Here’s a structured solution for a sample CAT 2023 Quant Slot 1 problem, assuming a common question type (e.g., Data Interpretation or Algebra). Since the exact problem isn’t specified, I’ll create a representative example and solve it step-by-step.
Problem Statement
slot 1: Data Interpretation
A survey was conducted to analyze the average monthly expenditure of households in three cities: Mumbai, Delhi, and Chennai. The table below shows the data for 2022:
City
Total Households
Average Expenditure (₹)
Mumbai
1,200
45,000
Delhi
800
55,000
Chennai
1,000
50,000
What is the overall average monthly expenditure across all three cities?
If the number of households in Mumbai increased by 20% in 2023, what would be the new total expenditure for Mumbai?
Solution
1. Overall Average Monthly Expenditure
Total expenditure for each city:
Mumbai: (1,200 \times 45,000 = ₹54,000,000)
Delhi: (800 \times 55,000 = ₹44,000,000)
Chennai: (1,000 \times 50,000 = ₹50,000,000)
Total expenditure across all cities:
(54,000,000 + 44,000,000 + 50,000,000 = ₹148,000,000)
Total households: (1,200 + 800 + 1,000 = 3,000)
Overall average:
(\frac{148,000,000}{3,000} = ₹49,333.33)
Answer: ₹49,333.33
2. New Total Expenditure for Mumbai (2023)
2023 households in Mumbai:
(1,200 \times 1.20 = 1,440)
New expenditure:
(1,440 \times 45,000 = ₹64,800,000)
Answer: ₹64,800,000
Key Concepts Tested
Data Interpretation: Calculating averages, totals, and percentages.
Arithmetic Operations: Multiplication, division, and percentage increase.
Common Mistakes to Avoid
Forgetting to convert percentages to decimals (e.g., 20% = 1.20).
Miscalculating total expenditure by adding averages instead of multiplying by households.
Exam Strategy
For data interpretation questions, break down the problem into smaller steps (e.g., calculate individual city expenditures first).
Use approximations for quick estimates (e.g., rounding to nearest 1,000 for faster math).
Let me know if you’d like solutions for other question types (e.g., Algebra, Geometry)!
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