Official Solution: Is \(|x - 6| > 5\) ? Is \(|x - 6| > 5\) ?
Is \(x - 6 < -5\) or \(x - 6 > 5\)?
Is \(x < 1\) or \(x > 11\)?
Another way to evaluate "Is |x - 6| > 5?" is to use the distance concept. \(|x - 6|\) represents the distance between \(x\) and 6 on the number line. For that distance to be greater than 5, \(x\) must be either less than 1 or greater than 11:
--------1--------6--------11
-------- (1) \(x\) is an integer.
This statement is clearly not sufficient, as \(x\) could be any integer value.
(2) \(x^2 < 1\).
The above implies that \(-1 < x < 1\). Since \(-1 < x < 1\), then \(x\) is less than 1, and thus the answer to the question is YES. Sufficient.
Answer: B