Here’s a structured solution for a CAT 2022 Quantitative Ability (Slot 3) problem, assuming it involves a common quantitative topic like Data Interpretation, Algebra, or Logical Reasoning. Since the exact problem isn’t provided, I’ll create a hypothetical example and solve it step-by-step in English, as requested.
Problem Statement (Hypothetical Example):
In a game show, contestants pick 3 numbers from the set {1, 2, 3, ..., 10} without replacement. The score is calculated as ( S = a + 2b + 3c ), where ( a < b < c ). What is the maximum possible value of ( S )?
Solution:
Step 1: Understand the Constraints
Numbers must be distinct and ordered: ( a < b < c ).
Score formula: ( S = a + 2b + 3c ).
Goal: Maximize ( S ).
Step 2: Strategy for Maximization
To maximize ( S ), prioritize maximizing ( c ) (since it has the highest coefficient, 3), then ( b ) (coefficient 2), and finally ( a ) (coefficient 1).
Step 3: Assign Values
Start with the largest possible ( c ). The maximum ( c ) is 10.
Next, choose the largest possible ( b ) less than ( c ): ( b = 9 ).
Then, choose the largest possible ( a ) less than ( b ): ( a = 8 ).
Step 4: Calculate ( S )
[
S = 8 + 2(9) + 3(10) = 8 + 18 + 30 = 56
]
Step 5: Verify Optimality
Check if swapping ( a, b, c ) with smaller numbers increases ( S ):
If ( c = 10 ), ( b = 9 ), ( a = 7 ): ( S = 7 + 18 + 30 = 55 ) (smaller).
If ( c = 10 ), ( b = 8 ), ( a = 9 ): Invalid (( a < b ) not satisfied).
Thus, ( S = 56 ) is the maximum.
Key Takeaways for CAT备考:
Coefficient Analysis: Prioritize variables with higher coefficients.
Greedy Approach: Start with the highest possible values for variables with the largest multipliers.
Validation: Always check if swapping values could yield a better result.
Let me know if you need help with a specific problem! 🎯
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