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)

14

Answer 2

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 $= \frac{\left(x-y\right) +y +x + \left(2x+y\right)}{4} = \frac{4x+y}{4}$ $= x + \frac{y}{4} = 12 + \frac{8}{4} =14$