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JEE Main 201323 AprilOnline
Exam
JEE Main
Year
2013
Date
23 April
Mode
Online
Subject
Mathematics
Chapter
Statistics

JEE Main 2013 · 23 April · Online · Mathematics · Statistics

If the median and the range of four numbers \ x, y, 2 x+y, x-y\ ,...

If the median and the range of four numbers {x,y,2x+y,x−y}\{x, y, 2 x+y, x-y\}, where 0<y<x<2y0 < y < x < 2 y, are 10 and 28 respectively, then the mean of the numbers is :

Options

  1. A18
  2. B10
  3. C5
  4. D14

Correct answer

D. 14

Step-by-step solution

Since 0<y<x<2y0 < y < x < 2 y∴y>x2⇒x−y<x2∴x−y<y<x<2x+y\begin{aligned} & \therefore \quad y>\frac{x}{2} \Rightarrow x-y < \frac{x}{2} \\ & \therefore x-y < y < x < 2 x+y \end{aligned}Hencemedian=y+x2=10⇒x+y=20Hence median =\frac{y+x}{2}=10 \Rightarrow x+y=20 And range =(2x+y)−(x−y)=x+2y=(2 x+y)-(x-y)=x+2 y But range =28=28\therefore x+2 y=28FromFromequations (i) and (ii), x=12,y=8∴ Mean =(x−y)+y+x+(2x+y)4=4x+y4\begin{aligned} & x=12, y=8 \\ & \therefore \text{ Mean } \\ & =\frac{(x-y)+y+x+(2 x+y)}{4}=\frac{4 x+y}{4} \end{aligned} =x+\frac{y}{4}=12+2+\frac{8}{4}=14
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