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 →

x^n = x^(n+2)

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 103
Joined: Mon May 04, 2009 11:53 am
Thanked: 6 times
by navalpike » Fri Jul 03, 2009 7:58 pm
I’ve seen this in another link but the explanation did not help.

x^n = x^(n+2) for any integer n. Is it true that x>0?

1. x=(x^2) – 2
2. 2x < x^5

Kindly show your thought process. Thanks.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Thu Jul 24, 2008 9:10 pm

by vamsikrishnach » Sat Jul 04, 2009 2:27 am
Heey..the given eqn can be simplified to x=+1 or -1.

Coming to option 1,you can simplify it to x(x-1)=2 and only -1 or 2 satisifie this eqn. So with this we can say x = -1. So question is answered that x is < 0.

Option 2 does not give integer values for x so ,IMO ans is A
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 472
Joined: Sun Mar 29, 2009 6:54 pm
Thanked: 56 times

Re: x^n = x^(n+2)

by ssmiles08 » Sat Jul 04, 2009 2:34 pm
navalpike wrote:I’ve seen this in another link but the explanation did not help.

x^n = x^(n+2) for any integer n. Is it true that x>0?

1. x=(x^2) – 2
2. 2x < x^5

Kindly show your thought process. Thanks.
the question stem further simplified:

x^(n+2) - x^n = 0.

x^n(x^2 - 1) = 0

(x^2 - 1) = (x-1)(x+1)

so it can be written as x^n(x+1)(x-1) = 0.

1)
x^2 - x - 2 = 0

(x-2)(x+1) = 0

from here we can conclude that x = -1 given the help of the question stem. SUFF.

2) x can be various values depending on n. x = -1, 2, n can be 0, 2...so on INSUFF.

IMO A.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 103
Joined: Mon May 04, 2009 11:53 am
Thanked: 6 times

by navalpike » Sun Jul 05, 2009 9:51 am
1)
x^2 - x - 2 = 0

(x-2)(x+1) = 0

from here we can conclude that x = -1 given the help of the question stem. SUFF.
But can we also not conlude that x = 2?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 472
Joined: Sun Mar 29, 2009 6:54 pm
Thanked: 56 times

by ssmiles08 » Sun Jul 05, 2009 3:13 pm
navalpike wrote:
But can we also not conlude that x = 2?
No because in the question stem it tells you that x must +1 or -1 or 0.

(x^2 - 1) = (x-1)(x+1)

for x^n = 0, x= 0.


when statement 1 tells us that x = 2 or x = -1, we can take out 2 b/c it tells you x can only be -1, 1 or 0.

in this case, we can confirm x = -1.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 338
Joined: Fri Apr 17, 2009 1:49 amFollowed by: 3 members
Thanked: 9 times

by kaulnikhil » Sun Jul 05, 2009 11:03 pm
Doesnt the second ans also help us to reach the conclusion that X=-1
all other values which we get for second dont match with x=1 or x=0
which we have obtained from the question ..hence according to me second also is sufficient ..
Am i on the right track ??
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
MBA Student
Posts: 532
Joined: Wed Jan 28, 2009 1:39 pmFollowed by: 9 members
Location: Barcelona
Thanked: 33 times
GMAT Score:640

by hk » Mon Jul 06, 2009 12:54 pm
I would go with D

the question can be simplified as X= -1 , 0, 1

And then main question is => is x>0?

1) Substitute value of x as -1, 1, 0 and you will find out that only x=-1 solves the equation. => Sufficient
2) Similarly substitute the same values of x and you will find that only x=-1 will solve the inequality!!! => Sufficient!!
Wanna know what I'm upto? Follow me on twitter: https://twitter.com/harikrish
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1