CAT 2018 Slot 2: Quantitative Ability Solutions
Indian Scenario-Based Problem Solving
Problem 1: Market Share Competition
Scenario: Three companies (A, B, C) compete in the Indian e-commerce market. Company A holds 40% market share, B holds 35%, and C holds 25%. The market grows by 15% annually. After 3 years, Company A aims to capture 50% market share. How much faster must Company A grow compared to the industry average to achieve this?
Solution:
Current Market:
Total = 100 units (A: 40, B: 35, C: 25)
Annual growth = 15% ⇒ Total after 3 years = (100 \times (1.15)^3 ≈ 152.11) units.
Target for A:
50% of 152.11 = (76.06) units.
Current A: 40 units ⇒ Required growth = (76.06 - 40 = 36.06) units.
Growth Rate Calculation:
Let A’s growth rate = (1 + r), Industry rate = 1.15.
Equation: (40 \times (1 + r)^3 = 76.06)
(\Rightarrow (1 + r)^3 = \frac{76.06}{40} ≈ 1.9015)
(\Rightarrow 1 + r ≈ \sqrt[3]{1.9015} ≈ 1.23) ⇒ (r ≈ 23%).
Faster Than Industry:
Industry growth = 15%, A’s required growth = 23%.
Difference: (23% - 15% = 8%).
Answer: Company A must grow 8% faster than the industry average.
Problem 2: Probability & Surveys
Scenario: A survey in India found that 30% of users prefer Product X, 25% prefer Product Y, and 45% are indifferent. If 5% of X-preferers and 10% of Y-preferers switch to Product Z, what percentage of the total population now prefers Z?
Solution:
Assume Total Population = 1000 people.
Original Distribution:
X: 30% = 300
Y: 25% = 250
Indifferent: 45% = 450
Switchers to Z:
From X: (5% \times 300 = 15)
From Y: (10% \times 250 = 25)
Total Z = (15 + 25 = 40).
New Distribution:
X: (300 - 15 = 285)
Y: (250 - 25 = 225)
Z: 40
Indifferent: 450
Percentage for Z:
(\frac{40}{1000} \times 100 = 4%).
Answer: 4% of the total population prefers Product Z.
Problem 3: Algebra & Workforce
Scenario: In an Indian factory, 120 workers produce 480 units daily. If 20% more workers join and productivity increases by 10%, how many units are produced daily?
Solution:
Original Workforce: 120 workers → 480 units.
New Workforce: (120 + 20% \times 120 = 144) workers.
Productivity per Worker:
(\frac{480}{120} = 4) units/worker/day.
New Productivity: (4 \times 1.10 = 4.4) units/worker/day.
Total Units: (144 \times 4.4 = 633.6 ≈ 634) units.
Answer: 634 units daily.
Key Takeaways:
Use scenario-based math (growth, probability, workforce) common in CAT.
Convert percentages to absolute numbers for clarity.
Check for rounding conventions (CAT often uses nearest whole numbers).
Let me know if you need further clarification! 🇮🇳📊
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