rsarashi wrote:If x is not equal to 0, is |x| less than 1?

1) x/|x| < x


(2) |x| > x

OAC

For |x| to be less than 1, x must be greater than -1 and less than 1.

Target question: -1 < x < 0 ?

(1) x/|x| < x

- If x is positive, then x/|x| = 1. So 1 < x. This would give us a "no" answer to the question.
- If x is negative, then x/|x| = -1. So -1 < x. But since x is negative, we can add: -1 < x < 0. This would give is a "yes" answer to the question.

If we get a "no" answer when x < 0 and a "yes" answer when x > 0, this is insufficient.

(2) |x| > x

If x were positive, it would be equal to |x|. So this is telling us that x must be negative. However, just knowing that it is negative is not enough to tell us whether |x| < 1. Insufficient.

Together:
Statement 2 tells us that x must be negative, so x/|x| = -1 ---> -1 < x < 0. This would give is a "yes" answer to the question.
Sufficient.

The answer is C.

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This question comes from Manhattan Prep CATs.