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 →

inequality, modulus and 2 variables

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members
Thanked: 448 times
GMAT Score:650

by theCodeToGMAT » Fri Nov 22, 2013 6:46 am
|10y - 4| < |10x + 6|

==> 10y - 4 < 10x + 6
==> 10y < 10x + 10
==> y <x + 1

And,

==> -(10y - 4) < 10x + 6
==> 4 - 10y < 10x + 6
==> 10y + 10x > -2
==> 10y > -2 -10x
R A H U L
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member
Thanked: 25 times

by Mathsbuddy » Fri Nov 22, 2013 9:59 am
How can we express y in terms of x. More precisely, how to form different cases to solve the below inequality

|10y - 4| < |10x + 6|

As both sides are positive, we can square both sides without conflict:


(10y - 4)^2 < (10x + 6)^2


(10y - 4)^2 - (10x + 6)^2 < 0

100y^2 -80y + 16 - 100x^2 - 120x - 36 < 0

100y^2 -80y - 100x^2 - 120x - 20 < 0

Would that start our journey in the wrong direction?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 29
Joined: Thu Mar 11, 2010 3:23 am
Thanked: 1 times

by Haldiram Bhujiawala » Fri Nov 22, 2013 10:28 am
vishalpathak wrote:How can we express y in terms of x. More precisely, how to form different cases to solve the below inequality

|10y - 4| < |10x + 6|
Please check the Manhattan guides for ways to form different cases to solve the inequality. The guide provides different scenarios for evaluating different cases. It's very comprehensive however a bit lengthy. Alternatively, since both sides of inequality have modulus value expresions, the values of the expression will be positive. So we can safely consider only the positive value of each expresion and solve accordingly. Rest part of the question can be solved as shown by Mathsbuddy. I hope there won't be any difficulty solving mathsbuddy's way.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Wed Sep 11, 2013 4:33 am

by vishalpathak » Fri Nov 22, 2013 10:41 am
Haldiram Bhujiawala wrote:
vishalpathak wrote:How can we express y in terms of x. More precisely, how to form different cases to solve the below inequality

|10y - 4| < |10x + 6|
Please check the Manhattan guides for ways to form different cases to solve the inequality. The guide provides different scenarios for evaluating different cases. It's very comprehensive however a bit lengthy. Alternatively, since both sides of inequality have modulus value expresions, the values of the expression will be positive. So we can safely consider only the positive value of each expresion and solve accordingly. Rest part of the question can be solved as shown by Mathsbuddy. I hope there won't be any difficulty solving mathsbuddy's way.
When we square both sides of an equation, we add aditional root to the equation. I am not sure whether squaring is the right method. However, I do not know the correct method myself

Regards,
Vishal
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Wed Sep 11, 2013 4:33 am

by vishalpathak » Fri Nov 22, 2013 10:53 am
the following comes to my mind for this problem

when x < -6/10, 10x + 6 is -ve
Hence

0 < 10y-4 < -(10x + 6) -- (y has to be > 4/10 for this eqn to hold true)

when x > -6/10 10x + 6 is +ve
Hence

0 < 10y-4 < (10x + 6) -- (y has to be > 4/10 for this eqn to hold true)

This can help us find a range of y in terms of x

Similarly we can have 2 more eqns when y < 4/10

These 4 eqns can help us find the required ranges.

I am not confident about the solution though
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 46
Joined: Sat Feb 27, 2010 2:58 am
Location: GMAT

by GMATSUCKER » Fri Nov 22, 2013 11:05 am
vishalpathak wrote:
When we square both sides of an equation, we add aditional root to the equation. I am not sure whether squaring is the right method. However, I do not know the correct method myself
When you find the roots of the Quadratics you should always plug back the roots in the original inequation to check whether they satisfy the original inequation. If they satisfy then generally they are the solution to the inequation.

As a general rule an expression represents a quantity or an idea. So if you square both sides of the inequation it does not affect the inequality. And squaring is the most safest way to ensure that the quantity on both sides are actually positive so as to be consistent with the modulus. I think Mathsbuddy will be able to shed more light on the approach.
Last edited by GMATSUCKER on Sat Nov 23, 2013 1:22 am, edited 1 time in total.
GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT
What's life without GMAT !!!!!!!!
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] » Fri Nov 22, 2013 6:47 pm
Hi All,

The GMAT Quant section is not a "math test"; it's a test of your critical thinking skills and math is the subject through which those skill tests are run. While you will end up doing plenty of math in that section, it's important to know what the concepts are "in context" of the question that is asked AND what appears in the 5 answer choices. In many cases, "doing math" is not the most efficient way to get to the correct answer.

All that having been said, what is the context for the attached math inequality? What were you asked? What is in the 5 answer choices?

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
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Wed Sep 11, 2013 4:33 am

by vishalpathak » Fri Nov 22, 2013 10:33 pm
[email protected] wrote:Hi All,

The GMAT Quant section is not a "math test"; it's a test of your critical thinking skills and math is the subject through which those skill tests are run. While you will end up doing plenty of math in that section, it's important to know what the concepts are "in context" of the question that is asked AND what appears in the 5 answer choices. In many cases, "doing math" is not the most efficient way to get to the correct answer.

All that having been said, what is the context for the attached math inequality? What were you asked? What is in the 5 answer choices?

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

My attempt is to formulate a strategy to solve such problems. I understand your point about looking at the options and not doing maths but I was wondering if I have to do maths then what would be the process for a question like this

I do not have a question that involves 2 variables, modulus and inequality but if there was one then what would be the process to solve it?

Regards,
Vishal
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] » Sat Nov 23, 2013 2:24 pm
Hi vishalpathak,

In Absolute Value/Modulus questions, I usually end up TESTing Values - it's fast, easy and works on most of these types of questions.

Based on what you've claimed (that you have seen NO questions that fit these parameters), then I have to ask WHY you're focused on a math concept that you haven't seen, and likely won't see, on the GMAT? It seems like a bad use of your time.

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
Post new topic Post Reply
• Page 1 of 1