falguni is the one who ends up promoted (she's in Elite from Quarter 2 on), her constant rating must be the group's maximum, 3.
Step 2: With Dolly's constant rating fixed at 2 and Falguni's at 3, Eklavya is left with the only remaining Quarter 1 Novice rating, 1.
Step 3: Falguni's promotion leaves Eklavya in Novice for Quarter 2, where Lalu's ratings must again be \( \{1,2,3\} \): Bunty = 1 (given), Dolly = 2 (constant), so Eklavya = 3.
Step 4: Score = sum of ratings received so far, \( 1 + 3 \).
\[ \boxed{4} \]
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Question: 2

Based on the above information about employee movements between Elite and Novice across the quarters, how many employees changed groups more than once up to the beginning of Quarter 4?

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In movement/transition puzzles:

First fix the group memberships at each time step.
Then create a simple table of positions over time for each person.
Counting changes from that table is much less error-prone than trying to track everyone mentally.
Updated On: Jul 4, 2026
Show Solution

Correct Answer: 0

Solution and Explanation

Step 1: Only three quarter-ends occur before Quarter 4 begins, and each swaps exactly one Elite member out and one Novice member in, only \( 3 \times 2 = 6 \) "movement slots" exist in total.
Step 2: The clue that Asha, Bunty and Chintu are all in Novice by Quarter 4 forces each of them to be demoted at a different one of the three quarter-ends, using up all three demotion slots.
Step 3: That leaves exactly three promotion slots, filled in turn by Falguni, Eklavya and Dolly, three different people, none repeated.
Step 4: Six movement slots exactly match the six employees, each appearing exactly once, so no one changes groups more than once.
\[ \boxed{0} \]
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Question: 3

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

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When cumulative scores determine promotions, always keep a running total per quarter—this quickly resolves later questions about individual scores.
Updated On: Jul 4, 2026
Show Solution

Correct Answer: 5

Solution and Explanation

Step 1: Bunty is demoted after Quarter 1, so his Q1 rating is the minimum of Elite's \( \{1,2,3\} \), i.e. \( 1 \).
Step 2: His Q2 Novice rating is directly given: \( 1 \).
Step 3: In Quarter 3, Novice consists of Asha, Bunty and Dolly. Asha = 1 and Dolly = 2 are given, so by the distinct-ratings rule Bunty takes the leftover value, 3.
Step 4: Cumulative score = \( 1+1+3 \).
\[ \boxed{5} \]
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Question: 4

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

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When a puzzle allows multiple consistent scenarios, try to construct at least two: if a particular value changes between them, it is {not} uniquely determined; if it remains the same across all valid setups, then it is.
Updated On: Jul 4, 2026
Show Solution

Correct Answer: 4

Solution and Explanation

Step 1: Four employees have their entire rating history forced by direct clues or the "constant rating" rule: Bunty (1,1,3), Dolly (2,2,2), Falguni (3,3,3), Eklavya (1,3,2), each totals to a single determinate score at the end of Quarter 3.
Step 2: Asha and Chintu only have their combined Quarter 1 ratings fixed (the remaining \( \{2,3\} \) after Bunty takes 1), no clue distinguishes which of them received 2 versus 3.
Step 3: Checking both possible assignments against the Quarter 2-end and Quarter 3-end swap rules (including the tie-break checks) shows both remain fully valid, so Asha's and Chintu's individual Quarter 3 scores each have two possible values.
Step 4: That leaves \( 6 - 2 = 4 \) employees whose Quarter 3 score is certain.
\[ \boxed{4} \]
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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.

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To test if a statement is {necessarily} true, try to construct at least two fully valid scenarios:

If the statement changes truth value between them, it is {not} necessary.
If it stays true in {all} valid scenarios you can build, it is a strong candidate for being necessarily true.
Updated On: Jul 2, 2026
  • Neither I nor II
  • Both I and II
  • Only I
  • Only II
Show Solution

The Correct Option is D

Solution and Explanation

Alternate method (two-case stress test): Build both possible grids and read off Asha's ratings.



The only undecided cell is Asha vs Chintu's Q1 Elite rating, the pair $\{2,3\}$.



Grid 1 — Asha Q1 $=2$: Asha's ratings come out $2, 1, 1$ across Q1, Q2, Q3.



Grid 2 — Asha Q1 $=3$: Asha's ratings come out $3, 1, 1$ across Q1, Q2, Q3.



Now test the statements. Statement I says Asha Q1 $=2$: true in Grid 1 but false in Grid 2, so not necessary. Statement II says Asha Q2 $=1$: true in both grids, so necessary.



Only Statement II holds in every case.



Final answer: Only II.

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