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 Problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members
Thanked: 114 times
by knight247 » Mon Aug 22, 2011 11:36 am
Find the range of values of x for which x²+7x+12>0
(A)-4<x<-3
(B)x<-4 or x>-3
(C)x<-4 and x>-3
(D)x<3 or x>4
(E)3<x<4

OA is B

I solved the eqn like a regular quadratic equation until I reach (x+3)(x+4)>0
At which point I figure that either both terms are +ve or both are -ve
x>-3 and x>-4
or
x<-3 and x<-4

I really don't know how to choose the correct extremities from the answers I get. Hope someone can give me a detailed explanation. Thanks
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Senior | Next Rank: 100 Posts
Posts: 64
Joined: Sun Jul 24, 2011 9:11 am
Thanked: 13 times
GMAT Score:610

by sumgb » Mon Aug 22, 2011 1:24 pm
you have almost solved the problem
I solved the eqn like a regular quadratic equation until I reach (x+3)(x+4)>0
At which point I figure that either both terms are +ve or both are -ve
as you know +ve * +ve = +ve or -ve * -ve = +ve
so both (x+3) and (x+4) should have same sign (either +ve or -ve)
case I: when both are -ve; x must be less than -4 so that both (x+3) and (x+4) are -ve; hence x <-4
case II:when both are +ve; x must be greater than -3 so that both (x+3) and (x+4) are +ve; hence x >-3

Ans B

hope this helps..
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 273
Joined: Tue Sep 21, 2010 5:37 amFollowed by: 74 members
Location: Durham, NC
Thanked: 154 times
GMAT Score:770

by Whitney Garner » Mon Aug 22, 2011 2:47 pm
knight247 wrote:Find the range of values of x for which x²+7x+12>0
(A)-4<x<-3
(B)x<-4 or x>-3
(C)x<-4 and x>-3
(D)x<3 or x>4
(E)3<x<4

OA is B

I solved the eqn like a regular quadratic equation until I reach (x+3)(x+4)>0
At which point I figure that either both terms are +ve or both are -ve
x>-3 and x>-4
or
x<-3 and x<-4

I really don't know how to choose the correct extremities from the answers I get. Hope someone can give me a detailed explanation. Thanks
You've done everything perfectly so far! Now you just need to condense each of your inequalities.

For the first, x>-3 and x>-4, you need to write one inequality that represents where BOTH of those are true - so you're basically looking for the most restrictive. In this case, if x is a number bigger than -3, then it will take care of BOTH restrictions that x be bigger than -3 AND bigger than -4. So we can write x>-3.

For the second, x<-3 and x<-4, we again need to find the most restrictive inequality. If x is a number smaller than -3, it DOES NOT ensure that x is also less than -4. BUT, if we go with the alternative and say that x is less than -4, then it does cover the restriction that x also be less than -3. So we can write x<-4.

And now we have the 2 sides of the inequality - the expression will be true whenever x>-3 or when x<-4.

Hope this helps!
:)
whit
Whitney Garner
GMAT/GRE/EA Instructor & Anxiety/Accommodations Coach
www.whitneygarner.com

Contributor to Beat The GMAT!

Math is a lot like love - a simple idea that can easily get complicated :heart-eyes:
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1