Title: CAT 2019 LRDI Slot 1 Solution
Content: Detailed Explanation for Indian Game (CAT) 2019 LRDI Section
1. Question Overview
The LRDI (Logical Reasoning, Data Interpretation, and Data Analysis) section in CAT 2019 Slot 1 included a set of data interpretation questions followed by logical reasoning problems. Below is a sample question and its solution:
Question 1 (Data Interpretation):
A survey was conducted to analyze the sales of four products (A, B, C, D) across three cities (X, Y, Z) in 2018 and 2019. The table below shows the percentage change in sales for each product in each city:
Product
City X (2018-2019)
City Y (2018-2019)
City Z (2018-2019)
A
+15%
-10%
+20%
B
+5%
+25%
-15%
C
-10%
+30%
+10%
D
+20%
+5%
+5%
Additional Information:
In 2018, sales of Product B in City Y were 10% of the total sales in City Y.
Total sales in City Z increased by 12% from 2018 to 2019.
Task:
Calculate the ratio of total sales of Product C in City Y in 2019 to the total sales of Product D in City Z in 2019.
Solution:
Step 1: Define Variables
Let the total sales in each city in 2018 be:
City X: ( X_{2018} )
City Y: ( Y_{2018} )
City Z: ( Z_{2018} )
Step 2: Calculate 2019 Sales
Using percentage changes:
Product C in City Y (2019):
( C_{Y2019} = C_{Y2018} \times 1.30 )
Product D in City Z (2019):
( D_{Z2019} = D_{Z2018} \times 1.05 )
Step 3: Use Additional Information
Sales of Product B in City Y (2018): ( 0.10 \times Y_{2018} ).
Total sales in City Z (2019): ( Z_{2018} \times 1.12 ).
Step 4: Relate Variables
Assume total sales in City Z (2018) = ( Z_{2018} ).
Total sales in City Z (2019) = ( 1.12 Z_{2018} ).
Product D contributed 5% of City Z’s 2019 sales:
( D_{Z2019} = 0.05 \times 1.12 Z_{2018} = 0.056 Z_{2018} ).
Step 5: Product C in City Y
Product C’s 2019 sales in City Y depend on its 2018 sales. However, without explicit data, assume Product C was 10% of City Y’s 2018 sales (hypothetical for calculation):
( C_{Y2018} = 0.10 Y_{2018} )
( C_{Y2019} = 0.10 Y_{2018} \times 1.30 = 0.13 Y_{2018} ).
Step 6: Ratio Calculation
Ratio ( = \frac{C_{Y2019}}{D_{Z2019}} = \frac{0.13 Y_{2018}}{0.056 Z_{2018}} ).
Step 7: Simplify Using Total Sales
Assume total sales in City Y (2018) and City Z (2018) are equal (( Y_{2018} = Z_{2018} )):
Ratio ( = \frac{0.13}{0.056} = \frac{130}{56} = \frac{65}{28} \approx 2.32:1 ).
Answer: ( \boxed{\frac{65}{28}} )
Key Takeaways for CAT LRDI:
Data Interpretation: Focus on percentage changes and relate them to absolute values using hypothetical assumptions.
Logical Reasoning: Use given constraints (e.g., "10% of total sales") to link variables.
Time Management: Skim questions first; tackle data-heavy questions after establishing relationships.
Let me know if you need further clarification or more sample questions!
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