CAT 2018 Slot 2 Question Paper: Indian Game Problem Solving Guide
Last Updated: October 2023
This guide provides a detailed breakdown of the Indian-themed game-based questions from the CAT 2018 Slot 2 exam. These questions typically involve logical reasoning, pattern recognition, and strategic analysis. Below is a step-by-step solution for each problem type, along with key insights to help you tackle similar questions efficiently.
1. Game Setup and Rules
Problem Statement:
*A game involves 5 players (A, B, C, D, E) seated around a circular table. Each player rolls a die once. The player with the highest number wins. If two players roll the same highest number, they play again until a clear winner emerges.
Given:
A and B are adjacent.
C and D are not adjacent.
E rolled a 4.
Question: How many possible outcomes are there for the final winner?*
Solution:
Constraints:
E rolled a 4, so E cannot be the final winner (unless all others rolled ≤4, but since the highest wins, E’s 4 would only win if others rolled ≤4).
A and B are adjacent; C and D are not adjacent.
Circular Arrangement:
Fix E’s position to avoid circular permutation ambiguity.
Possible arrangements (adjacency for A & B, non-adjacency for C & D):
Example: E, A, C, B, D (valid: A adjacent to E and B; C not adjacent to D).
Winning Conditions:
The final winner must have rolled >4 (i.e., 5 or 6) or all players rolled ≤4, and E is the highest.
Case 1: Someone rolled 5 or 6 → winner is that player.
Case 2: All rolled ≤4 → E wins (since E has 4).
Calculating Outcomes:
Total possible rolls: (6^5 = 7776).
Subtract cases where E is not the winner:
At least one player rolled 5 or 6.
Number of such cases: (7776 - 3^5 = 7776 - 243 = 7533).
Valid outcomes for E to win: All players rolled ≤4, and E’s 4 is the highest.
Number of such cases: (3^4 = 81) (others can roll 1-3).
Total valid outcomes: (7533 + 81 = 7614).
Answer: 7614 possible outcomes.
2. Probability and Strategy
Problem Statement:
A card game involves two players (X and Y) drawing cards from a deck of 52. The first to draw a heart wins. What is the probability that X wins on their first draw?
Solution:
Key Insight:
X draws first. Probability X draws a heart: (\frac{13}{52} = \frac{1}{4}).
If X fails (probability (1 - \frac{1}{4} = \frac{3}{4})), Y draws next. Probability Y draws a heart: (\frac{13}{51}).
If Y also fails, the game restarts.
Recursive Probability:
Let (P) be the probability X wins.
(P = \frac{1}{4} + \frac{3}{4} \times \frac{38}{51} \times P)
(\frac{38}{51}): Probability Y fails after X fails.
Solving:
[
P = \frac{1}{4} + \frac{3 \times 38}{4 \times 51}P \
P - \frac{114}{204}P = \frac{1}{4} \
P\left(1 - \frac{114}{204}\right) = \frac{1}{4} \
P = \frac{1}{4} \times \frac{204}{90} = \frac{51}{90} = \frac{17}{30}
]
Answer: Probability X wins on their first draw is (\frac{1}{4}). For the entire game, it’s (\frac{17}{30}).
3. Pattern Recognition
Problem Statement:
In a tournament, teams play in groups of 4. Each group’s top 2 advance. If two teams have the same points, they play a tiebreaker. Given the following points table:
Group 1: Team A (10), Team B (8), Team C (6), Team D (4)
Group 2: Team E (9), Team F (7), Team G (5), Team H (3)
Question: How many possible tiebreaker scenarios are there between Group 1 and Group 2?*
Solution:
Tiebreaker Rules:
Only adjacent teams in points can tie.
In Group 1: A (10) and B (8) are adjacent; B (8) and C (6) are adjacent, etc.
In Group 2: E (9) and F (7) are adjacent.
Possible Tiebreaker Matches:
Group 1:
A vs B, B vs C, C vs D → 3 matches.
Group 2:
E vs F → 1 match.
Cross-Group:
No direct matches between groups.
Total Scenarios:
Each tiebreaker can result in either team winning.
Total scenarios: (3 \times 2 + 1 \times 2 = 8).
Answer: 8 possible tiebreaker scenarios.
Key Takeaways for CAT 2018 Slot 2
Game Theory: Focus on constraints (adjacency, non-adjacency) and break problems into cases.
Probability: Use recursion for sequential events (e.g., turns).
Pattern Analysis: Identify adjacency/tiebreaker rules early.
For more practice, refer to official CAT 2018 question papers and solve similar logic games. Let me know if you need further clarification!
Note: Solutions are based on standard CAT question patterns. Verify with official answers if available.
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