\[ \frac{\left|x\right|-1}{x-1}=? \]

[Gmat_mission]

$$\frac{\left|x\right|-1}{x-1}=?$$

(1) x < 0
(2) |x| = -x

[spoiler]OA=E[/spoiler].

Why is not sufficient the first statement? Is not 1 the answer? I need some help here, please.

[Vincen]

$$\frac{\left|x\right|-1}{x-1}=?$$

(1) x < 0
(2) |x| = -x

[spoiler]OA=E[/spoiler].

Why is not sufficient the first statement? Is not 1 the answer? I need some help here, please.

Hello Gmat_mission.

Let's take a look at your question.

(1) x < 0

If x<0 then |x|=-x, and therefore $$\frac{\left|x\right|-1}{x-1}=\frac{-x-1}{x-1}=-\frac{x+1}{x-1}=?$$ Since we couldn't get an answer, we conclude that this statement is NOT SUFFICIENT.

(2) |x| = -x

This statement says exactly the same as the previous one. Therefore NOT SUFFICIENT.

(1) x < 0 and (2) |x| = -x

Both statements say the same thing. Hence NOT SUFFICIENT.

This is why the correct answer here is the option E