What is the value of x? (1) x^4+x^2+1=(1/x^4+x^2+1) (2) : Quant Question Archive [LOCKED]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 09:59

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
Manager
Joined: 30 Mar 2007
Posts: 179
Followers: 1

Kudos [?]: 35 [0], given: 0

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

### Show Tags

15 May 2007, 18:48
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0

What is the greatest integer n such that 13/n is an integer for all consecutive even integers r and s?
A. 10
B. 8
C. 6
D. 4
E. 2
Manager
Joined: 30 Mar 2007
Posts: 217
Followers: 1

Kudos [?]: 3 [0], given: 0

### Show Tags

15 May 2007, 19:12
both the que are not clear to me...
james
in first que
(1) x^4+x^2+1=(1/x^4+x^2+1) or x^4+x^2+1=1/(x^4+x^2+1)
(2) x3+x^2=0 or x^3+x^2=0

second que also i am clueless...help
Director
Joined: 26 Feb 2006
Posts: 904
Followers: 4

Kudos [?]: 107 [0], given: 0

### Show Tags

15 May 2007, 19:17
Jamesk486 wrote:
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0

i did not get 1 but 2 is sufficient.

x = -1.

second question: no idea what is the question is about?

Last edited by Himalayan on 15 May 2007, 19:19, edited 1 time in total.
Manager
Joined: 02 May 2007
Posts: 152
Followers: 1

Kudos [?]: 5 [0], given: 0

### Show Tags

15 May 2007, 19:18
Jamesk486 wrote:
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0

(A) it is

(1) x^4+x^2+1=(1/x^4+x^2+1)
=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = 1
=> x^4 + x^2 = 0
=> x^2(x^2 + 1) = 0
=> x = 0 => suff

(2) x^3 + x^2 = x^2(x + 1) = 0
=> x = 0 or x = -1 => insuff

Hence, (A)
Director
Joined: 26 Feb 2006
Posts: 904
Followers: 4

Kudos [?]: 107 [0], given: 0

### Show Tags

15 May 2007, 21:42
kirakira wrote:
Jamesk486 wrote:
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0

(A) it is

(1) x^4+x^2+1=(1/x^4+x^2+1)
=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = 1
=> x^4 + x^2 = 0
=> x^2(x^2 + 1) = 0
=> x = 0 => suff

(2) x^3 + x^2 = x^2(x + 1) = 0
=> x = 0 or x = -1 => insuff

Hence, (A)

you are correct in statement 2 but st 1 is also insufficient cuz:

=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = -1 or 1.

from 1 and 2, x should be 0.
seems C.
Director
Joined: 13 Mar 2007
Posts: 545
Schools: MIT Sloan
Followers: 4

Kudos [?]: 70 [0], given: 0

### Show Tags

15 May 2007, 21:56
In GMAT,

(x^2)^(1/2) = +x and not -x

as in -

9^(1/2) is always taken as +3

However, when we have a situation x^2 = 9, then we have to take into consideration of x = 3 and x = -3 !

Can also see the same in OG 11TH edition P-126 under Modulus

"note that (x^2)^(1/2) denotes the non-negative square root of x^2"

So if we consider the above, answer A
Manager
Joined: 02 May 2007
Posts: 152
Followers: 1

Kudos [?]: 5 [0], given: 0

### Show Tags

15 May 2007, 23:17
Himalayan wrote:
kirakira wrote:
Jamesk486 wrote:
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0

(A) it is

(1) x^4+x^2+1=(1/x^4+x^2+1)
=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = 1
=> x^4 + x^2 = 0
=> x^2(x^2 + 1) = 0
=> x = 0 => suff

(2) x^3 + x^2 = x^2(x + 1) = 0
=> x = 0 or x = -1 => insuff

Hence, (A)

you are correct in statement 2 but st 1 is also insufficient cuz:

=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = -1 or 1.

from 1 and 2, x should be 0.
seems C.

(x^4 + x^2 + 1) is always positive.
Manager
Joined: 30 Mar 2007
Posts: 179
Followers: 1

Kudos [?]: 35 [0], given: 0

### Show Tags

16 May 2007, 06:32
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x^3+x^2=0

the answer is supposed to be A
Director
Joined: 26 Feb 2006
Posts: 904
Followers: 4

Kudos [?]: 107 [0], given: 0

### Show Tags

16 May 2007, 08:07
kirakira wrote:
Himalayan wrote:
kirakira wrote:
Jamesk486 wrote:
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0

(A) it is

(1) x^4+x^2+1=(1/x^4+x^2+1)
=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = 1
=> x^4 + x^2 = 0
=> x^2(x^2 + 1) = 0
=> x = 0 => suff

(2) x^3 + x^2 = x^2(x + 1) = 0
=> x = 0 or x = -1 => insuff

Hence, (A)

you are correct in statement 2 but st 1 is also insufficient cuz:

=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = -1 or 1.

from 1 and 2, x should be 0.
seems C.

(x^4 + x^2 + 1) is always positive.

good point and you r right.
Intern
Joined: 15 Jan 2007
Posts: 38
Followers: 0

Kudos [?]: 2 [0], given: 0

### Show Tags

16 May 2007, 09:37
for qstn 1 1. is x^8 = 1 and 2. leads to x = 0 or x = -1. ==> x = -1
16 May 2007, 09:37
Display posts from previous: Sort by