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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
Vote for Target Test Prep, Newsweek Readers’ Choice Awards 2026
NEWSWEEK READERS’ CHOICE 2026

BIG NEWS! Target Test Prep has been nominated, and they’d love your vote!

TTP has worked incredibly hard to build the best test prep experience possible, and winning Newsweek’s 2026 Readers’ Choice Award for Best Test Prep would mean a lot to them. If TTP has helped you, they’d be incredibly grateful for your vote. You can vote once each day through September 9.

Vote for TTP
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Inequalities :If x is an integer, what is the value of x?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Sun Jun 30, 2019 9:06 pm
by prab.sahi06 » Sun Jul 07, 2019 3:45 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2
(2) |x^2 - |x|| = 2


Need hep .How to approach such problems in an efficient way. $$$$ $$$$ $$$$
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 » Sun Jul 07, 2019 4:12 am
prab.sahi06 wrote:If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2
(2) |x^2 - |x|| = 2
In statement 1, |x²| is redundant: since x² cannot be negative, |x²| = x².

Statement 1: |x-x²|=2
x - x² = ±2
x(1-x) = ±2.

The resulting equation implies that x is a factor of ±2, yielding the following options:
x=±1 or x=±2.
Check which of these values are valid solutions for |x-x²| = 2.

If x=1, then |x-x²| = |1 - 1²| = 0.
If x=-1, then |x-x²| = |-1 - (-1)²| = 2.
If x=2, then |x-x²| = |2 - 2²| = 2.
If x=-2, then |x-x²| = |-2 - (-2)²| = 6.

Since it's possible that x=-1 or that x=2, INSUFFICIENT.

Statement 2: |x² -|x||=2
x²-|x| = ±2
Since x² = |x|*|x|, we can factor out |x|:
|x| (|x|-1) = ±2.

The resulting equation implies that |x| is a factor of ±2, yielding the following options:
|x|=1 or |x|=2, with the result that x=±1 or x=±2.
Check which of these values are valid solutions for |x² -|x||=2.

If x=-1, then |x² -|x|| = |(-1)² - |-1|| = 0.
If x=1, then |x² -|x|| = |1² - |1|| = 0.
If x=2, then |x² -|x|| = |2² - |2|| = 2.
If x=-2, then |x² -|x|| = |(-2)² - |-2|| = 2.

Since it's possible that x=2 or that x=-2, INSUFFICIENT.

Statements 1 and 2 combined:
Both statements are satisfied only by x=2.
SUFFICIENT.

The correct answer is C.
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
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Sun Jun 30, 2019 9:06 pm

reply

by prab.sahi06 » Sun Jul 07, 2019 4:39 am
GMATGuruNY wrote:
prab.sahi06 wrote:If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2
(2) |x^2 - |x|| = 2
In statement 1, |x²| is redundant: since x² cannot be negative, |x²| = x².

Statement 1: |x-x²|=2
x - x² = ±2
x(1-x) = ±2.

The resulting equation implies that x is a factor of ±2, yielding the following options:
x=±1 or x=±2.
Check which of these values are valid solutions for |x-x²| = 2.

If x=1, then |x-x²| = |1 - 1²| = 0.
If x=-1, then |x-x²| = |-1 - (-1)²| = 2.
If x=2, then |x-x²| = |2 - 2²| = 2.
If x=-2, then |x-x²| = |-2 - (-2)²| = 6.

Since it's possible that x=-1 or that x=2, INSUFFICIENT.

Statement 2: |x² -|x||=2
x²-|x| = ±2
Since x² = |x|*|x|, we can factor out |x|:
|x| (|x|-1) = ±2.

The resulting equation implies that |x| is a factor of ±2, yielding the following options:
|x|=1 or |x|=2, with the result that x=±1 or x=±2.
Check which of these values are valid solutions for |x² -|x||=2.

If x=-1, then |x² -|x|| = |(-1)² - |-1|| = 0.
If x=1, then |x² -|x|| = |1² - |1|| = 0.
If x=2, then |x² -|x|| = |2² - |2|| = 2.
If x=-2, then |x² -|x|| = |(-2)² - |-2|| = 2.

Since it's possible that x=2 or that x=-2, INSUFFICIENT.

Statements 1 and 2 combined:
Both statements are satisfied only by x=2.
SUFFICIENT.

The correct answer is C.
I was considering so many cases and getting lost.

This is great.Thanks a lot !!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sat Jul 06, 2019 12:59 pm

by ScoreMaxx » Sun Jul 07, 2019 10:47 pm
Without simplification,
Statement 1: |x - |x^2|| = 2
|-1-|(-1)^2||=2 [X=-1]
Or
|2-|(2^2)||=2 [X=2]
We find that X=-1 or X=2; therefore, statement 1 alone is NOT SUFFICIENT.

Statement 2: |x^2 - |x|| = 2
|2^2-|2||=2 [X=2]
Or
|(-2)^2-|-2||=2 [X=-2]

We find that X=2 or X=-2; therefore, statement 2 alone is NOT SUFFICIENT.

Statement 1+2: from statement 1 and 2, we find that X=2. SUFFICIENT.
Answer: C
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1