Is x >3

(1) (x-1)^2 > 4 --> \(x-1<-2\) or \(x-1>2\) --> \(x<-1\) or \(x>3\). Not sufficient.

(2) (x-1)^2 > 9 --> \(x-1<-3\) or \(x-1>3\) --> \(x<-2\) or \(x>4\). Not sufficient.

(1)+(2) Intersection of the ranges from (1) and (2) gives: \(x<-2\) or \(x>4\), so \(x\) may or may not be greater than 3. Not sufficient.

Answer: E.
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Bunuel's solution is perfect, so I won't re-use that strategy.
Another approach is to TEST some values of x.

Target question: Is x >3?

Statement 1: (x-1)² > 4
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 10, in which case, x > 3
Case b: x = -10, in which case, x < 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (x-1)² > 9
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 10, in which case, x > 3
Case b: x = -10, in which case, x < 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
NOTE: since we were able to use the same values of x to show that statements 1 and 2 ALONE are not sufficient, we can re-use them to show that statements 1 and 2 COMBINED are not sufficient
Case a: x = 10, in which case, x > 3
Case b: x = -10, in which case, x < 3
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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