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

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Senior Manager
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Given X/|X| < X. Which of the following must be true [#permalink]

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06 Aug 2006, 14:35
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Given

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
_________________

for every person who doesn't try because he is
afraid of loosing , there is another person who
keeps making mistakes and succeeds..

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SVP
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06 Aug 2006, 15:32
I will go for /x/<1

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Senior Manager
Joined: 06 Jul 2004
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Location: united states

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06 Aug 2006, 15:40
"I will go for /x/<1"

and why would you do that?
_________________

for every person who doesn't try because he is
afraid of loosing , there is another person who
keeps making mistakes and succeeds..

Kudos [?]: 136 [0], given: 0

Senior Manager
Joined: 14 Jul 2005
Posts: 399

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06 Aug 2006, 16:34
X/|X| < X

divide by X on both sides 1/|x| < 1
multiply with |x| on both sides

1<|x| i.e. |x|>1

Hence will go with E

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Director
Joined: 07 Jun 2004
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06 Aug 2006, 16:42
I will go with A

take examples X > 1 then any value > x 1.1 or 1 milllion will be both positive and the answer will be 1 so 1 < any value > x

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Manager
Joined: 22 Jul 2006
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06 Aug 2006, 17:09
I will go for E

X/|X| < X implies

X/X < X or X/(-X) > X
so, x > 1 or x <-1. The only option which satisfies this condition is 'E'

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Manager
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06 Aug 2006, 21:25
shoonya wrote:
Given

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

rewrite as x < x * |x|
or x < x*n - where n is any +ve number(integer or fraction)
only possible solution is when n > 1

A for me.

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VP
Joined: 29 Dec 2005
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06 Aug 2006, 22:15
shoonya wrote:
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

straight A. no matter the value of x, x > x/lxl. since x>1 and x/lxl is always 1. so its pretty clear that x>x/lxl.

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Senior Manager
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06 Aug 2006, 23:30
X/|X| < X (X!=0 )
1. if X > 0 then 1 < X (X/X < X => 1<X)
2. if X < 0 then -1 < X <0 (X/-X < X => -1 < X)
Combine 1 and 2
-1<X<0 and X>1

Thus A.
_________________

The only thing that matters is what you believe.

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Senior Manager
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06 Aug 2006, 23:37
A

Agree with proff. explanation

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SVP
Joined: 30 Mar 2006
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07 Aug 2006, 04:52
Clear winner A.

A satisfies the condition perfectly

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Senior Manager
Joined: 14 Jul 2005
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07 Aug 2006, 08:24
Can any of you explain if what I did was actually wrong ?

i.e.

X/|X| < X

divide by X on both sides 1/|x| < 1
multiply with |x| on both sides

1<|x| i.e. |x|>1

Hence will go with E

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Senior Manager
Joined: 21 Jun 2006
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07 Aug 2006, 14:18
A is the only one which works
Take X = 3
3/|3|=1<3

Take x=-3
-3||-3|=-1>X

Take X =1
Then LHS = RHS

X>1 is the only one that works

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Manager
Joined: 20 Mar 2006
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07 Aug 2006, 18:17
shoonya wrote:
Given

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

x< x|x|
when x> 0 |x| = x which implies x< x^2 or x(x-1) > 0 i.e x>1
when x<0 |x| = -x which implies x<-x^2 or x(x+1) < 0 i.e -1<x<0

Hence A

Heman

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Manager
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08 Aug 2006, 08:00
gmatornot wrote:
Can any of you explain if what I did was actually wrong ?

i.e.

X/|X| < X

divide by X on both sides 1/|x| < 1
multiply with |x| on both sides

1<|x| i.e. |x|>1

Hence will go with E

You can not divide by x, because you don't know the sign of x. If x is -ve you would need to flip the ineqality sign.

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VP
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08 Aug 2006, 08:54
Path wrote:
gmatornot wrote:
Can any of you explain if what I did was actually wrong ?

i.e.

X/|X| < X

divide by X on both sides 1/|x| < 1
multiply with |x| on both sides

1<|x| i.e. |x|>1

Hence will go with E

You can not divide by x, because you don't know the sign of x. If x is -ve you would need to flip the ineqality sign.

agree that you cannot divide both sides by x. ok, lets suppose you are when x is +ve, but if x is a fraction x/lxl>x.

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Manager
Joined: 08 Aug 2006
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Location: Michigan

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08 Aug 2006, 09:08
I'll try the old plug numbers routine

2/l2l<2
and so on so my answer is A

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Current Student
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Schools: Wharton'11 HBS'12

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08 Aug 2006, 12:40
actually freethinking has the best explanation...and this how u shud approach || questions...

freetheking wrote:
X/|X| < X (X!=0 )
1. if X > 0 then 1 < X (X/X < X => 1<X)
2. if X < 0 then -1 < X <0 (X/-X < X => -1 < X)
Combine 1 and 2
-1<X<0 and X>1

Thus A.

Kudos [?]: 319 [0], given: 2

08 Aug 2006, 12:40
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# Given X/|X| < X. Which of the following must be true

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