CAT 2020 Set Theory Question (Medium)

Question

Among 100 students, x have birthdays in January, x have birthdays in February, and so on. If x max x , x , ..., x , then the smallest possible value of x is

Accepted Answer

Step 1 Even Distribution Pigeonhole Principle If we divide 100 students evenly among 12 months 12 8 3 This means Every month must have at least 8 students . But because we can t assign fractional students, some months will have to take 1 extra student i.e., 9 students . --- Step 2 Distribute the Ext

CAT 2020

Quantitative

Set Theory

Medium

Among 100 students, x₁ have birthdays in January, x₂ have birthdays in February, and so on. If x₀ = max(x₁, x₂, ..., x₁₂), then the smallest possible value of x₀ is

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