80 of the 100 elements of D are equal to x. The remaining 20

Question

80 of the 100 elements of D are equal to x. The remaining 20 elements are equal to y. What is |x-y|?

 (1) The standard deviation of D is 400
 (2) x< y< 0

ps_dahiya · Answer

A

Mean = M = (80x+20y)/100
SD^2 = 80(x-M)^2 + 20(y-M)^2

St1: SD^2 = 160000

160000 = 80 ^2 + 20 ^2

solving this we get (x-y)^2 = 10000
so |x-y| i.e range = 100

St2: Clearly INSUFF.

freetheking · Answer

IMO, A.
S1.
Mean = 0.8x+0.2y
Variance =  /100
=  /100
=  /100
=  /100

std = sqrt( /100) = 400
4|x-y|/10 = 400
|x-y|=1000
sufficient.

S2. insufficient.

kevincan · Answer

Great, though SD^2=(80(x-M)^2+20(y-M)^2)/ 100

Futuristic · Answer

A 

M = (80x+20y)/100 = 0.8x + 0.2y

SD^2 = (80(x-M)^2 + 20(y-M)^2)/100

Now,

x-M = 0.2(x-y)
y-M = 0.8(y-x)

Let x-y = t

SD^2 = something in terms of t2. solve for t, which is the same as |x-y|

2 is clearly insuff.

80 of the 100 elements of D are equal to x. The remaining 20

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