CAT 2021 Slot 1 Paper: Analyzing a Sample Game-Based Logic Problem
Introduction
The CAT (Common Admission Test) 2021 exam included a logic-based reasoning section with a hypothetical "India-themed game" scenario. Below is a reconstructed example of a typical question from Slot 1, followed by a detailed solution. This problem tests analytical reasoning, conditional statements, and sequence deduction.
Sample Question (Hypothetical):
Five players—A, B, C, D, and E—participate in a game called "Rajasthan Rummy." The game follows these rules:
Rule 1: A player cannot play two consecutive cards of the same suit.
Rule 2: The sequence must start with a Spade and end with a Heart.
Rule 3: If a card is a King, the next card must be a Queen.
Rule 4: B and D cannot be adjacent in the sequence.
Given the initial card suit sequence: Spade, Heart, Diamond, Club, determine the possible valid completion of the sequence.
Solution:
Understand the Constraints:
The sequence starts with Spade (S) and ends with Heart (H).
The current sequence is: S, H, D, C.
Next card must be a Heart (Rule 2).
Apply Rule 1 (No consecutive suits):
Previous suit is Club (C). The next card must be Heart (H) but cannot follow Club.
Conflict: Rule 2 requires ending with H, but Rule 1 forbids C followed by H.
Reinterpret Rule 2: The sequence must start with S and end with H, but the ending H could be the final card.
Adjust Sequence to Meet All Rules:
Current sequence: S, H, D, C.
Next card must be H (Rule 2), but Rule 1 prohibits C → H.
Fix: Insert a card between C and H to break the consecutive suits.
Possible intermediate suits: Spade (S) or Diamond (D).
Check Rule 3 (King → Queen):
Assume the intermediate card is Spade (S). If S is a King, the next card must be Queen (Q). However, the final card must be H, which may not be a Queen.
If intermediate card is Diamond (D), no King/Qwen constraint applies.
Final Valid Sequence:
S, H, D, C, S, H
Verify all rules:
No consecutive suits: S→H→D→C→S→H (valid).
Starts with S, ends with H (Rule 2).
No King/Qwen conflicts (assumed no Kings in intermediate cards).
B and D are not adjacent (if B and D are assigned to positions 2 and 3, this is violated; adjust player positions accordingly).
Alternative Solution:
If the intermediate card is a Heart (H), but Rule 1 prohibits C→H. Thus, invalid.
Only valid completion is S, H, D, C, S, H.
Key Takeaways for CAT备考:
Prioritize Endgame Constraints: Always check the final requirement (e.g., ending with H) early.
Leverage Intermediate Variables: Insert temporary cards to resolve conflicts between rules.
Player Adjacency: For problems involving player positions (e.g., B and D not adjacent), map players to sequence positions and use exclusion principles.
Common Pitfalls:
Overlooking Rule 1’s consecutive suit restriction.
Ignoring the interdependence of Rules 2 and 3.
Failing to test intermediate card possibilities.
This approach ensures systematic deduction and aligns with CAT’s emphasis on logical structuring. For authentic practice, refer to official CAT mock tests and analyze similar game-based problems.
Note: The above question is a hypothetical reconstruction. Actual CAT 2021 questions may differ. Always verify with official resources.
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