NEW HERE? LEARN MORE
closeclose
It is currently 30 Sep 2023, 16:14
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3

12 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
avatar
P
gmatt1476
Senior Manager
Senior Manager
Joined: 04 Sep 2017
Posts: 318
What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  21 Sep 2019, 16:35
5
Kudos
48
Bookmarks
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

63% (01:37) correct 37% (01:53) wrong based on 1423 sessions

Hide Show timer Statistics

What is the value of x?


(1) \(x^4 + x^2 + 1 =\frac{1}{x^4 + x^2 + 1}\)

(2) \(x^3 + x^2 = 0\)



DS64402.01
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Reply
User avatar
S
Karmesh
Manager
Manager
Joined: 18 Apr 2019
Posts: 68
Location: India
Schools: IESE '22 CEIBS '22 (II)
GMAT 1: 720 Q48 V40
GPA: 4
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  30 Sep 2019, 08:34
16
Kudos
6
Bookmarks
gmatt1476 wrote:
What is the value of x?


(1) \(x^4 + x^2 + 1 =\frac{1}{x^4 + x^2 + 1}\)

(2) \(x^3 + x^2 = 0\)



DS64402.01


You actually don't need to solve this one. JUST THINK.

1. Take the denominator to the other side and we have ( x^4 + x^2 + 1 )^2 =1
When will LHS be equal to 1? before looking any further just give it a thought.
.
x^4 and x^2 are both +ve, so the only case possible is when x=0.
S1 SUFF

2. x^3 can be -ve, so apart from 0 you can also have x=-1. This gives us 2 values.
INSUFF

A
User avatar
P
shridhar786
Senior Manager
Senior Manager
Joined: 31 May 2018
Posts: 337
Location: United States
Concentration: Finance, Marketing
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  22 Sep 2019, 21:05
7
Kudos
1
Bookmarks
STATEMENT (1)--\(x^4+x^2+1\) = \(\frac{1}{x^4+x^2+1}\)
let \(x^4+x^2+1\) = t
\(t^2\) = 1
(t+1)(t-1) = 0
t cant be -1 (\(x^4+x^2+1\) = +ve)
so t = 1
\(x^4+x^2+1\) = 1
\(x^2(x^2+1)\) = 0
x = 0
SUFFICIENT

STATEMENT (2)--\(x^3+x^2\) = 0
\(x^2(x+1)\) = 0
x can be 0, -1
INSUFFICIENT

A is the answer
General Discussion
User avatar
D
QuantMadeEasy
Senior Manager
Senior Manager
Joined: 28 Feb 2014
Posts: 467
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE:Engineering (Education)
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  22 Sep 2019, 22:48
gmatt1476 wrote:
What is the value of x?


(1) \(x^4 + x^2 + 1 =\frac{1}{x^4 + x^2 + 1}\)

(2) \(x^3 + x^2 = 0\)



DS64402.01


(1) Simplifying the expression we get (x^2+1)^2 = 1
(x^2+1) = =/-1
x^2 = 0 or x^2 = -1(not possible)

Sufficient

(2) x^2(x+1)=0
x=0 or -1. No sufficient

A is correct
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 7775
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  13 Jun 2020, 10:57
gmatt1476 wrote:
What is the value of x?


(1) \(x^4 + x^2 + 1 =\frac{1}{x^4 + x^2 + 1}\)

(2) \(x^3 + x^2 = 0\)



DS64402.01



#1
\(x^4 + x^2 + 1 =\frac{1}{x^4 + x^2 + 1}\)
or say (x^4 + x^2 + 1)^2 = 1
so x has to be 0
sufficient
#2
\(x^3 + x^2 = 0\)
x can be -1 or 0
insufficient
OPTION A
User avatar
G
Ekland
Senior Manager
Senior Manager
Joined: 15 Oct 2015
Posts: 383
Concentration: Finance, Strategy
Schools: Fordham '18 Schulich Jan '18 Desautels '19 Haskayne(Calgary) Alberta"19 Jindal '19 Owen '19 Olin '19 (I) Queens"18
GPA: 3.93
WE:Account Management (Education)
GMAT ToolKit User
What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  Updated on: 17 Jun 2020, 12:19
gmatt1476 wrote:
What is the value of x?


(1) \(x^4 + x^2 + 1 =\frac{1}{x^4 + x^2 + 1}\)

(2) \(x^3 + x^2 = 0\)



DS64402.01


Squaring a number can NEVER give you negative value or zero.

U can only get zero if and only if the number you're squaring is zero itself.

