Data Sufficiency - 33

Is |x - 1| less than 1 ?

1). (x - 1)^2 less than and equal to 1
2). x^2 - 1 greater than 0

Answer: E

|x-1| less than 1 is only true when 0 less than x less than 1

From statement (1): (x-1)^2<=1
True when 0<=x<=2
If x=0.5, then |x-1| less than 1 is true
If x=2, then |x-1| less than 1 is not true
Hence insufficient

From statement (2): x^2>1 means x>1 and x<-1
True when x=1.5, but not when x=3
Hence insufficient

Statement (1) and (2) together: 1 is less than x is less than and equal to 2
Taking x=1.5 and x=2
Hence insufficient