mokap25 wrote:

Is |x-1| < 1?

(1) (x-1)^2 <= 1

(2) x^2 - 1 > 0

From statement 1: If (x-1)^2 <= 1, the value of x varies from 0 to 2 i.e. x is non-negative.

(x-1)^2 <= 1

(x-1) (x-1) <= 1

i) x-1 <= 1

x-1 <= 1

x <= 2

If x is 2, |x-1| = |2-1| = 1 ..........No.

If x is 1.5, |x-1| = |1.5-1| = 0.5.. Yes.

ii) x-1 => 1

x => 0

If x is 0, |x-1| = |0-1| = 1 ..........No.

If x is 0.5, |x-1| = |0.5-1| = 0.5.. Yes.

Not sufficient......

From statement 2: x^2 - 1 > 0

x^2 > 1

i) either, x > 1

ii) or x < -1

If x is 1.1, |x-1| = |1.1-1| = 0.1 .......... yes.

If x is -1.1, |x-1| = |-1.1-1| = -2.1. No.

From 1 and 2: the value of x varies from 0 to 2 but still insufficient.

E.