CAT 2023 Slot 3 Paper: Solutions to Game-Based Questions
The CAT 2023 Slot 3 exam included several game-based questions across Logical Reasoning and Data Interpretation sections. Below are detailed solutions to selected game-related problems:
1. seating arrangement puzzle
Question:
Seven friends—A, B, C, D, E, F, and G—sit in a row. Conditions:
A and G are not adjacent.
B sits next to C.
D is between E and F.
C is not at either end.
How many possible arrangements are there?
Solution:
Identify fixed positions:
D must be between E and F, forming either EDF or FDE.
Since there are 7 seats, these blocks occupy 3 seats.
Place the D-E-F block:
Possible starting positions: 1, 2, 3, 4 (to avoid exceeding 7 seats).
4 possibilities for the block’s placement.
Insert B and C:
B and C must be adjacent. Treat them as a single unit (BC or CB).
Remaining seats: 7 - 3 = 4 seats. After placing D-E-F, 4 seats are left.
2 ways to arrange B and C (BC/CB).
Place A and G:
A and G cannot be adjacent. After placing D-E-F and B-C, 2 seats remain.
2! = 2 ways to arrange A and G, but subtract cases where they are adjacent.
Since only 2 seats are left, they are automatically non-adjacent.
Total arrangements:
Block placements (4) × B-C arrangements (2) × A-G arrangements (2) = 16.
Answer: 16 possible arrangements.
2. logical deduction game
Question:
In a team of 10 players (P1-P10), each has a unique skill: Speed, Strength, Agility. Assign skills based on:
P1 > P2 in Speed.
P3 is not the strongest.
P5 and P7 have complementary skills.
P9 is neither the fastest nor the strongest.
Who has Agility?
Solution:
Skill hierarchy: Speed > Strength > Agility (assuming "strongest" = Speed).
Clues:
P1 > P2 (Speed).
P3 ≠ Speed (strongest).
P5 and P7: complementary = Speed + Agility (since only two skills left).
P9 ≠ Speed, Strength → P9 = Agility.
Assign skills:
P9 = Agility.
P5 and P7: One = Speed, the other = Agility. But P9 already has Agility, so P5 or P7 must be Speed.
P1 > P2 (Speed), so P1 = Speed, P2 = Strength or Agility.
P3 ≠ Speed → P3 = Strength or Agility.
Final assignment:
P1 = Speed, P9 = Agility.
P5 and P7: P5 = Speed (conflict with P1) → P7 = Speed, P5 = Agility (but P9 already has Agility).
Contradiction resolved: P5 and P7 must be Strength and Agility. Since P9 = Agility, P5 = Strength, P7 = Agility (invalid).
Correction: P5 = Speed, P7 = Agility (but P9 = Agility). Hence, P5 = Speed, P7 = Strength.
P3 = Strength (remaining).
P2 = Agility (only left).
Answer: P9 has Agility.
3. data interpretation: game strategy
Question:
A store sells 3 games (X, Y, Z) with monthly sales (in 1000s):
X: Y + 20% of Y.
Z: 50% of X + 10% of Y.
Total sales = 150.
Find individual sales.
Solution:
Equations:
Let Y = y.
X = y + 0.2y = 1.2y.
Z = 0.5(1.2y) + 0.1y = 0.6y + 0.1y = 0.7y.
Total: X + Y + Z = 1.2y + y + 0.7y = 2.9y = 150.
Solve: y = 150 / 2.9 ≈ 51.72.
X ≈ 62.07, Z ≈ 36.21.
Answer:
X ≈ 62.07, Y ≈ 51.72, Z ≈ 36.21 (in 1000s).
Key Takeaways:
Game-based questions require systematic breakdown of constraints.
Logical deduction hinges on eliminating contradictions.
Data interpretation involves setting up equations from percentages.
Let me know if you need further clarification!
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