Bunuel wrote:

Are the integers x, y and z consecutive?

(1) The arithmetic mean (average) of x, y and z is y.

(2) y-x = z-y

x,y,z WILL be consecutive Integers if y=x+1 and z=x+2

Stat 1 The arithmetic mean (average) of x, y and z is y.

i.e AM=(x+y+z)/3=y

=>x+y+z=3y

=>x+z=2y -->

(1)=>(x+z)/2=y

i.e y is avg. of x & z

so MUST that x<y<z and y-x=z-y

Therefore x,y,z are in AP

i.e x,y,z can be CONSECUTIVE Integers such as (1,2,3) or NON CONSECUTIVE integers such as (1,5,9)

So Stat 1 NOT Sufficient

Stat 2 y-x = z-y

i.e x+z=2y ->

(1) - derived from statement 1

So Stat 2 ALSO NOT sufficient

BOTH 1 & 2 also does NOT give a unique solution. Therefore NOT sufficient.

So Option "E"

The detailed explanation is for understanding the concept.

BUNUEL/Experts pl. validate the above analysis.Thanks