Question 13.

Among 100 students, x1x_{1} have birthdays in January, x2x_{2} have birthdays in February, and so on. If x0x_{0} = max(x1x_{1}, x2x_{2}, ..., x12x_{12}), then the smallest possible value of x0x_{0} is

A
8
B
10
C
12
D
9

Question Explanation

Text Explanation

x0=max(x1,x2,,x12)x_0 = \max(x_1, x_2, \ldots, x_{12})

x0x_0 will be minimum if (x1,x2,,x12)(x_1, x_2, \ldots, x_{12}) are close to each other.

10012=8.33\frac{100}{12} = 8.33

Therefore, (max(x1,x2,,x12))(\max(x_1, x_2, \ldots, x_{12})) will be minimum if ((x1,x2,,x12)((x_1, x_2, \ldots, x_{12}) = (9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8)).

Hence, Option D is correct.

Video Explanation
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