CAT Quantitative Ability Questions | CAT Number System questions

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CAT/2020.1

Question . 12

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

A : 8 B : 10 C : 12 D : 9

View Answer

Explanatory Answer

Method of solving this CAT Quantitative Ability Question from Number System question

Correct Option: D

To find the smallest possible value of x0, we need to distribute the birthdays among the 12 months in a way that minimizes the maximum value among x1, x2, ..., x12.

Since we have 100 students in total, let's start by distributing the birthdays evenly across the 12 months. This would mean each month would have approximately 100/12 = 8.33 students. However, since we can't have a fraction of a student, we'll distribute the birthdays as evenly as possible.

For the first 8 months (January to August), we can assign 8 students each, totaling 8 * 8 = 64 students. This leaves us with 100 - 64 = 36 students.

To minimize the maximum value, we'll distribute these remaining 36 students across the remaining 4 months (September to December), giving each month 9 students.

Now let's look at the values of x0, x1, x2, ..., x12:

x0 = max(x1, x2, ..., x12) = max(8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9) = 9

Therefore, the smallest possible value of x0 is 9.

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