Data Sufficiency

diebeatsthegmat wrote:If \frac{x}{|x|}<x which of the following must be true about x?

(A) x>1

(B) x>-1

(C) |x|<1

(D) |x|=1

(E) |x|^2>1

a is my answer choice. whats yours>?

The notation in the question "\frac{x}{|x|}<x" is used in a mathematical typesetting environment called TeX - it's not something you'll ever see on the GMAT. The question should begin:

If x/|x| < x, which of the following...

Now x/|x| is either equal to 1 (if x is positive) or to -1 (if x is negative). So we can rephrase the inequality:

* if x > 0, then 1 < x
* if x < 0, then -1 < x

So there are two ranges of possible values for x; either x > 1, or -1 < x < 0.

From here you can see that the only answer which *must* be true is B, since if x is in either of the ranges above, x is certainly greater than -1. Most of the other answers (besides D) *could* be true, but are not always true.

sourabh33 wrote:Hi Ian

I have a small doubt regarding statements A & B.

I can't think of any value of x>1 that will not be true for the equation x/|x| < X
Versus For option B (x>-1), when x = 0, then the equation x/|x| < X may not be true

Please help.

I think you must be looking at the question backwards. We *know* that x/|x| is less than x. We want to know which answer choice *must* be true. It doesn't need to be true that x > 1, because x could be equal to -0.5, so A cannot be the right answer.

I think you're trying to answer the opposite question. That is, you're assuming that answer A is true, and you're trying to prove that x/|x| is less than x. It certainly is if x > 1, but that doesn't make A correct here, because that's not what the question is asking you to do.