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# What is the value of x^6/(x^2+1)?

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Math Expert
Joined: 02 Sep 2009
Posts: 55172
What is the value of x^6/(x^2+1)?  [#permalink]

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02 Oct 2017, 23:59
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Difficulty:

65% (hard)

Question Stats:

49% (01:25) correct 51% (01:16) wrong based on 168 sessions

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What is the value of $$\frac{x^6}{x^2+1}$$?

(1) |x| = –x
(2) x^2 = x

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Re: What is the value of x^6/(x^2+1)?  [#permalink]

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03 Oct 2017, 00:18
Bunuel wrote:
What is the value of $$\frac{x^6}{x^2+1}$$?

(1) |x| = –x
(2) x^2 = x

Question : x^6/(x^2+1) = ?

Statement 1: |x| = –x

i.e. x is LESS than or EQUAL to 0

x = 0, x^6/(x^2+1) = 0
x = -1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

Statement 2: x^2 = x
i.e. x = 0 or 1
x = 0, x^6/(x^2+1) = 0
x = 1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

COmbining the two statements

x = 0
i.e. x^6/(x^2+1) = 0
SUFFICIENT

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Re: What is the value of x^6/(x^2+1)?  [#permalink]

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03 Oct 2017, 07:38
GMATinsight wrote:
Bunuel wrote:
What is the value of $$\frac{x^6}{x^2+1}$$?

(1) |x| = –x
(2) x^2 = x

Question : x^6/(x^2+1) = ?

Statement 1: |x| = –x

i.e. x is LESS than or EQUAL to 0

x = 0, x^6/(x^2+1) = 0
x = -1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

Statement 2: x^2 = x
i.e. x = 0 or 1
x = 0, x^6/(x^2+1) = 0
x = 1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

COmbining the two statements

x = 0
i.e. x^6/(x^2+1) = 0
SUFFICIENT

I have a small query .

As per my understanding |x| = –x means that x is negative while |x| = x means that x is either positive or 0.

Regards,
Sandeep
Math Expert
Joined: 02 Sep 2009
Posts: 55172
Re: What is the value of x^6/(x^2+1)?  [#permalink]

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03 Oct 2017, 07:45
sandeep211986 wrote:
GMATinsight wrote:
Bunuel wrote:
What is the value of $$\frac{x^6}{x^2+1}$$?

(1) |x| = –x
(2) x^2 = x

Question : x^6/(x^2+1) = ?

Statement 1: |x| = –x

i.e. x is LESS than or EQUAL to 0

x = 0, x^6/(x^2+1) = 0
x = -1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

Statement 2: x^2 = x
i.e. x = 0 or 1
x = 0, x^6/(x^2+1) = 0
x = 1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

COmbining the two statements

x = 0
i.e. x^6/(x^2+1) = 0
SUFFICIENT

I have a small query .

As per my understanding |x| = –x means that x is negative while |x| = x means that x is either positive or 0.

Regards,
Sandeep

Correct, except if |x| = –x, x can be 0 too: |0| = -0 = 0.
_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2929
Location: India
GMAT: INSIGHT
Schools: Darden '21
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Re: What is the value of x^6/(x^2+1)?  [#permalink]

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03 Oct 2017, 10:32
sandeep211986 wrote:
GMATinsight wrote:
Bunuel wrote:
What is the value of $$\frac{x^6}{x^2+1}$$?

(1) |x| = –x
(2) x^2 = x

Question : x^6/(x^2+1) = ?

Statement 1: |x| = –x

i.e. x is LESS than or EQUAL to 0

x = 0, x^6/(x^2+1) = 0
x = -1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

Statement 2: x^2 = x
i.e. x = 0 or 1
x = 0, x^6/(x^2+1) = 0
x = 1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

COmbining the two statements

x = 0
i.e. x^6/(x^2+1) = 0
SUFFICIENT

I have a small query .

As per my understanding |x| = –x means that x is negative while |x| = x means that x is either positive or 0.

Regards,
Sandeep

0 is neither positive nor negative therefore

-0 = +0 = 0

Hence, |x| = -x means that x≤0

Other way around, x can be anything that satisfies the expression |x| = -x and zero satisfies this expression.

You might need this clarification for many other good questions as well.

Posted from my mobile device
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GMATinsight
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Intern
Joined: 04 May 2014
Posts: 45
Concentration: Strategy, Operations
Re: What is the value of x^6/(x^2+1)?  [#permalink]

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16 Apr 2018, 09:09
Statement 1: lxl=-x, lxl+x=0, Lets take two cases, one x is negative number other x is positive number
if x is positive then equation becomes, x+x=0, 2x=0, x=0
if x is negative then equation becomes, l-xl + (-x) =0, x-x=0, infinite soltions
Insufficient
Statement 2: Solving equation 2 gives x = 0 or 1. Insufficient

Statement 1 & 2 together gives, x = 0, hence the question will have unique value of 0.

Re: What is the value of x^6/(x^2+1)?   [#permalink] 16 Apr 2018, 09:09
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