For the data sufficiency question:

Is |x – 5| < 5?

(1) x < -4

(2) x < 4

The answer is given as:

In order for |x – 5| < 5, then (x – 5) would need to be between -5 and 5.
-5 < (x – 5) < 5
-5 + 5 < x < 5 + 5
0 < x < 10
Therefore, the question can be rephrased as “Is x greater than 0 but less than 10?”

(1) SUFFICIENT: Knowing that x < -4 is enough to let us answer the rephrased question with a definite “No.” Remember, on data sufficiency questions, a definite “no” answer is sufficient. The only insufficient answer to a yes/no question is “maybe” or “it depends.”

(2) INSUFFICIENT: Knowing that x < 4 is not enough to let us answer the rephrased question. For example, x could be 3, and the answer would be “Yes.” However, x could be -100, and the answer would be “No.” Therefore, the answer is “maybe,” which is insufficient.

The correct answer is A.

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HOWEVER, wouldn't it be possible if x < -4 for x to be -100? Wouldn't that make statement 1 insufficient also?

No!!! If x=-100, then the answer is NO. Definitive.

Yeah, remember: "ALWAYS NO" and "ALWAYS YES" are both SUFFICIENT.
The only INSUFFICIENT answer on yes/no questions is "MAYBE".

If you consider statement A, the answer to the prompt question is "ALWAYS NO". Pick a few numbers and see for yourself if you don't like the algebraic derivation.

If x = -4.00001, then |x - 5| = |-9.00001| = 9.00001, which is NOT less than 5.
If x = -100, then |x - 5| = |-105| = 105, which is NOT less than 5.

You can't get something that IS less than 5 with statement (1). In fact, everything you get will be more than 9. So that's ALWAYS NO, which is SUFFICIENT.