Data Sufficiency - 31

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

From statement (1): (x - 1) ^2 less than and equal to 1
Now this is true only if 0 is less than and equal to x and x is less than and equal to 2. (We know that (x - 1) ^2 less than 1 is only true when 0 is less than x and x is less than 2)
When we take x = 0.5, then |x-1| less than 1 is true
When we take x = 2, then |x-1| less than1 does not holds true
Hence insufficient

From statement (2): x^2 greater than 1 => x is less than -1 and x is greater than 1
When we take x = 1.5, then x^2 greater than 1 is true
When we take x = 3, then x^2 greater than 1 does not holds true
Hence insufficient

Taking both statements (1) and (2) together -- We have 1 is less than x and x is less than and equal to 2
When we take x = 1.5, then 1 is less than x and x is less than and equal to 2 is true
When we take x = 2, then 1 is less than x and x is less than and equal to 2 does not holds true Hence insufficient