BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is | x | <1?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Thu Dec 08, 2011 11:34 am
|x|<1? Is -1<x<1?
st(1) x/|x|<x implies x<x|x|, if x>0 then 1<|x|. If x<0, then 1>|x| Not Sufficient
st(2) x<|x| implies x is negative only. Not Sufficient
combined st(1&2): st(2) x is -ve and x<0 with st(1) 1>|x| Sufficient, as we answer No to this question.

colakumarfanta wrote:Is | x | <1?
(1) x / | x | <x
(2) x <| x |
OA C
Success doesn't come overnight!
Top
Master | Next Rank: 500 Posts
Posts: 218
Joined: Wed Nov 23, 2011 8:05 pm
Thanked: 26 times
Followed by:4 members

by chieftang » Thu Dec 08, 2011 3:13 pm
I stink at these!

I had to test values.

Is -1 < x < 1 ?

(1)
x / |x| < x
x < x * |x| <---- Plug in values inside and outside the range

2: 2 < 4 TRUE
-1/2: -1/2 < -1/4 TRUE

So x can be inside or outside the range, can't answer yes or no.

INSUFFICIENT

(2)
x < |x| --> x < 0

x is therefore inside and outside the range. Can't answer yes or no.

INSUFFICIENT

(1+2)
x < x*|x| <---- Plug in values for x<0

-1/2: -1/2 < -1/4 TRUE

-1 < -1 FALSE

-3/2: -3/2 < -9/4 FALSE

Therefore it seems with statements 1&2 combined, the answer is yes.

SUFFICIENT

So we choose C


[/i]
Top
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Mon Dec 05, 2011 3:33 pm

by CollegeKart » Thu Dec 08, 2011 8:43 pm
option 1
says that x is always positive. But x can be fraction or integer i.e it can be less than or greater than 1

option 2
says that x is always negative. But x can be fraction or integer i.e it can be less than or greater than 1

option 1 and 2 combined

x / | x | <x <| x |

only negative fraction values can satisfy the condition. hence C
Top
Master | Next Rank: 500 Posts
Posts: 127
Joined: Mon May 11, 2009 10:04 am
Thanked: 5 times

by apex231 » Mon Dec 12, 2011 9:49 pm
Is | x | <1?
(1) x / | x | <x
x < |x| x - means x is positive but can't say whether its greater than or less than one.
Not sufficient

(2) x <| x | - means x is negative i.e. x < 0 but can't say whether x is less than or greater than -1.

1+2
x < |x| x , and x is negative i.e. negative x multiplied by positive x is less than negative x. this is only possible if -1<x<0.

Hence, C
Last edited by apex231 on Mon Dec 12, 2011 10:09 pm, edited 1 time in total.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Mon Dec 12, 2011 10:00 pm
colakumarfanta wrote:Is | x | <1?
(1) x / | x | <x
(2) x <| x |
OA C

Statement 1: x/|x| < x
If x is positive, 1/|x| < 1 => |x| > 1
If x is negative, 1/|x| > 1 => |x| < 1

Not sufficient

Statement 2: |x| > x
Only if x is negative, then |x| = -x > x
So we know x is negative, but we don't have enough information to conclude whether |x| less than 1 or not.

Not sufficient

1 & 2 Together: From statement 2, x is negative.
From statement 1, if x is negative then, 1/|x| > 1 => |x| < 1

Sufficient

The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Post new topic Post Reply
• Page 1 of 1