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 →

Inequalities....help plz

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
Legendary Member
Posts: 576
Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member
Thanked: 97 times

by liferocks » Mon May 24, 2010 7:38 pm
Here we are looking for a yes/no for question Is 2<x<4
From 1
(x-2)(x-3)<0
so 2<x<3...

hence ans for Is 2<x<4--yes

From 2

5x(x-5)>0
or x(x-5)>0

so x and x-5 should have same sign .Hence the values of x which will satisfy this are x<0 and x>5

so x cannot have a value between 2 and 4

hence ans for Is 2<x<4--no

since we can definitely give an answer for 'Is 2<x<4? ' from both statements independently

Ans is option D
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760

by sanju09 » Tue May 25, 2010 1:04 am
[email protected] wrote:Hi all,

Is 2<x<4?

1) x"2-5x+6<0
2)5x"2-25x>0

The answer is D which means both are sufficient...I don't understand why 2 is enough.

Thank you.
What is the source? Findings from the two statements would never contradict on real GMAT.
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 27
Joined: Mon Apr 26, 2010 9:30 pm
Location: Johannesburg, South Africa

by [email protected] » Tue May 25, 2010 2:28 am
liferocks wrote:Here we are looking for a yes/no for question Is 2<x<4
From 1
(x-2)(x-3)<0
so 2<x<3...

hence ans for Is 2<x<4--yes

From 2

5x(x-5)>0
or x(x-5)>0

so x and x-5 should have same sign .Hence the values of x which will satisfy this are x<0 and x>5

so x cannot have a value between 2 and 4

hence ans for Is 2<x<4--no

since we can definitely give an answer for 'Is 2<x<4? ' from both statements independently

Ans is option D
:)

i do not get your answer, correct me if i am wrong please but:

statement 1: x^2-5x+6 < 0 => (x-3)(x-2) < 0 => x<3 or x<2 ... this is insuffient, isn't it?

statement 2: 5X^2-25X > 0 => 5x(x-5) > 0 => x>0 or x>5 ... this is insufficient!

from the statements above it's hard to tell if x is between 2 and 4 (i.e. 2<x<4).

i think the asnwer is (E)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 576
Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member
Thanked: 97 times

by liferocks » Tue May 25, 2010 2:39 am
[email protected] wrote: statement 1: x^2-5x+6 < 0 => (x-3)(x-2) < 0 => x<3 or x<2 ... this is insuffient, isn't it?

statement 2: 5X^2-25X > 0 => 5x(x-5) > 0 => x>0 or x>5 ... this is insufficient!
these two inferences are in correct.
(x-3)(x-2) < 0 range of values of x is 2<x<3 for any other value the inequality will not satisfy.You can pickup any value and check

Similarly if 5x(x-5) > 0 range of values of x is x<0 and x>5..any value from 0 to 5 will not satisfy the inequality.you can pickup any value and verify this.
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members
Thanked: 137 times

by thephoenix » Tue May 25, 2010 3:03 am
[email protected] wrote:
liferocks wrote:Here we are looking for a yes/no for question Is 2<x<4
From 1
(x-2)(x-3)<0
so 2<x<3...

hence ans for Is 2<x<4--yes

From 2

5x(x-5)>0
or x(x-5)>0

so x and x-5 should have same sign .Hence the values of x which will satisfy this are x<0 and x>5

so x cannot have a value between 2 and 4

hence ans for Is 2<x<4--no

since we can definitely give an answer for 'Is 2<x<4? ' from both statements independently

Ans is option D
:)

i do not get your answer, correct me if i am wrong please but:

statement 1: x^2-5x+6 < 0 => (x-3)(x-2) < 0 => x<3 or x<2 ... this is insuffient, isn't it?

statement 2: 5X^2-25X > 0 => 5x(x-5) > 0 => x>0 or x>5 ... this is insufficient!

from the statements above it's hard to tell if x is between 2 and 4 (i.e. 2<x<4).

i think the asnwer is (E)
(x-3)(x-2) < 0===> if x-3<0 then x-2>0 or if x-2<0 then x-3>0 an invalid condition===> 2<x<3 the only condition will satisfy the inequality
Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 27
Joined: Mon Apr 26, 2010 9:30 pm
Location: Johannesburg, South Africa

by [email protected] » Tue May 25, 2010 3:27 am
thephoenix wrote:
[email protected] wrote:
liferocks wrote:Here we are looking for a yes/no for question Is 2<x<4
From 1
(x-2)(x-3)<0
so 2<x<3...

hence ans for Is 2<x<4--yes

From 2

5x(x-5)>0
or x(x-5)>0

so x and x-5 should have same sign .Hence the values of x which will satisfy this are x<0 and x>5

so x cannot have a value between 2 and 4

hence ans for Is 2<x<4--no

since we can definitely give an answer for 'Is 2<x<4? ' from both statements independently

Ans is option D
:)

i do not get your answer, correct me if i am wrong please but:

statement 1: x^2-5x+6 < 0 => (x-3)(x-2) < 0 => x<3 or x<2 ... this is insuffient, isn't it?

statement 2: 5X^2-25X > 0 => 5x(x-5) > 0 => x>0 or x>5 ... this is insufficient!

from the statements above it's hard to tell if x is between 2 and 4 (i.e. 2<x<4).

i think the asnwer is (E)
(x-3)(x-2) < 0===> if x-3<0 then x-2>0 or if x-2<0 then x-3>0 an invalid condition===> 2<x<3 the only condition will satisfy the inequality
:?:

i still do not get it but it's fine. thanks.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Mon May 24, 2010 6:31 pm

by [email protected] » Tue May 25, 2010 2:36 pm
Thank you everyone
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 151
Joined: Thu Apr 22, 2010 4:07 pm
Thanked: 14 times

by Haaress » Tue May 25, 2010 3:28 pm
I guess what Mogorosi is questioning is,

Given that (x-2)(x-3)< 0 , then why not say ( just as you would for an equation) , either (x-2)< 0 or (x-3)< 0 but rather (x-2)>0 and (x-3)<0 ...and ultimately 2<x<3. I know this creating a mental graph but that not going to be possible here. Is there a general rule?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members
Thanked: 335 times

by Patrick_GMATFix » Tue May 25, 2010 3:44 pm
Hey Haress, mogorosi

Technically you are correct to think that if a product of two factors is positive, either factor could be positive and the other negative. However in this case we don't need to worry about the possibility that (x-2) is negative and (x-3) is positive.

(x-2)(x-3) is negative, so one factor must be positive and the other negative. Because (x-2) is greater than (x-3) for any value of x*, (x-2) must be the positive factor and (x-3) must be the negative factor.

x-2>0 --> x > 2
x-3<0 ---> x < 3

Merge the two to get 2<x<3


Does that make sense?
-Patrick

*To compare x-2 to x-3, subtract x from both sides and you get -2 vs. -3. The left is greater than the right.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1