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 →

Number Line problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 46
Joined: Sun Sep 12, 2010 12:32 pmFollowed by: 1 member
Thanked: 1 times
by mgm » Wed Sep 11, 2013 4:20 am
Is the number x positive?

(1) On the number line, 0 is closer to x - 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.

It is a good problem , probably a repeat post...
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Wed Sep 11, 2013 8:39 am
Is the number x positive?

(1) On the number line, 0 is closer to x - 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.
|x| = the distance between 0 and x.
|x-y| = the distance between 0 and x-y.
|x+y| = the distance between 0 and x+y.

Statement 1: On the number line, 0 is closer to x - 1 than to x.
|x-1| < |x|.
Since there is absolute value notation on each side, we can square the inequality.
(x-1)² < x²
x² - 2x + 1 < x²
-2x < -1
x > 1/2.
Thus, x must be positive.
SUFFICIENT.

Statement 2: On the number line, 0 is closer to x than to x + 1.
|x| < |x+1|.
Since there is absolute value notation on each side, we can square the inequality.
x² < (x+1)²
x² < x² + 2x + 1
-2x < 1
x > -1/2.
Thus, x could be negative or positive.
INSUFFICIENT.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 234
Joined: Tue Jul 16, 2013 9:00 am
Location: West Virginia
Thanked: 9 times

by Java_85 » Wed Sep 11, 2013 8:41 am
IMO A is the answer.

(1) x>0.5 this statement is valid --> x is positive --> YES --> A or D
(2) this statement is valid for x=-0.2 or x=0.2 --> x could be negative --> We don't know if x is positive or negative --> A
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Thu Sep 12, 2013 1:34 pm
Hi mgm,

For this DS question, you'll find it pretty easy to TEST values:

We're asked if x is positive? This is a YES/NO question. We don't know anything about x to start.

For this question you'll find that drawing a picture might be helpful; Number Properties will also make this question a bit easier to handle. Remember what the question's asking for though: Is x positive?

If x > 0 then the answer is YES
If x = 0 then the answer is NO
If x < 0 then the answer is NO

Fact 1 tells us that 0 is closer to (x - 1) than to x.

Here, consider the possibilities...
Could x = 0??? Is 0 closer to -1 than to 0?
No, it's not, so x CANNOT = 0

Could x = a negative?
Try x = -1
Is 0 closer to -2 than to -1
No, it's not, so x CANNOT = a negative

If x CANNOT = 0 and x CANNOT = a negative, then all that's left are positives!!!!
So x MUST be positive and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2 tells us that 0 is closer to x than to (x+1)

Let's consider the possibilities here:

Could x = 0???
0 is closer to 0 than to 1, so 0 IS POSSIBLE and the answer to the question is NO.

Could x = 1???
0 is closer to 1 than to 2, so 1 IS POSSIBLE and the answer to the question is YES.
These results are inconsistent.
Fact 2 is INSUFFICIENT

Final Answer:
A

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Fri Sep 13, 2013 5:51 am
mgm wrote:Is the number x positive?

(1) On the number line, 0 is closer to x - 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.
Another approach is the sketch the cases on a number line.

Target question: Is x positive?

Statement 1: On the number line, 0 is closer to x - 1 than to x.
First, recognize that x-1 will always be to the left of x.
Second, recognize that there are 3 possible ways to place x-1 and x with relation to zero.
Image
If zero is closer to x-1 than to x, then we can rule out case #2, leaving us with cases #1 and #3 as possible scenarios.
If case #1 is true, we can see that x must be positive
If case #3 is true, we can see that x must be positive
Since both possible cases yield the same answer to the target question, we can answer the target question with certainty.
So, statement 1 is SUFFICIENT

Statement 2: On the number line, 0 is closer to x than to x + 1.
Recognize that x+1 will always be to the right of x.
Also recognize that there are 3 possible ways to place x and x+1 with relation to zero.
Image
If zero is closer to x than to x+1, then we can rule out case #2, leaving us with cases #1 and #3 as possible scenarios.
If case #1 is true, we can see that x is negative
If case #3 is true, we can see that x is positive
Since the two possible cases yield different answers to the target question, we cannot answer the target question with certainty.
So, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1