Data Sufficiency (DS) | Re: Given that x is a real number, is −1 < x < 3? (1) | |x − 1| − 1 | < 1

Yes, it should definitely be sufficient. It might be easier to see why with a 250-level example question:

Is x > 0?
1. x = 5
2. x > 3

If you see a question like this, the answer is D. The question is not asking "can x be equal to any positive number at all?" The question is asking "can you be certain that x is a positive number?" Using Statement 1, x clearly cannot be equal to *any* positive number at all -- x is exactly equal to 5. But that's certainly sufficient,
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