Question

If the median and the range of four numbers {x, y, 2x + y, x - y}, where 0 < y < x < 2y, are 10 and 28 respectively, then the mean of the numbers is :

• A. 18
• B. 10
• C. 5
• D. 14

Answer 1

Answer: (D)

Since 0 < y < x < 2y
$\therefore y>\frac{x}{2}\Rightarrow x-y<\frac{x}{2}$
$\therefore x-y<y<x<2x+y$
Hence median $=\frac{y+x}{2}=10$
$\Rightarrow x+y=20$ ...(i)
And range = (2x + y) - (x - y) = x + 2y
But range = 28
$\therefore$ x + 2y = 28 ...(ii)
From equations (i) and (ii),
x = 12, y = 8
$\therefore$ Mean $=\frac{\left(x-y\right)+y+x+\left(2x+y\right)}{4}=\frac{4x+y}{4}$
$=x+\frac{y}{4}=12+\frac{8}{4}=14$