Title: 2023 DILR Slot 3: Analyzing Indian Games Through Logical Reasoning
Question Context
The 2023 DILR Slot 3 included a set of questions based on a hypothetical Indian game called "Kshetra", a mix of strategy and probability. The game involves teams competing in rounds with specific rules for scoring, elimination, and ranking. Below is a detailed solution for a sample question from this slot:
Question Statement
In Kshetra, 4 teams (A, B, C, D) participate in 3 rounds. Each round awards points based on performance. Teams are ranked by total points, with ties resolved by head-to-head wins. Given the following data, determine the final standings:
Round 1:
A scored 15 points, B scored 10% less than A.
C and D scored equal points, 20% more than B.
Total points per round: 100.
Round 2:
D led by 5 points over C, who led by 3 points over A.
B scored half of D’s points.
Total points: 90.
Round 3:
C secured 1st place with 25% of the total points.
A and B had a 2:1 ratio, while D scored 10 points less than A.
Total points: 120.
Constraints:
No team repeated the same rank in consecutive rounds.
Head-to-head ties in Round 3 were broken by C defeating D.
Solution
Step 1: Calculate Round 1 Scores
A: 15 points
B: 15 - (10% of 15) = 13.5 points
C + D: Equal, and 20% more than B = (1.2 \times 13.5 = 16.2).
Thus, C = D = 8.1 points (since (16.2 / 2 = 8.1)).
Step 2: Round 2 Scores
Let D = x, C = x - 5, A = (x - 5) - 3 = x - 8.
B = x / 2.
Total: (x + (x - 5) + (x - 8) + (x/2) = 90).
Solving: (3.5x - 13 = 90 \Rightarrow x = 28).
D = 28, C = 23, A = 20, B = 14.
Step 3: Round 3 Scores
Total points: 120.
C = 25% of 120 = 30 points.
Let A = 3k, B = 2k, D = 3k - 10.
Total: (30 + 3k + 2k + (3k - 10) = 120).
(8k + 20 = 120 \Rightarrow k = 12.5).
A = 37.5, B = 25, D = 27.5.
Step 4: Aggregate Scores
| Team | Round 1 | Round 2 | Round 3 | Total |
|------|---------|---------|---------|-----------|
| A | 15 | 20 | 37.5 | 72.5 |
| B | 13.5 | 14 | 25 | 52.5 |
| C | 8.1 | 23 | 30 | 61.1 |
| D | 8.1 | 28 | 27.5 | 63.6 |
Step 5: Apply Constraints
No consecutive ranks:
In Round 1: A > B > C = D.
In Round 2: D > C > A > B.
In Round 3: C > D > A > B (since C > D by head-to-head).
Final Standings (by total points):
D (63.6)
C (61.1)
A (72.5) → Wait, A has 72.5, which is higher than D and C.
Correction: A’s total is 72.5, making it 1st place.
Final order: A (72.5) > D (63.6) > C (61.1) > B (52.5).
Key Logical Insights:
Fraction Handling: Convert percentages to decimals carefully (e.g., 10% of 15 = 1.5).
Equation Setup: Use algebraic variables for unknowns in Round 2 and 3.
Constraint Application: Ensure no team repeats the same rank consecutively (e.g., D was 1st in Round 2 but 3rd in Round 3).
Common Mistakes:
Forgetting to update ranks across rounds.
Arithmetic errors in percentage calculations.
Misinterpreting "half of D’s points" in Round 2.
Exam Strategy:
Prioritize data consistency checks (e.g., total points per round).
Use grid tables for multi-round aggregation.
Double-check head-to-head tiebreakers in final rankings.
Final Answer:
1st: A (72.5), 2nd: D (63.6), 3rd: C (61.1), 4th: B (52.5).
This solution combines data interpretation (calculating scores) with logical deduction (applying constraints) to mirror the DILR Slot 3 pattern.
|
