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Inequalities problem

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by psm12se » Mon Sep 02, 2013 11:02 am
If x≠0 and (x /|x|)<x, which of the following must be true?

a. x>1
b. x>−1
c. |x|<1
d. |x|>1
e. −1<x<0

I spent sometime on the problem and came up with the answer as A but the OA is B
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by GMATGuruNY » Mon Sep 02, 2013 12:26 pm
I posted two different approaches here:

https://www.beatthegmat.com/modulus-ps-t112185.html
https://www.beatthegmat.com/let-get-abso ... 27383.html
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by [email protected] » Mon Sep 02, 2013 1:55 pm
Hi psm12se,

Mitch provides the correct explanation for this prompt, but there is an additional point worth noting...

First, we're told that ( X / |X| ) < X

So X CANNOT = -1, 0 or 1

X CAN = anything greater than 1.......so, X > 1

Also, X CAN = any negative fraction.......so 0 > X > -1

We need an answer that contains ALL of those possibilities.

The correct answer IS B. Based on what we know about the possible values of X, X MUST be greater than - 1. This DOESN'T mean that every value greater than -1 is a possible solution, it means that THIS one description defines every possible value of X that fits the beginning info.

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