Inequality

[nahid078]

Please someone solve this one.

[800_or_bust]

Please someone solve this one.

(1) is INSUFFICIENT. Note that (x-1)^2 must be between 0 and 1 inclusive (a square quantity cannot be negative). This means x must lie in the interval between 0 and 2. If x = 2, then (2-1)^2 = 1, but |2-1| = 1. If x = 1.5, then (1.5-1)^2 = 0.25, but |0.25-1| = 0.75. Therefore, |x-1| can be less than one, but it does not have to be so (it can also equal 1 in the case where x = 0 or x = 2).

(2) is INSUFFICIENT. This equation can be expressed as x^2 > 1, which means x must either be greater than 1 or x must be less than -1. If x = 1.5, then |1.5 - 1| = 0.5, which is less than one. However, if x = 5, then |5 - 1| = 4, which is greater than one.

Combined (1) and (2) are still INSUFFICIENT. The two cases I gave for (1) are both still applicable after considering Statement (2). x could be 2 or x could be 1.5... If x = 2, then |2 - 1| = |1| = 1, which is not less than one. If x = 1.5, then |1.5 - 1| = |0.5| = 0.5, which is less than one.

Answer choice E.