• Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep

What is x?

This topic has 2 expert replies and 1 member reply

What is x?

Post
What is x?

(1) |x| < 2

(2) |x| = 3x - 2

OA=B.

How should I solve this DS question? How can I get the value of x from statement (2)?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Gmat_mission wrote:
What is x?

(1) |x| < 2

(2) |x| = 3x - 2
Statement 1:
Here, x can be any value between -2 and 2.
INSUFFICIENT.

Statement 2:
Case 1: signs unchanged
x = 3x - 2
2 = 2x
1 = x
x = 1.

Case 2: signs changed in the absolute value
-x = 3x - 2
2 = 4x
2/4 = x
x = 1/2.

When an equation has absolute value only ON ONE SIDE, plug the two solutions back into the original equation to ensure that both are valid.

If we plug x=1 into |x| = 3x-2, we get:
|1| = 3*1 - 2
1 = 1.
This works.
x=1 is a valid solution for |x| = 3x-2.

If we plug x=1/2 into |x| = 3x-2, we get:
|1/2| = 3(1/2) - 2
1/2 = -1/2.
Doesn't work.
x=1/2 is NOT a valid solution for |x| = 3x-2.

Thus, Statement 2 has only one valid solution:
x=1.
SUFFICIENT.

The correct answer is B.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
Legendary Member Default Avatar
Joined
07 Sep 2017
Posted:
808 messages
Followed by:
3 members
Upvotes:
6
Post
Hello.

(1) |x|<2.

this implies that x can be 0, 1, 1.5, -10, . . . . . NOT Sufficient.

(2) |x|=3x-2.

Using the definition of absolute value we get two cases: $$(a)\ \ x=3x-2\ \Leftrightarrow\ 2=2x\ \Leftrightarrow\ x=1.$$ $$(b)\ \ -x=3x-2\ \Leftrightarrow\ 2=4x\ \Leftrightarrow\ x=\frac{1}{2}.$$ Now, let's plug the solutions in the original equation: $$\left|1\right|=3\left(1\right)-2\ \Leftrightarrow\ \ 1=3-2\ \Leftrightarrow\ 1=1.$$ $$\left|\frac{1}{2}\right|=3\left(\frac{1}{2}\right)-2\ \Leftrightarrow\ \ \frac{1}{2}=\frac{3}{2}-2\ \Leftrightarrow\ \frac{1}{2}\ne-\frac{1}{2}.$$ Hence, x=1/2 is not a solution.

Therefore, we get one unique solution x=1. Thus, this statement is SUFFICIENT.

The correct answer is the option B.

  • +1 Upvote Post
  • Quote
  • Flag
Post
Gmat_mission wrote:
What is x?

(1) |x| < 2

(2) |x| = 3x - 2
Statement One Alone:

|x| < 2

We see that x < 2 or:

-x < 2

x > -2

So, -2 < x < 2.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

|x| = 3x - 2

When x is positive we have:

x = 3x - 2

-2x = -2

x = 1

When x is negative we have:

-x = 3x - 2

2 = 4x

1/2 = x

We see that x = 1 matches our assumption that x is positive whereas x = ½ does not match our assumption that x is negative (because x = ½, which is a positive value). Thus, x can be only 1.

Answer: B

_________________
Jeffrey Miller Head of GMAT Instruction

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 Jay@ManhattanReview 83 first replies
2 Brent@GMATPrepNow 68 first replies
3 fskilnik 55 first replies
4 GMATGuruNY 36 first replies
5 ceilidh.erickson 13 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik

GMAT Teacher

199 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

160 posts
3 image description Scott@TargetTestPrep

Target Test Prep

109 posts
4 image description Jay@ManhattanReview

Manhattan Review

95 posts
5 image description GMATGuruNY

The Princeton Review Teacher

90 posts
See More Top Beat The GMAT Experts