Question 19

Suppose a, b and c are three real numbers such that Max(a, b, c) + Min(a, b, c) = 15, and Median(a, b, c) - Mean(a, b, c) = 2. Then the median of a, b and c is

Solution

Let us assume $$a<b<c$$

Max(a, b, c) = c

Min(a, b, c) = a

Median(a, b, c) = b

Mean(a, b, c) = (a+b+c)/3

Now, Max(a, b, c) + Min(a, b, c) = 15

=> $$c+a=15\rightarrow1$$

Also, Median(a, b, c) - Mean(a, b, c) = 2

=> $$b-\dfrac{\left(a+b+c\right)}{3}=2$$

=> $$2b-(a+c)=6\rightarrow2$$

Adding eq. 1 and eq. 2 -

=> $$2b=21$$

=> $$b=10.5$$

Thus, the median of a, b, and c = b = 10.5

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