• 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • 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

Absolute value & the number line

This topic has 3 expert replies and 0 member replies
BlueDragon2010 Senior | Next Rank: 100 Posts Default Avatar
Joined
31 Mar 2009
Posted:
91 messages
Followed by:
1 members

Absolute value & the number line

Post Wed Feb 19, 2014 7:40 am


Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

A) |x| <= 3
B) |x| <= 5
C) |x-2| <= 3
D) |x-1| <= 4
E) |x+1| <= 4

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Wed Feb 19, 2014 1:07 pm
Hi BlueDragon2010,

Patrick and Mitch have both pointed out how useful the answer choices can be to solving this question. The GMAT writers create questions (for both the Quant and Verbal sections) that can usually be answered in a variety of ways. Many of those questions come with "hints" as to which option is fastest. In this case, the five answers are equations so one of them MUST be the equation that describes what you see in the number line. Using those 5 options as a gauge, you can quickly deduce which is a match and which 4 are not. You'll see several questions on Test Day in which TESTING THE ANSWERS will be the fastest option to solving the problem, so keep this approach in mind as you study.

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Wed Feb 19, 2014 7:59 am
BlueDragon2010 wrote:


Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

A) |x| <= 3
B) |x| <= 5
C) |x-2| <= 3
D) |x-1| <= 4
E) |x+1| <= 4
|x-y| = the DISTANCE between x and y

The midpoint of the range = -1.
x can be any value from -5 (4 places BELOW -1) to 3 (4 places ABOVE -1).
In other words: the distance between x and -1 is less than or equal to 4.
In math terms:
|x-(-1)| ≤ 4.
|x+1| ≤ 4.

The correct answer is E.

An alternate approach is to plug numbers into the answer choices.
The correct answer choice must work for EVERY value between -5 and 3, inclusive -- and for no values outside this range.
Since |x| = the distance between x and 0, start with the value furthest from 0:
Let x=-5.
Eliminate any answer choice in which x=-5 doesn't work.

Answer choice A: |x|≤3
|-5|≤3.
5≤3.
Doesn't work. Eliminate A.

Answer choice B: |x|≤5
|-5|≤5
5≤5.
This works. Hold onto B.

Answer choice C: |x-2|≤3
|-5-2|≤3
7≤3.
Doesn't work. Eliminate C.

Answer choice D: |x-1|≤4
|-5-1|≤4
6≤4.
Doesn't work. Eliminate D.

Answer choice E: |x+1|≤4
|-5+1|≤4
4≤4.
This works. Hold onto E.

Only B and E remain.
Answer choice B -- |x|≤5 -- includes every value from -5 to 5, but the needed range is only from -5 to 3.
Eliminate B.

The correct answer is E.

_________________
Mitch Hunt
GMAT Private Tutor
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.

  • +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.

GMAT/MBA Expert

Patrick_GMATFix GMAT Instructor
Joined
21 May 2010
Posted:
1053 messages
Followed by:
98 members
Upvotes:
335
Post Wed Feb 19, 2014 7:52 am
One approach: plug in the two boundaries from the graph (-5 and 3) into each answer choice. In the wrong answers, at least one of the numbers will result in an invalid statement. In the right answer, both of these numbers will result in a valid equality. For instance plugging -5 and 3 into |x+1|<=4 will result in 4=4. This is the right answer.

The full solution below is taken from the GMATFix App.

ttp://www.youtube.com/watch?v=ho3bnSx43LA" target="_blank">

-Patrick

_________________


    Ask me about tutoring.

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 Roland2rule 181 topics
2 lheiannie07 110 topics
3 ardz24 60 topics
4 LUANDATO 55 topics
5 swerve 52 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

153 posts
2 image description GMATGuruNY

The Princeton Review Teacher

125 posts
3 image description Scott@TargetTestPrep

Target Test Prep

123 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

111 posts
5 image description EconomistGMATTutor

The Economist GMAT Tutor

83 posts
See More Top Beat The GMAT Experts