JEE Main2013MathematicsStatisticsActual

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

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Correct answer

D. 14

Step-by-step solution

Since 0 x 2 x-y < x 2 & x-y < y < x < 2 x+y aligned Hence median = y+x 2 =10 x+y=20 And range =(2 x+y)-(x-y)=x+2 y But range =28 x+2 y=28 From equations (i) and (ii), aligned & x=12, y=8 & Mean & = (x-y)+y+x+(2 x+y) 4 = 4 x+y 4 aligned =x+ y 4 =12+ 8 4 =14

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