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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Mod X. A 700-800 ques

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 77
Joined: Mon Jul 12, 2010 12:14 am
Location: India
GMAT Score:710
by rb90 » Fri Sep 10, 2010 3:50 am
If x is not equal to 0, is |x| less than 1?

(1) ( x/|x| ) < x

(2) |x| > x

The actual answer is C (both together are sufficient)
I need help understanding the working.
Really need the help people.
Thanks.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members
Thanked: 215 times

by kvcpk » Fri Sep 10, 2010 4:07 am
rb90 wrote:If x is not equal to 0, is |x| less than 1?

(1) ( x/|x| ) < x

(2) |x| > x

The actual answer is C (both together are sufficient)
I need help understanding the working.
Really need the help people.
Thanks.
Question is asking whether x lies between -1 and 1

(1) ( x/|x| ) < x
there can be only 2 cases. x>0 or x<0
1) x>0
then |x|=x
x/x <x
1<x
x>1
So when x>0, x>1 [doesnot fall between -1 and 1]
2)x<0
then |x|=-x
x/(-x) <x
-1<x
x>-1
So, when x<0, -1<x<0 [falls between -1 and 1]
Contradicting results.
hence INSUFF


stmt2) |x| > x
again 2 cases.
x>0:
x>x.. Not possible.
x<0:
-x>x
2x<0
x<0 [no info if it falls between -1 and 1 only.]
Hence INSUFF

Combining:
We see that only x<0 is possible.
and for x<0, from stmt1 we know falls between -1 and 1.
Hence sufficient.

Hope this helps. Let me know if you have trouble getting this.
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 509
Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members
Location: Irvine, CA
Thanked: 199 times
GMAT Score:750

by tpr-becky » Fri Sep 10, 2010 11:25 am
We need to know whether x is a fraction (the only way that an absolute value can be less than 1)

1) x/ \x\ will always be 1 or negative one (depending on the pos/neg nature of x) When x is greater than one this equation always works. BUT this also works if x is a negative fraction - a negative number over it's absolute value will always be -1 so the only time this can be less than x will be when x is a fraction. So here we can't tell if x is positive or negative and thus BCE

2) if \x\>x that means that x has to be negative because x and \x\ will always be the same distance from zero on the number line it is just a matter of positive/negative. here becuase the absolute value is greater than the original number the original number must be negative. the only problem here is that we are asking about fractions, not pos/neg so this doesn't give us enough info. thus CE

When we put them together #2 tells us that x is negative and when x is negative #1 tells us that is has to be a fraction - therefore together we know that x is a negative fraction and therefore \x\ is less than 1.
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 98
Joined: Sat Feb 06, 2010 11:56 pm
Thanked: 5 times

by anantbhatia » Fri Sep 10, 2010 11:34 pm
I think this was a very good question. Confused me a lot. But I couldn't understand the solution from the above two replies. So, I solved it in my way.

1.
|x|<1 means
-1<x<1 . Asked is if this condition is true.


2.
x/|x|<x means

either

x-x^2<0 critical pts- 0,1

or

x>-x^2 or x^2+x >0 critical pts 0, -1

Graphs for them are shown in the figure. Hence A cannot satisfy and A, D eliminated.

3.
From second condition we get
-x<x
satisfies only for x<0 and hence cannot satisfy alone. B eliminiated.

From the above equations, we get the range -1<x<0 which satisfies the above equations 1,3 and hence the answer (C)

Experts please let me know if the above understanding was correct.

Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1