It is currently 23 Jun 2017, 07:04

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# X/ |X| < X. Which of the following must be true about X?

Author Message
Manager
Joined: 26 Dec 2004
Posts: 56
Location: Greece - Land of Feta
X/ |X| < X. Which of the following must be true about X? [#permalink]

### Show Tags

09 Sep 2005, 20:40
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Explanation

If X > 0, the inequality turns into X > 1. If X < 0, the inequality turns into X > -1. In each of the cases X > -1, therefore X > -1 is true for all possible X. Counter-examples to show that other choices are not necessarily true:
(A),(D),(E) X = -1/2;
(C) X = 5.

The OA is B but I'm having a little trouble understanding why it is not A. For example, if X>-1 then X could = 1 and 1/1 is NOT < 1...But if A is the case and X > 1 it seems to work....Can any help a gmat brother out??
Manager
Joined: 13 Aug 2005
Posts: 135

### Show Tags

09 Sep 2005, 22:21
x/lxl < x => x<xlxl
if x>0
lxl>1 => x>1 or x<-1, combined with x>0: x>1
if x<0
lxl<1 => -1<x<1, combined with x<0: -1<x<0

Only X>-1 satisfies both possibilities. but not x>1 which violets the second one.
Manager
Joined: 06 Aug 2005
Posts: 197

### Show Tags

10 Sep 2005, 06:40
Excluding the case X=0,

X / |X| = sign(X)

So X / |X| = 1 if X>0, and = -1 if X<0

So if X<= -1 then X / |X| = -1 >= X

So if X / |X| < X then X > -1
Manager
Joined: 26 Dec 2004
Posts: 56
Location: Greece - Land of Feta

### Show Tags

10 Sep 2005, 15:18
You guys rock on multiple levelts...

Cheers,
Thanks!   [#permalink] 10 Sep 2005, 15:18
Display posts from previous: Sort by