A


___________________________________
Give a kudos for Gmatclub's sake

Originally posted by Ekland on 13 Jun 2020, 13:14.
Last edited by Ekland on 17 Jun 2020, 12:19, edited 2 times in total.
User avatar
S
dimri10
Manager
Manager
Joined: 16 May 2011
Posts: 241
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE:Law (Law)
GMAT ToolKit User
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  13 Jun 2020, 13:29
1
Kudos
Statement 2 gives us 2 solution
Statement 1 in fact states that X=1/X
The only number that is equal to its reciprocal is |1|, means: -1 or 1.
The long term x^4+x^2+1 must be positive so in order to make 1=1 , X must be 0. Only one value is sufficient

Posted from my mobile device
User avatar
P
Basshead
VP
VP
Joined: 09 Jan 2020
Posts: 1006
Location: United States
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  12 Nov 2020, 17:05
1
Bookmarks
What is the value of x?

(1) \(x^4 + x^2 + 1 =\frac{1}{x^4 + x^2 + 1}\)

\((x^4 + x^2 + 1)^2 = 1\)

The only way the above = 1 is if x = 0. SUFFICIENT.

(2) \(x^3 + x^2 = 0\)

x\(^2(x+1) = 0\)
\(x = 0\) or \(x = -1\). INSUFFICIENT.

Answer is A.
_________________
Help me get better -- please critique my responses!
Signature Read More
User avatar
B
DeeptiManyaExpert
Manager
Manager
Joined: 13 Jul 2019
Posts: 52
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  29 Jan 2021, 05:43
Question is to find value of x.

(1) Be careful with the Rational equations. Make sure that the denominator should not become zero with the value you get for x. Simplify the expression to get \((x^4 + x^2+1)^2 = 1\)
\((x^4 + x^2 + 1) = ±1\)
Since \(x^4 \)and\( x^2\) are positive, RHS cannot be negative.
Think of the values for x which can make the statement true.
x = 0
Sufficient

(2) x\(^2(x + 1) = 0\)
=> x = 0 or -1
Not sufficient

Thus, the answer is A.

Hope this helps. :)
avatar
B
sacharya
Intern
Intern
Joined: 24 Jul 2013
Posts: 21
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  29 Mar 2022, 20:25
Stmt 1:
\((x^{4} + x^{2} + 1)^{2}\)=1

\((x^{4} + x^{2} + 1) = 1\) ---> (1) OR
\((x^{4} + x^{2} + 1) = -1\) ----> (2)

Solving (1) \((x^{4} + x^{2} + 1) = 1\)

\((x^{4} + x^{2})=0\)

\(x^{2}(x^{2}+1)=0\)
Therefore, x=0

Considering 2 , \((x^{4} + x^{2} + 1) = -1\) --> Not possible since \(x^{4}\) , \(x^{2}\) and 1 are all positive
Hence, stmt 1 sufficient

Stmt 2:
\(x^{3}+x^{2}=0\)
\(x^{2}(x+1)=0\)
x=0 or x=-1 , 2 solutions
Not sufficient

Ans. A
User avatar
B
yogendraaaa
Intern
Intern
Joined: 25 Mar 2018
Posts: 3
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  27 Jan 2023, 01:20
Karmesh wrote:
gmatt1476 wrote:
What is the value of x?


(1) \(x^4 + x^2 + 1 =\frac{1}{x^4 + x^2 + 1}\)

(2) \(x^3 + x^2 = 0\)



DS64402.01


You actually don't need to solve this one. JUST THINK.

1. Take the denominator to the other side and we have ( x^4 + x^2 + 1 )^2 =1
When will LHS be equal to 1? before looking any further just give it a thought.
.
x^4 and x^2 are both +ve, so the only case possible is when x=0.
S1 SUFF

2. x^3 can be -ve, so apart from 0 you can also have x=-1. This gives us 2 values.
INSUFF

A



But the question doesn't specify that X is a real number? Is it safe to assumer that GMAT sums only concern real numbers?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 89505
CAT Tests Forum Quiz Mode
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] New post  27 Jan 2023, 02:42
1
Kudos
Expert Reply
yogendraaaa wrote:
Karmesh wrote:
gmatt1476 wrote:
What is the value of x?


(1) \(x^4 + x^2 + 1 =\frac{1}{x^4 + x^2 + 1}\)

(2) \(x^3 + x^2 = 0\)



DS64402.01


You actually don't need to solve this one. JUST THINK.

1. Take the denominator to the other side and we have ( x^4 + x^2 + 1 )^2 =1
When will LHS be equal to 1? before looking any further just give it a thought.
.
x^4 and x^2 are both +ve, so the only case possible is when x=0.
S1 SUFF

2. x^3 can be -ve, so apart from 0 you can also have x=-1. This gives us 2 values.
INSUFF

A



But the question doesn't specify that X is a real number? Is it safe to assumer that GMAT sums only concern real numbers?


On the GMAT all numbers used are real numbers by default.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
GMAT Club Bot
gmatclubot
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
27 Jan 2023, 02:42
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderator:
Bunuel
Math Expert
89505 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions