Last visit was: 16 Sep 2024, 23:20 It is currently 16 Sep 2024, 23:20
Toolkit
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

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.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Senior Manager
Joined: 04 Sep 2017
Posts: 334
Own Kudos [?]: 21340 [63]
Given Kudos: 61
Manager
Joined: 18 Apr 2019
Posts: 67
Own Kudos [?]: 96 [23]
Given Kudos: 86
Location: India
GMAT 1: 720 Q48 V40
GPA: 4
Senior Manager
Joined: 31 May 2018
Posts: 327
Own Kudos [?]: 1611 [9]
Given Kudos: 132
Location: United States
Concentration: Finance, Marketing
General Discussion
Senior Manager
Joined: 28 Feb 2014
Posts: 470
Own Kudos [?]: 616 [1]
Given Kudos: 74
Location: India
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]
1
Kudos
gmatt1476
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
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 8064
Own Kudos [?]: 4330 [1]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
1
Kudos
gmatt1476
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
Manager
Joined: 16 May 2011
Posts: 240
Own Kudos [?]: 315 [1]
Given Kudos: 64
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE:Law (Law)
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
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
Director
Joined: 09 Jan 2020
Posts: 948
Own Kudos [?]: 240 [1]
Given Kudos: 432
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]
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.

Math Expert
Joined: 02 Sep 2009
Posts: 95555
Own Kudos [?]: 659397 [1]
Given Kudos: 87276
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
1
Kudos
yogendraaaa
Karmesh
gmatt1476
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.
Senior Manager
Joined: 15 Oct 2015
Posts: 366
Own Kudos [?]: 1625 [0]
Given Kudos: 342
Concentration: Finance, Strategy
GPA: 3.93
WE:Account Management (Education)
What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
gmatt1476
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.
Manager
Joined: 13 Jul 2019
Posts: 50
Own Kudos [?]: 146 [0]
Given Kudos: 13
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
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

Hope this helps.
Intern
Joined: 24 Jul 2013
Posts: 20
Own Kudos [?]: 3 [0]
Given Kudos: 111
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
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
Intern
Joined: 25 Mar 2018
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 13
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
Karmesh
gmatt1476
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?
Non-Human User
Joined: 09 Sep 2013
Posts: 34881
Own Kudos [?]: 881 [0]
Given Kudos: 0
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
Moderator:
Math Expert
95555 posts