If x is a non-zero number, Is x|x|0

Question

If x is a non-zero number, Is  \frac{x}{|x|}<x?

(1) \frac{−3}{x}<0

(2)  \frac{x}{|x|}>0

Source: e-GMAT

LeoN88 · Answer

Statement 1.

-3/x < 0 says us that x is +ve for sure,
Let's check the stem with two +ve values

When x= 5, Stem is yes
When x=1/2, Stem is no. Insufficient

Statement 2. It also tells us one thing that X>0.
When x= 5, Stem is yes
When x=1/2, Stem is no. Insufficient.

1+2 doesn't give us any new info. Insufficient E.
 EgmatQuantExpert  is my approach okay?

nick1816 · Answer

1. When x is negative, if x/|x|-1 Range of x =(-1,0) 2. When x is positive if x/|x|1 Range of x =(1,∞) Statement 1- -3/x<0 x can be any positive number x/|x|1 x/|x|>x is true when 00 Again x can be any positive real number x/|x|1 x/|x|>x is true when 00 Same explanation!!!

NandyMazumdar · Answer

Here's what I did:

What I need to find: Is x/|x| < x?
1> -3/x < 0:
=> 3/x > 0 => Doesn't help us understand the value of x/|x| => Insufficient

2> x/|x| > 0
=> x/(-x) > 0 or x/x > 0
=> -1 < 0 or 1 > 0
=> Both statements are correct but still don't give us a value for x/|x| => Insufficient.

Let me know if this method makes sense.

mzaid · Answer

Bunuel, could you please explain this.

Bunuel · Answer

If x is a non-zero number, Is \frac{x}{|x|}0 . This also implies that x is positive (If x were negative, then we'd get x/(-x) = -1, which is less than 0, not more, as given here). x > 0, implies that |x| = x. So, the question, as above, becomes: is \frac{x}{x} 0. If 0 < x <= 1, then the answer to the question will be NO but if x > 1, the answer to the question will be YES. Not sufficient. Answer: E.

mzaid · Answer

Bunuel, I am not getting the second option. When you say X is negative then wont x/|x|  = -x/-x =1. Am I missing anything here.

Bunuel · Answer

No. If x is negative, then |x| = -x, so x/|x| becomes x/(-x).

mzaid · Answer

Bunuel, Sorry but I dont understand why we are not considering the numerator x as negative. As in first statement the negative x doesn't fulfill the condition, so we considered it positive. What is lacking in my concept here ?

Bunuel · Answer

I guess, you asking why we are not changing x to -x, knowing that x is negative. x (in numerator) itself denotes a negative number, so no need to replace it. For example, if given that x + y = 10, and x is negative, are you rewriting this to -x + y = 10?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x is a non-zero number, Is x|x|<x? (1) −3x<0 (2) x|x|>0

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions