If x is not equal to 0, is the absolute value of x less than

[julia.gilroy]

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

(1) x/|x|< x

(2) |x| > x

(1) INSUFFICIENT: If x > 0, this statement tells us that x > x/x or x > 1. If x < 0, this
statement tells us that x > x/-x or x > -1. This is not enough to tell us if -1 < x < 1.


I am having difficulty understanding the provided explanation for statement 1. Why is it that if x<0, x> x/-x? If x<0, shouldn't the inequality be -x>-x/-x?

[www.mbachase.com]

[Attention mbachase.com: we appreciate your desire to help GMAT students. Unfortunately, we don't host posts from competitors on our forums. If you'd like to offer free services to your students (and I think that's a great idea!), then you might consider starting your own forums. Good luck! Stacey]

[Ben Ku]

Hi Judy,

When dealing with absolute values, |x| = x if x is positive, and |x|=-x if x is negative.

If we look at (1), if x is negative, then x/(-x)< x, so -1 < x. I think the confusion is because the explanation switches the left and right sides, writing "x > x/-x", which of course is the same thing.

Hope that helps.

[yousuf_azim]

Hello,

What is the ans?

BR

[StaceyKoprince]

the answer is C