Title: CAT 2024 QA Slot 2: Solving Quantitative Ability Problems Through Indian Game Strategy
The CAT (Common Admission Test) 2024 Quantitative Ability (QA) section will likely include problems that blend mathematical concepts with logical reasoning. Given India’s rich gaming culture, questions inspired by traditional or popular Indian games could appear. Below, we analyze potential QA problems inspired by Indian games and provide strategies to solve them efficiently.
1. Game-Based Probability Question
Example Problem:
In a Rummy game, you have a hand of 13 cards from a deck of 52 cards (values 1-10, four suits). What is the probability of forming a sequence of three consecutive numbers (e.g., 3-4-5) with at least one card repeated?
Solution Strategy:
Break Down the Problem:
Total ways to form a sequence: Choose 3 consecutive numbers (e.g., 1-2-3, 2-3-4, ..., 8-9-10) → 8 possible sequences.
For each sequence, calculate valid combinations with at least one repeat.
Combinatorial Calculations:
Total sequences without restriction: (8 \times 4^3) (4 suits per card).
Subtract sequences with all distinct cards: (8 \times 4 \times 3 \times 2).
Probability = (\frac{\text{Valid Sequences}}{\text{Total Possible Sequences}}).
Key Insight: Use complementary probability to simplify calculations.
2. Strategic Decision-Making in Kabaddi
Example Problem:
A Kabaddi team has 7 players. The captain can choose a player to rotate every 10 minutes. What is the minimum number of rotations needed to ensure each player gets at least 3 turns in a 60-minute game?
Solution Strategy:
Model the Problem:
Total rotations = (60 / 10 = 6) rotations.
Each rotation assigns 1 player.
constraint: Each player needs ≥3 turns.
Pigeonhole Principle:
If 7 players need 3 turns each, total required turns = (7 \times 3 = 21).
But only 6 rotations are available → Impossible.
Reinterpret: The question likely assumes rotations can involve multiple players. Adjust the model accordingly.
Alternative Approach:
If rotations allow substituting 1 player per turn, total substitutions = 6.
Distribute 6 substitutions among 7 players. The minimum turns a player can get = (\lfloor 6/7 \rfloor = 0).
To ensure fairness, use optimization: Assign 3 turns to 2 players and 2 turns to 5 players.
Key Insight: Clarify constraints and use resource allocation principles.
3. Algebraic Word Problem Inspired by Ludo
Example Problem:
In a Ludo game, you roll two dice. What is the probability that the sum of the dice is a prime number AND the difference between the numbers is exactly 1?
Solution Strategy:
Prime Numbers in Ludo: Possible sums = 2, 3, 5, 7, 11.
Valid Outcomes:
Sum is prime and difference = 1.
Valid pairs: (1,2), (2,1), (2,3), (3,2), (4,5), (5,4), (5,6), (6,5).
Probability: ( \frac{8}{36} = \frac{2}{9} ).
Key Insight: List valid outcomes systematically to avoid missing cases.
4. Data Interpretation from Board Games
Example Problem:
*A survey of 1000 players shows the following preferences for Indian board games:
30% prefer Ludo,
25% prefer Rummy,
20% prefer Carrom,
15% prefer国际象棋 (Xiangqi),
10% prefer others.
If 20% of Ludo players also play Rummy, how many players play both Ludo and Rummy?*
Solution Strategy:
Calculate Overlapping Players:
Total Ludo players = (1000 \times 30% = 300).
20% of Ludo players also play Rummy = (300 \times 20% = 60).
Key Insight: Direct percentage application without complex Venn diagrams.
CAT QA 2024 Preparation Tips
Practice Game-Inspired Problems: Use traditional games to build intuition for probability, combinatorics, and strategy.
Time Management: Allocate 1-2 minutes per question for game-based problems.
Check Constraints: Always verify if the problem requires "at least" or "exactly" conditions.
By integrating game logic with mathematical rigor, CAT 2024 aspirants can tackle QA questions efficiently. For more practice, refer to past CAT papers and Indian gaming strategy analyses.
Word Count: 500
Target Audience: CAT 2024 candidates preparing for QA section.
Keywords: CAT 2024, QA, Quantitative Ability, Indian Games, Probability, Combinatorics.
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