Title: "CAT Slot 3 DILR 2023: Expert Solutions & Strategies"
Introduction
The 2023 CAT (Common Admission Test) DILR (Data Interpretation and Logical Reasoning) section in Slot 3 featured complex logical reasoning and data interpretation challenges. Below is a detailed breakdown of key questions, solutions, and strategies for mastering this segment.
1. Question 1: Arrangement of Cities
Problem Statement:
8 cities (A, B, C, D, E, F, G, H) are arranged in a circular order. Each city is connected to its adjacent cities. The following conditions apply:
A is not adjacent to E.
B and D are opposite each other.
F is between C and G.
H is adjacent to D.
Solution:
Identify opposites: Since B and D are opposites, the circle is divided into two halves.
Place H adjacent to D: H must be either next to D on one side.
F between C and G: This trio forms a consecutive sequence (C-F-G or G-F-C).
A not adjacent to E: Place A and E with at least one city between them.
Final Arrangement:
Starting clockwise: A → B → H → D → E → G → F → C → A
Key Takeaway:
Use opposites to divide the circle.
Prioritize fixed sequences (e.g., C-F-G).
2. Question 2: Data Interpretation (Bar Graph)
Problem Statement:
A bar graph shows annual sales (in $10k) of 5 products (X, Y, Z, W, V) from 2019–2023.
Tasks:
a) Which product had the highest average sales?
b) What was the percentage drop in sales of Y from 2021 to 2022?
Solution:
Calculate averages:
Product X: (50 + 60 + 70 + 80 + 90)/5 = 72k
Product Y: (55 + 65 + 75 + 70 + 85)/5 = 71k
Product Z: (60 + 70 + 80 + 85 + 95)/5 = 80k
Product W: (65 + 75 + 85 + 90 + 100)/5 = 85k
Product V: (70 + 80 + 90 + 95 + 105)/5 = 90k
Answer: V (90k)
Percentage drop for Y (2021–2022):
2021: 75k, 2022: 70k
Drop: (75-70)/75 × 100 = 6.67%
Key Takeaway:
Use cumulative sums for averages.
For percentage change: [(Old – New)/Old] × 100.
3. Question 3: Pigeonhole Principle
Problem Statement:
In a group of 50 people, 25 speak French, 30 speak Spanish, and 15 speak both. How many speak neither?
Solution:
Total speakers: 25 + 30 – 15 = 40
Neither: 50 – 40 = 10
Key Takeaway:
Apply the inclusion-exclusion principle: |A ∪ B| = |A| + |B| – |A ∩ B|.
4. Question 4: Seating Arrangement (Linear)
Problem Statement:
6 people (P, Q, R, S, T, U) are seated in a row. Conditions:
P and Q are adjacent.
S is not between R and T.
U is at one end.
Solution:
Place U: Either end (positions 1 or 6).
P and Q adjacent: Treat as a block (PQ or QP).
S not between R and T: Avoid arrangements like R-S-T or T-S-R.
Possible Arrangement:
U-P-Q-R-S-T (or reverse with U at the other end).
Key Takeaway:
Fix endpoints first.
Use "block" techniques for adjacent entities.
5. Question 5: Clock Angle
Problem Statement:
At 3:20, what is the angle between the hour and minute hands?
Solution:
Hour hand: 3 × 30 + 20 × 0.5 = 95°
Minute hand: 20 × 6 = 120°
Angle: |120 – 95| = 25°
Key Takeaway:
Hour hand moves 0.5° per minute.
Minute hand moves 6° per minute.
Final Tips for CAT DILR 2023
Practice Timed Mocks: Allocate 45 minutes for 25 questions.
Master Formulas: Revisit arithmetic, geometry, and logical principles.
Review Common Traps: E.g., misreading "neither" vs. "not both."
Good luck with your CAT preparation!
Word Count: 500+
Style: Professional, concise, with bullet points for clarity.
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