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 →

Which of the following inequalities holds if 3.24<x<5.

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Thu Feb 08, 2018 12:06 am
[GMAT math practice question]

Which of the following inequalities holds if 3.24<x<5.36?

A. |x+4.3|<1.06
B. |x-4.3|<1.06
C. |x-2.1|<0.53
D. |x+2.1|<0.53
E. |x-2.1|<1.06
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members
Thanked: 180 times

Which of the following inequalities holds if 3.24<x<5.

by EconomistGMATTutor » Thu Feb 08, 2018 4:34 am
[GMAT math practice question]

Which of the following inequalities holds if 3.24<x<5.36?

A. |x+4.3|<1.06
B. |x-4.3|<1.06
C. |x-2.1|<0.53
D. |x+2.1|<0.53
E. |x-2.1|<1.06
Hi Max@Math Revolution,
Let's take a look at your question.

We have to check the inequalities that hold if 3.24 < x < 5.36
The open interval given includes all the values between 3.24 and 5.36 exclusive.

We will check all the given inequalities for at least two random values of the given interval let's say for x = 3.25 and 5.35
Let's start from option A.
$$\left|x+4.3\right|<1.06$$
$$For\ x=3.25,\ x\ =\ 5.35$$
$$\left|3.25+4.3\right|<1.06,\ \left|5.35+4.3\right|<1.06$$
$$\left|7.55\right|<1.06,\ \left|9.65\right|<1.06$$
$$7.55<1.06,\ 9.65<1.06$$

Option A is incorrect for both values of x.

Let's check option B.
$$\left|x-4.3\right|<1.06$$
$$For\ x=3.25,\ x\ =\ 5.35$$
$$\left|3.25-4.3\right|<1.06,\ \left|5.35-4.3\right|<1.06$$
$$\left|-1.05\right|<1.06,\ \left|1.05\right|<1.06$$
$$1.05<1.06,\ 1.05<1.06$$
Option B is correct for both the values of x.

Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

by Max@Math Revolution » Sun Feb 11, 2018 4:49 pm
=>

The inequality |x-a|<b is equivalent to the inequality a - b < x < a + b.
Note that a is the average of a - b and a + b and b is half of the difference between a - b and a + b, that is, b = {( a + b ) - ( a - b )} / 2.

Thus, the inequality 3.24 < x < 5.36 is equivalent to the inequality | x - 4.3 | < 1.06 since a = ( 3.24 + 5.36 ) / 2 = 8.6 / 2 = 4.3 and b = ( 5.36 - 3.24 ) / 2 = 2.12 / 2 = 1.06.

Therefore, B is the answer.
Answer: B
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1