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Question 142

In 12 consecutive odd numbers the arithmetic mean of the first five numbers is 85. The difference of the medians ofthe first five numbers and the last five numbers is

Solution

Let the first odd number be 2n+1.
Hence, the first five odd numbers would be: 2n+1, 2n+3, 2n+5, 2n+7, 2n+9
Median of these: 2n+5

The last 5 odd numbers would be: 2n+15, 2n+17, 2n+19, 2n+21, 2n+23
The median of these numbers: 2n+19

Hence, the difference between the medians = 2n+19 - 2n - 5 = 14

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