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1. (x - 1)^2 <= 1 --> x e [0,2]. insufficient 2. x^2 - 1 > 0 --> x e (-∞,1)&(1,+∞). insufficient 1&2 x e (1,2]. insufficient.

I think I am loosing it ....

I was able to get exactly where you finished but then I argued that using 1&2 we know that x e (1,2]....meaning |x-1| will never be less than 1. And hence we can answer the question stem as a yes or no.....That is |x-1| is actually > 1

1. (x - 1)^2 <= 1 --> x e [0,2]. insufficient 2. x^2 - 1 > 0 --> x e (-∞,1)&(1,+∞). insufficient 1&2 x e (1,2]. insufficient.

I think I am loosing it ....

I was able to get exactly where you finished but then I argued that using 1&2 we know that x e (1,2]....meaning |x-1| will never be less than 1. And hence we can answer the question stem as a yes or no.....That is |x-1| is actually > 1

So why should it not be C ?

Combining 1 & 2 we get x e (1,2] but this is still not sufficient since the question is really asking is x e (0,2). Picking 1.5 for instance leads to a "yes", while picking 2 leads to a "no". _________________

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