Title: CAT 2024 Slot 3 Quantitative Ability Solutions & Strategies for Game-Based Problems
Introduction
The CAT (Common Admission Test) 2024 exam includes a Quantitative Ability (QA) section with challenging game-based problems. These questions often involve logical reasoning, data interpretation, and mathematical modeling. Below are key strategies and solutions for common game-related topics in Slot 3 QA.
1. Game Theory & Combinatorics
Example Question:
A team of 8 players is divided into two groups of 4 each. In how many ways can this be done if two specific players must be in different groups?
Solution:
Total ways without restrictions: ( \binom{8}{4} = 70 ).
Subtract cases where both specific players are in the same group:
Fix both players in Group 1. Choose 2 more from 6: ( \binom{6}{2} = 15 ).
Similarly for Group 2: ( 15 ).
Total invalid cases: ( 15 \times 2 = 30 ).
Valid ways: ( 70 - 30 = 40 ).
Key Strategy: Use combinatorial logic and subtract invalid cases to avoid overcounting.
2. Probability & Game Scenarios
Example Question:
A game involves rolling two dice. What is the probability that the sum is 7 or the product is 12?
Solution:
Total outcomes: ( 6 \times 6 = 36 ).
Sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 outcomes.
Product = 12: (3,4), (4,3), (2,6), (6,2) → 4 outcomes.
Overlap (sum 7 and product 12): None.
Probability: ( \frac{6 + 4}{36} = \frac{10}{36} = \frac{5}{18} ).
Key Strategy: Use mutually exclusive events and avoid double-counting overlaps.
3. Data Interpretation (DI) with Games
Example Question (Table Analysis):
A table shows the number of participants in three games (X, Y, Z) across two age groups (18–25, 26–35). Solve the following:
Age Group
Game X
Game Y
Game Z
18–25
120
80
150
26–35
90
110
60
What % of 26–35 participants played Game Y?
How many more participants played Game Z in 18–25 than in 26–35?
Solution:
Total 26–35: ( 90 + 110 + 60 = 260 ).
% in Game Y: ( \frac{110}{260} \times 100 \approx 42.31% ).
Difference in Game Z: ( 150 - 60 = 90 ).
Key Strategy: Calculate totals first, then derive percentages and differences.
4. Time Management Tips
Skim questions quickly—game-based problems often require multiple steps.
分配时间: Allocate 2 minutes for easy combinatorics, 3–4 minutes for complex probability.
验证答案: Use approximations (e.g., for % questions) to check reasonableness.
5. Common Pitfalls to Avoid
Miscounting combinations: Use ( \binom{n}{k} ) formulas rigorously.
Overlooking overlaps: Apply inclusion-exclusion principles for probability.
Ignoring units: Convert percentages to decimals before calculating.
Final Practice advice:
Solve 3–4 game-based QA questions daily from CAT 2024 mock tests.
Focus on topics like permutations/combinations, probability, and data tables.
Good luck with your CAT 2024 preparation! 🚀
Let me know if you need further clarification on specific questions!
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